CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES

Size: px
Start display at page:

Download "CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES"

Transcription

1 CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable and measurement varable are synonyms for data that can be recorded as numercal values and then ordered accordng to those values. The relatonshp between weght and heght s an example of a relatonshp between two quanttatve varables. The questons we ask about the relatonshp between two varables often concern specfc numercal features of the assocaton. For example, we may want to know how much weght wll ncrease on average for each one-nch ncrease n heght. Or, we may want to estmate what the college grade pont average wll be for a student whose hgh school grade pont average was 3.5. We wll use three tools to descrbe, pcture and quantfy the relatonshp between two quanttatve varables: Scatter plot, a two-dmensonal graph of data values. Correlaton, a statstc that measures the strength and drecton of a lnear relatonshp between two quanttatve varables. Regresson equaton, an equaton that descrbes the average relatonshp between a quanttatve response varable and an explanatory varable. 5.1 Lookng for Patterns wth Scatter Plots A scatter plot s a two dmensonal graph of the measurements for two numercal varables. A pont on the graph represents the combnaton of measurements for an ndvdual observaton. The vertcal axs, whch s called the y-axs, s used to locate the value of one of the varables. The horzontal axs, called the x-axs, s used to locate the values of the other varable. As we learned n Chapter 2, when lookng at relatonshps we can often dentfy one of the varables as an explanatory varable that may explan or cause dfferences n the response varable. The term dependent varable s used as a synonym for response varable. In a scatter plot, the response varable s plotted on the vertcal axs (the y-axs), so t may also be called the y varable. The explanatory varable s plotted along the horzontal axs (the x-axs) and may be called the x varable. Questons to Ask about a Scatter Plot What s the average pattern? Does t look lke a straght lne or s t curved? What s the drecton of the pattern? How much do ndvdual ponts vary from the average pattern? Are there any unusual data ponts? 156

2 Example 1. Heght and Hand-Span Table 5.1 dsplays the frst 12 observatons of a data set that ncludes the heghts (n nches) and fully stretched hand-spans (n centmeters) of 167 college students. The data values for all 167 students are the raw data for studyng the connecton between heght and hand-span. Imagne how dffcult t would be see the pattern n the data f all 167 observatons were shown n Table 5.1. Even when we just look at the data for 12 students, t takes a whle to confrm that there does seem to be a tendency for taller people to have larger hand-spans. Fgure 5.1 s a scatter plot that dsplays the hand-span and heght measurements for all 167 students. The hand-span measurements are plotted along the vertcal axs (y) and the heght measurements are plotted along the horzontal axs. Each pont represents the two measurements for an ndvdual. Table 5.1 Hand-Spans and Heght Ht.(n) Span(cm) and so on, for n=167 observatons Fgure 5.1. Hand-Span and Heght We see that taller people tend to have greater hand-span measurements than shorter people do. When two varables tend to ncrease together, as they do n Fgure 5.1, we say that they have a postve assocaton. Another noteworthy characterstc of the graph s that we can 157

3 descrbe the general pattern of ths relatonshp wth a straght lne. In other words, the hand-span and heght measurements may have a lnear relatonshp. Postve and Negatve Assocaton Two varables have a postve assocaton when the values of one varable tend to ncrease as the values of the other varable ncrease. Two varables have a negatve assocaton when the values of one varable tend to decrease as the values of the other varable ncrease. Example 2. Drver Age and the Maxmum Legblty Dstance of Hghway Sgns In a study of the legblty and vsblty of hghway sgns, a Pennsylvana research frm determned the maxmum dstance at whch each of thrty drvers could read a newly desgned sgn. The thrty partcpants n the study ranged n age from 18 to 82 years old. The government agency that funded the research hoped to mprove hghway safety for older drvers, and wanted to examne the relatonshp between age and the sgn legblty dstance. Table 5.2 lsts the data and Fgure 5.2 shows a scatter plot of the ages and dstances. The sgn legblty dstance s the response varable so that varable s plotted on the y-axs (the vertcal axs). The maxmum readng dstance tends to decrease as age ncreases, so there s a negatve assocaton between dstance and age. Ths s not a surprsng result. As a person gets older, hs or her eyesght tends to get worse so we would expect the dstances to decrease wth age. The researchers collected the data to determne numercal estmates for two questons about the relatonshp: How much does the dstance decrease when age s ncreased? For drvers of any specfc age, what s the average dstance at whch the sgn can be read? We ll examne these questons n the next secton. For now, we smply pont out that the pattern n the graph looks lnear, so a straght lne equaton that lnks dstance to age wll help us answer these questons. Table 5.2 Data Values for Example 2 Age Dstance Age Dstance Age Dstance

4 Fgure 5.2 Drver Age and the Maxmum Dstance at Whch Hghway Sgn s Read (Source: Adapted from data collected by Last Resource, Inc., Bellefonte, PA) 5.2 Descrbng Lnear Patterns wth a Regresson Lne Scattter plots show us a lot about a relatonshp, but we often want more specfc numercal descrptons of how the response and explanatory varables are related. Imagne, for example, that we are examnng the weghts and heghts of a sample of college women. We mght want to know what the ncrease n average weght s for each one-nch ncrease n heght. Or, we mght want to estmate the average weght for women wth a specfc heght, lke Regresson analyss s the area of statstcs used to examne the relatonshp between a quanttatve response varable and one or more explanatory varables. A key element of regresson analyss s the estmaton of an equaton that descrbes how, on average, the response varable s related to the explanatory varables. Ths regresson equaton can be used to answer the types of questons that we just asked about the weghts and heghts of college women. A regresson equaton can also be used to make predctons. For nstance, t mght be useful for colleges to have an equaton for the connecton between verbal SAT score and college grade pont average (GPA). They could use that equaton to predct the potental GPAs of future students, based on ther verbal SAT scores. Some colleges actually do ths knd of predcton to decde whom to admt, but they use a collecton of varables to predct GPA. The predcton equaton for GPA usually ncludes hgh school GPA, hgh school rank, verbal and math SAT scores, and possbly other factors such as a ratng of the student s hgh school or the qualty of an applcaton essay. There are many types of relatonshps and many types of regresson equatons. The smplest knd of relatonshp between two varables s a straght lne, and that s the only type we wll dscuss here. Straght-lne relatonshps occur frequently n practce, so ths s a useful and mportant type of regresson equaton. Before we use a straght lne regresson model, however, we should always examne a scatterplot to verfy that the pattern actually s lnear. We remnd you of the musc preference and age example where a straght lne defntely does not descrbe the pattern of the data. Interpretng the Regresson Equaton and Regresson Lne When the best equaton for descrbng the relatonshp between x and y s a straght lne the resultng equaton s called the regresson lne. Ths lne s used for two purposes: to estmate the average value of y at any specfed value of x to predct the value of y for an ndvdual, gven that ndvdual's x value 159

5 Example 1 Revsted. Descrbng Heght and Hand-Span wth a Regresson Lne In Fgure 5.1, we saw that the relatonshp between hand-span and heght has a straghtlne pattern. Fgure 5.6 dsplays the same scatterplot as Fgure 5.1, but now a lne s shown that descrbes the average relatonshp between the two varables. To determne ths lne, we used statstcal software (Mntab) to fnd the best lne for ths set of measurements. We ll dscuss the crteron for "best" later. Presently, let s focus on what the lne tells us about the data. The lne drawn through the scatterplot s the regresson lne and t descrbes how average hand-span s lnked to heght. For example, when the heght s 60 nches, the vertcal poston of the lne s at about 18 centmeters. To see ths, locate 60 nches along the horzontal axs (x axs), look up to the lne, and then read the vertcal axs to determne the hand-span value. The result s that we can estmate that people 60 nches tall have an average hand-span of about 18 centmeters (roughly 7 nches). We can also use the lne to predct the hand-span for an ndvdual whose heght s known. For nstance, someone 60 nches tall s predcted to have a hand-span of about 18 centmeters. Fgure 5.6 Regresson Lne Descrbng Hand-Span and Heght If we estmate the average hand-span at a dfferent heght, we can determne how much hand-span changes, on average, when heght s vared. Let s use the lne to estmate the average hand-span for people who are 70 nches tall. We see that the vertcal locaton of the regresson lne s somewhere betweeen 21 and 22 centmeters, perhaps about 21.5 centmeters (roughly 8.5 nches). So, when heght s ncreased from 60 nches to 70 nches, average hand-span ncreases from about 18 centmeters to about 21.5 centmeters. The average hand-span ncreased by 3.5 centmeters (about 1.5 nches) when the heght was ncreased by 10 nches. Ths s a rate of 3.5/10 = 0.35 centmeters per one nch ncrease n heght, whch s the slope of the lne. For each one-nch dfference n heght, there s about a 0.35 centmeter average dfference n hand-span. 160

6 Algebra Remnder The equaton for a straght lne relatng y and x s: y = b 0 + b 1 x where b 0 s the "y-ntercept" and b 1 s the slope. When x = 0, y = y-ntercept. The slope of a lne can be determned by pckng any two ponts on the lne, and then calculatng dfference between y values y2 y1 slope = = dfference between x values x2 x1 The letter y represents the vertcal drecton and x represents the horzontal drecton. The slope tells us how much the y varable changes for each ncrease of one unt n the x varable. We ordnarly don t have to read the regresson lne as we just dd. Statstcal software wll tell us the regresson equaton, the specfc equaton used to draw the lne. For the hand-span and heght relatonshp, the regresson equaton determned by statstcal software s: Hand-span = Heght. When emphass s on usng the equaton to estmate the average hand-spans for specfc heghts, we may wrte: Average Hand-span = Heght When emphass s on usng the equaton to predct an ndvdual hand-span, we mght nstead wrte: Predcted Hand-span = Heght In most stuatons, the correct statstcal nterpretaton of a regresson equaton s that t estmates the average value of a response varable (y) for ndvduals wth a specfc value of the explanatory varable (x). The equaton Hand-span = Heght tells us how to draw the lne, but not all ndvduals follow ths pattern exactly. Look agan at Fgure 5.6, n whch we see that the lne descrbes the overall pattern, but we also see substantal ndvdual devaton from ths lne. Let's use the regresson equaton to estmate the average hand-spans for some specfc heghts. For heght=60, average hand-span = (60) = = 18 cm. For heght=70, average hand-span = (70) = = 21.5 cm In the equaton, the value 0.35 multples the heght. Ths value s the slope of the straght lne that lnks hand-span and heght. Consstent wth our estmates above, the slope n ths example tells us that hand-span ncreases by 0.35 centmeters, on average, for each ncrease of one nch n heght. We can use the slope to estmate the average dfference n hand-span for any dfference n heght. If we consder two heghts that dffer by 7 nches, our estmate of the dfference n handspans would be = 2.45 centmeters, or approxmately one nch. The Equaton for the Regresson Lne All straght lnes can be expressed by the same formula n whch y s the varable on the vertcal axs and x s the varable on the horzontal axs. The equaton for a regresson lne s: yˆ = b0 + b1x. In any gven stuaton, the sample s used to determne numbers that replace b 0 and b 1. ŷ s spoken as y-hat and t s also referred to ether as predcted y or estmated y. b 0 s the ntercept of the straght lne. The ntercept s the value of y when x = 0. b 1 s the slope of the straght lne. The slope tells us how much of an ncrease (or decrease) there s for the y varable when the x varable ncreases by one unt. The sgn of the slope tells us whether y ncreases or decreases when x ncreases. 161

7 Interpretng a Regresson Lne ŷ estmates the average y for a specfc value of x. It also can be used as a predcton of the value of y for an ndvdual wth a specfc value of x. The slope of the lne estmates the average ncrease n y for each one unt ncrease n x. The ntercept of the lne s the value of y when x=0. Note that nterpretng the ntercept n the context of statstcal data only makes sense f x=0 s ncluded n the range of observed x- values. Example 2 Revsted: Drver Age and the Maxmum Legblty Dstance of Hghway Sgns The regresson lne y ˆ = x descrbes how the maxmum sgn legblty dstance (the y varable) s related to drver age (the x varable). Statstcal software was used to calculate ths equaton and to create the graph shown n Fgure 5.7. Earler, we asked these two questons about dstance and age: How much does the dstance decrease when age s ncreased? For drvers of any specfc age, what s the average dstance at whch the sgn can be read? The slope of the equaton can be used to answer the frst queston. Remember that the slope s the number that multples the x varable and the sgn of the slope ndcates the drecton of the assocaton. Here, the slope tells us that, on average, the legblty dstance decreases 3 feet when age ncreases by one year. Ths nformaton can be used to estmate the average change n dstance for any dfference n ages. For an age ncrease of 30 years, the estmated decrease n legblty dstance s 90 feet because the slope s 3 feet per year. The queston about estmatng the average legblty dstances for a specfc age s answered by usng the specfc age as the x value n the regresson equaton. To emphasze ths use of the regresson lne, we wrte t as: Average dstance = Age Here are the results for three dfferent ages: AGE AVERAGE DISTANCE (20) = 517 feet (50) = 427 feet (80) = 337 feet The equaton can also be used to predct the dstance measurement for an ndvdual drver wth a specfc age. To emphasze ths use of the regresson lne, we wrte the equaton as: Predcted dstance = Age For example, we can predct that the legblty dstance for a 20-year old wll be 517 feet and for an 80-year old wll be 337 feet. 162

8 Fgure 5.7 Regresson Lne For Drver Age and Sgn Legblty Dstance The Least Squares Lne, Errors and Resduals We can use statstcal software to estmate the regresson lne, but how does the computer fnd the best equaton for a set of data? The most commonly used method s called least squares and the regresson lne determned by ths method s called the least squares lne. The phrase least squares s actually a shortened verson of least sum of squared errors. Ths crteron focuses on the dfferences between the values of the response varable (y) and the regresson lne. The response varable s emphaszed because we often use the equaton to predct that varable for specfc values of the explanatory varable (x). Therefore, we should mnmze how far off the predctons wll be n that drecton. For any gven lne, we can calculate the predcted value of y for each pont n the observed data. To do ths for any partcular pont, we use the observed x value n the equaton. We then determne the predcton error for each pont. An error s smply the dfference between the observed y value and the predcted value ŷ. These errors are squared and added up for all of the ponts n the sample. The least squares lne mnmzes the sum of the squared errors. Ths termnology s somewhat msleadng, snce the amount by whch ndvdual dffers from the lne s seldom due to "errors" n the measurements. A more neutral term for the dfference ( y yˆ ) s that t s the resdual for that ndvdual. The Least Squares Crteron When we use a lne to predct the values of y, the sum of squared dfferences between the observed values of y and the predcted values s smaller for the least squares lne than t s for any other lne. There s a mathematcal soluton that produces general formulas for the slope and ntercept of the least squares lne. These formulas are used by all statstcal software, spreadsheet programs, and statstcal calculators. To be complete, we nclude the formulas. You won t need them f you use the computer to do a regresson analyss. 163

9 Formulas for the slope and ntercept of the least squares lne b 1 s the slope and b 0 s the ntercept. b b 1 0 = ( x ( x = y b x 1 x)( y x) x represents the x measurement for the th observaton. y represents the y measurement for the th observaton. x represents the mean of the x measurements. y represents the mean of the y measurements. y) Example 2 Revsted. Errors for the Hghway Sgn data The least squares regresson lne for Example 2 s y ˆ = x where y = maxmum sgn legblty dstance and x = drver age. For ths equaton, the calculaton of the errors and the squared errors for the frst three data ponts shown n Table 5.2 s: x y y ˆ = x error = y yˆ squared error (18) = = (20) = = (22) = = 5 25 Ths process can be carred out for all 30 data ponts. The sum of the squared errors s smaller for the lne y ˆ = x than t would be for any other lne

10 5.3 Measurng Strength and Drecton wth Correlaton The lnear pattern s so common that a statstc was created to characterze ths type of relatonshp. The statstcal correlaton between two quanttatve varables s a number that ndcates the strength and the drecton of a straght-lne relatonshp. The strength of relatonshp s determned by the closeness of the ponts to a straght lne. The drecton s determned by whether one varable generally ncreases or generally decreases when the other varable ncreases. As used n statstcs, the meanng of the word correlaton s much more specfc than t s n everyday lfe. A statstcal correlaton only descrbes lnear relatonshps. Whenever a correlaton s calculated, a straght lne s used as the frame of reference for evaluatng the relatonshp. When the pattern s nonlnear, as t was for the musc preference data shown n Fgure 5.3, a correlaton s not an approprate way to measure the strength of the relatonshp. Correlaton s represented by the letter r. Sometmes ths measure s called the "Pearson product moment correlaton" or the "correlaton coeffcent." The formula for correlaton s complcated. Fortunately, all statstcal software programs and many calculators provde a way to easly calculate ths statstc. A Formula for Correlaton 1 x x y y r = n 1 s x s y n s the sample sze. x s the x measurement for the th observaton. x s the mean of the x measurements. s x s the standard devaton of the x measurements. y s the y measurement for the th observaton. y s the mean of the y measurements. s y s the standard devaton of the y measurements. Interpretng the Correlaton Coeffcent Some specfc features of the correlaton coeffcent are: Correlaton coeffcents are always between 1 and +1. The magntude of the correlaton ndcates the strength of the relatonshp, whch s the overall closeness of the ponts to a straght lne. The sgn of the correlaton does not tell us about the strength the lnear relatonshp. A correlaton of ether +1 or 1 ndcates that there s a perfect lnear relatonshp and all data ponts fall on the same straght lne. The sgn of the correlaton ndcates the drecton of the relatonshp. A postve correlaton ndcates that the two varables tend to ncrease together (a postve assocaton). A negatve correlaton ndcates that when one varable ncreases the other s lkely to decrease (a negatve assocaton). A correlaton of 0 ndcates that the best straght lne through the data s exactly horzontal, so that knowng the value of x does not change the predcted value of y. 165

11 Example 1 Revsted. The correlaton between hand-span and heght The relatonshp between hand-span and heght appears to be lnear, so a correlaton s useful for characterzng the strength of the relatonshp. For these data, the correlaton s r = +0.74, a value that ndcates a somewhat strong postve relatonshp. A look back at Fgure 5.1 shows us that average hand-span defntely ncreases when heght ncreases, but wthn any specfc heght there s some natural varaton among ndvdual hand-spans. Example 2 Revsted. The Correlaton between Age and Sgn Legblty Dstance The correlaton for the data shown n Fgure 5.2 s r = 0.8, a value that ndcates a somewhat strong negatve assocaton between the varables. The Interpretaton of r 2, the Squared Correlaton The squared value of the correlaton s frequently used to descrbe the strength of a relatonshp. A squared correlaton, r 2, always has a value between 0 and 1, although some computer programs wll express ts value as a percentage between 0 and 100%. By squarng the correlaton, we retan nformaton about the strength of the relatonshp, but we lose nformaton about the drecton. Researchers typcally use the phrase proporton of varaton explaned by x n conjuncton wth the squared correlaton, r 2. For example, f r 2 = 0.60 (or 60%), the researcher may wrte that the explanatory varable explans 60% of the varaton n the response varable. If r 2 = 0.10 (or 10%), the explanatory varable only explans 10% of the varaton n the response varable. Ths nterpretaton stems from the use of the least squares lne as a predcton tool. Let s consder Example 1 agan. For that example, the regresson equaton s hand-span = heght. The correlaton s 0.74 and r 2 = (0.74) 2 = 0.55 (or 55%). We can say that heght explans 55% of the varaton n hand-span, but what does t mean to say ths? Suppose that we gnore the heght nformaton when we make predctons of hand-span. In other words, suppose we don t use the least squares lne to predct hand-span. For the 167 students n the data set, y, the average hand-span s about 20.8 centmeters. If we gnore the least squares lne, we could use ths value to predct the hand-span for any ndvdual, regardless of hs or her heght. Our predcton equaton s smply hand span = For both ths equaton and the least squares equaton nvolvng heght, we can compute the sum of squared dfferences between the actual hand-span values and the predcted values. The sum of squared dfferences between observed y values and the sample mean y s called the total varaton n y or sum of squares total and s denoted as SSTO. The sum of squared dfferences between observed y values and the predcted values based on the least squares lne s called the sum of squared errors and s denoted by SSE. Remember that errors are sometmes called resduals, and a synonym for sum of squared errors s resdual sum of squares. Whenever the correlaton s not 0, the least squares lne wll produce generally better predctons than the sample mean so SSE wll be smaller than SSTO. The squared correlaton expresses the reducton n squared predcton error as a fracton of the total varaton. Ths leads to the formula 2 SSTO SSE r = SSTO It can be shown (usng algebra) that ths quantty s exactly equal to the square of the correlaton. Let s consder r 2 for Examples 5 and 7. In Example 5, the correlaton between left and rght hand-spans s 0.95 so r 2 s 0.90, or about 90%. Ths ndcates that the span of one hand s very predctable f we know the span of the other hand (see Fgure 5.8). In Example 7, the correlaton between televson vewng hours and age s only r = The squared correlaton s about As we can see from the scatter plot n Fgure 5.10, knowng a person s age doesn t help us predct how much televson he or she watches per day. 166

CHAPTER 14 MORE ABOUT REGRESSION

CHAPTER 14 MORE ABOUT REGRESSION CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp

More information

Causal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting

Causal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting Causal, Explanatory Forecastng Assumes cause-and-effect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of

More information

1. Measuring association using correlation and regression

1. Measuring association using correlation and regression How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a

More information

benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).

benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ). REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or

More information

SIMPLE LINEAR CORRELATION

SIMPLE LINEAR CORRELATION SIMPLE LINEAR CORRELATION Smple lnear correlaton s a measure of the degree to whch two varables vary together, or a measure of the ntensty of the assocaton between two varables. Correlaton often s abused.

More information

THE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES

THE METHOD OF LEAST SQUARES THE METHOD OF LEAST SQUARES The goal: to measure (determne) an unknown quantty x (the value of a RV X) Realsaton: n results: y 1, y 2,..., y j,..., y n, (the measured values of Y 1, Y 2,..., Y j,..., Y n ) every result s encumbered

More information

The OC Curve of Attribute Acceptance Plans

The OC Curve of Attribute Acceptance Plans The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4

More information

Calibration and Linear Regression Analysis: A Self-Guided Tutorial

Calibration and Linear Regression Analysis: A Self-Guided Tutorial Calbraton and Lnear Regresson Analyss: A Self-Guded Tutoral Part The Calbraton Curve, Correlaton Coeffcent and Confdence Lmts CHM314 Instrumental Analyss Department of Chemstry, Unversty of Toronto Dr.

More information

Linear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits

Linear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits Lnear Crcuts Analyss. Superposton, Theenn /Norton Equalent crcuts So far we hae explored tmendependent (resste) elements that are also lnear. A tmendependent elements s one for whch we can plot an / cure.

More information

8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by

8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by 6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng

More information

How To Calculate The Accountng Perod Of Nequalty

How To Calculate The Accountng Perod Of Nequalty Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.

More information

Can Auto Liability Insurance Purchases Signal Risk Attitude?

Can Auto Liability Insurance Purchases Signal Risk Attitude? Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159-164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? Chu-Shu L Department of Internatonal Busness, Asa Unversty, Tawan Sheng-Chang

More information

SPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:

SPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background: SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and

More information

n + d + q = 24 and.05n +.1d +.25q = 2 { n + d + q = 24 (3) n + 2d + 5q = 40 (2)

n + d + q = 24 and.05n +.1d +.25q = 2 { n + d + q = 24 (3) n + 2d + 5q = 40 (2) MATH 16T Exam 1 : Part I (In-Class) Solutons 1. (0 pts) A pggy bank contans 4 cons, all of whch are nckels (5 ), dmes (10 ) or quarters (5 ). The pggy bank also contans a con of each denomnaton. The total

More information

14.74 Lecture 5: Health (2)

14.74 Lecture 5: Health (2) 14.74 Lecture 5: Health (2) Esther Duflo February 17, 2004 1 Possble Interventons Last tme we dscussed possble nterventons. Let s take one: provdng ron supplements to people, for example. From the data,

More information

Faraday's Law of Induction

Faraday's Law of Induction Introducton Faraday's Law o Inducton In ths lab, you wll study Faraday's Law o nducton usng a wand wth col whch swngs through a magnetc eld. You wll also examne converson o mechanc energy nto electrc energy

More information

An Alternative Way to Measure Private Equity Performance

An Alternative Way to Measure Private Equity Performance An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate

More information

An Evaluation of the Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products and Services

An Evaluation of the Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products and Services An Evaluaton of the Extended Logstc, Smple Logstc, and Gompertz Models for Forecastng Short Lfecycle Products and Servces Charles V. Trappey a,1, Hsn-yng Wu b a Professor (Management Scence), Natonal Chao

More information

Staff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall

Staff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall SP 2005-02 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 14853-7801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent

More information

Brigid Mullany, Ph.D University of North Carolina, Charlotte

Brigid Mullany, Ph.D University of North Carolina, Charlotte Evaluaton And Comparson Of The Dfferent Standards Used To Defne The Postonal Accuracy And Repeatablty Of Numercally Controlled Machnng Center Axes Brgd Mullany, Ph.D Unversty of North Carolna, Charlotte

More information

DEFINING %COMPLETE IN MICROSOFT PROJECT

DEFINING %COMPLETE IN MICROSOFT PROJECT CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMI-SP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,

More information

Using Series to Analyze Financial Situations: Present Value

Using Series to Analyze Financial Situations: Present Value 2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated

More information

NPAR TESTS. One-Sample Chi-Square Test. Cell Specification. Observed Frequencies 1O i 6. Expected Frequencies 1EXP i 6

NPAR TESTS. One-Sample Chi-Square Test. Cell Specification. Observed Frequencies 1O i 6. Expected Frequencies 1EXP i 6 PAR TESTS If a WEIGHT varable s specfed, t s used to replcate a case as many tmes as ndcated by the weght value rounded to the nearest nteger. If the workspace requrements are exceeded and samplng has

More information

Exhaustive Regression. An Exploration of Regression-Based Data Mining Techniques Using Super Computation

Exhaustive Regression. An Exploration of Regression-Based Data Mining Techniques Using Super Computation Exhaustve Regresson An Exploraton of Regresson-Based Data Mnng Technques Usng Super Computaton Antony Daves, Ph.D. Assocate Professor of Economcs Duquesne Unversty Pttsburgh, PA 58 Research Fellow The

More information

Economic Interpretation of Regression. Theory and Applications

Economic Interpretation of Regression. Theory and Applications Economc Interpretaton of Regresson Theor and Applcatons Classcal and Baesan Econometrc Methods Applcaton of mathematcal statstcs to economc data for emprcal support Economc theor postulates a qualtatve

More information

Module 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur

Module 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..

More information

Latent Class Regression. Statistics for Psychosocial Research II: Structural Models December 4 and 6, 2006

Latent Class Regression. Statistics for Psychosocial Research II: Structural Models December 4 and 6, 2006 Latent Class Regresson Statstcs for Psychosocal Research II: Structural Models December 4 and 6, 2006 Latent Class Regresson (LCR) What s t and when do we use t? Recall the standard latent class model

More information

Lecture 2: Single Layer Perceptrons Kevin Swingler

Lecture 2: Single Layer Perceptrons Kevin Swingler Lecture 2: Sngle Layer Perceptrons Kevn Sngler kms@cs.str.ac.uk Recap: McCulloch-Ptts Neuron Ths vastly smplfed model of real neurons s also knon as a Threshold Logc Unt: W 2 A Y 3 n W n. A set of synapses

More information

Answer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy

Answer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy 4.02 Quz Solutons Fall 2004 Multple-Choce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multple-choce questons. For each queston, only one of the answers s correct.

More information

Section 5.4 Annuities, Present Value, and Amortization

Section 5.4 Annuities, Present Value, and Amortization Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today

More information

7.5. Present Value of an Annuity. Investigate

7.5. Present Value of an Annuity. Investigate 7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on

More information

Management Quality, Financial and Investment Policies, and. Asymmetric Information

Management Quality, Financial and Investment Policies, and. Asymmetric Information Management Qualty, Fnancal and Investment Polces, and Asymmetrc Informaton Thomas J. Chemmanur * Imants Paegls ** and Karen Smonyan *** Current verson: December 2007 * Professor of Fnance, Carroll School

More information

where the coordinates are related to those in the old frame as follows.

where the coordinates are related to those in the old frame as follows. Chapter 2 - Cartesan Vectors and Tensors: Ther Algebra Defnton of a vector Examples of vectors Scalar multplcaton Addton of vectors coplanar vectors Unt vectors A bass of non-coplanar vectors Scalar product

More information

Feature selection for intrusion detection. Slobodan Petrović NISlab, Gjøvik University College

Feature selection for intrusion detection. Slobodan Petrović NISlab, Gjøvik University College Feature selecton for ntruson detecton Slobodan Petrovć NISlab, Gjøvk Unversty College Contents The feature selecton problem Intruson detecton Traffc features relevant for IDS The CFS measure The mrmr measure

More information

CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol

CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL

More information

Calculation of Sampling Weights

Calculation of Sampling Weights Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a two-stage stratfed cluster desgn. 1 The frst stage conssted of a sample

More information

Statistical Methods to Develop Rating Models

Statistical Methods to Develop Rating Models Statstcal Methods to Develop Ratng Models [Evelyn Hayden and Danel Porath, Österrechsche Natonalbank and Unversty of Appled Scences at Manz] Source: The Basel II Rsk Parameters Estmaton, Valdaton, and

More information

We assume your students are learning about self-regulation (how to change how alert they feel) through the Alert Program with its three stages:

We assume your students are learning about self-regulation (how to change how alert they feel) through the Alert Program with its three stages: Welcome to ALERT BINGO, a fun-flled and educatonal way to learn the fve ways to change engnes levels (Put somethng n your Mouth, Move, Touch, Look, and Lsten) as descrbed n the How Does Your Engne Run?

More information

Forecasting the Direction and Strength of Stock Market Movement

Forecasting the Direction and Strength of Stock Market Movement Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract - Stock market s one of the most complcated systems

More information

Face Verification Problem. Face Recognition Problem. Application: Access Control. Biometric Authentication. Face Verification (1:1 matching)

Face Verification Problem. Face Recognition Problem. Application: Access Control. Biometric Authentication. Face Verification (1:1 matching) Face Recognton Problem Face Verfcaton Problem Face Verfcaton (1:1 matchng) Querymage face query Face Recognton (1:N matchng) database Applcaton: Access Control www.vsage.com www.vsoncs.com Bometrc Authentcaton

More information

Question 2: What is the variance and standard deviation of a dataset?

Question 2: What is the variance and standard deviation of a dataset? Queston 2: What s the varance and standard devaton of a dataset? The varance of the data uses all of the data to compute a measure of the spread n the data. The varance may be computed for a sample of

More information

Joe Pimbley, unpublished, 2005. Yield Curve Calculations

Joe Pimbley, unpublished, 2005. Yield Curve Calculations Joe Pmbley, unpublshed, 005. Yeld Curve Calculatons Background: Everythng s dscount factors Yeld curve calculatons nclude valuaton of forward rate agreements (FRAs), swaps, nterest rate optons, and forward

More information

Number of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000

Number of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000 Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from

More information

Regression Models for a Binary Response Using EXCEL and JMP

Regression Models for a Binary Response Using EXCEL and JMP SEMATECH 997 Statstcal Methods Symposum Austn Regresson Models for a Bnary Response Usng EXCEL and JMP Davd C. Trndade, Ph.D. STAT-TECH Consultng and Tranng n Appled Statstcs San Jose, CA Topcs Practcal

More information

STATISTICAL DATA ANALYSIS IN EXCEL

STATISTICAL DATA ANALYSIS IN EXCEL Mcroarray Center STATISTICAL DATA ANALYSIS IN EXCEL Lecture 6 Some Advanced Topcs Dr. Petr Nazarov 14-01-013 petr.nazarov@crp-sante.lu Statstcal data analyss n Ecel. 6. Some advanced topcs Correcton for

More information

The Use of Analytics for Claim Fraud Detection Roosevelt C. Mosley, Jr., FCAS, MAAA Nick Kucera Pinnacle Actuarial Resources Inc.

The Use of Analytics for Claim Fraud Detection Roosevelt C. Mosley, Jr., FCAS, MAAA Nick Kucera Pinnacle Actuarial Resources Inc. Paper 1837-2014 The Use of Analytcs for Clam Fraud Detecton Roosevelt C. Mosley, Jr., FCAS, MAAA Nck Kucera Pnnacle Actuaral Resources Inc., Bloomngton, IL ABSTRACT As t has been wdely reported n the nsurance

More information

+ + + - - This circuit than can be reduced to a planar circuit

+ + + - - This circuit than can be reduced to a planar circuit MeshCurrent Method The meshcurrent s analog of the nodeoltage method. We sole for a new set of arables, mesh currents, that automatcally satsfy KCLs. As such, meshcurrent method reduces crcut soluton to

More information

An Empirical Study of Search Engine Advertising Effectiveness

An Empirical Study of Search Engine Advertising Effectiveness An Emprcal Study of Search Engne Advertsng Effectveness Sanjog Msra, Smon School of Busness Unversty of Rochester Edeal Pnker, Smon School of Busness Unversty of Rochester Alan Rmm-Kaufman, Rmm-Kaufman

More information

The Development of Web Log Mining Based on Improve-K-Means Clustering Analysis

The Development of Web Log Mining Based on Improve-K-Means Clustering Analysis The Development of Web Log Mnng Based on Improve-K-Means Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.

More information

What is Candidate Sampling

What is Candidate Sampling What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble

More information

A machine vision approach for detecting and inspecting circular parts

A machine vision approach for detecting and inspecting circular parts A machne vson approach for detectng and nspectng crcular parts Du-Mng Tsa Machne Vson Lab. Department of Industral Engneerng and Management Yuan-Ze Unversty, Chung-L, Tawan, R.O.C. E-mal: edmtsa@saturn.yzu.edu.tw

More information

ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET *

ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET * ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET * Amy Fnkelsten Harvard Unversty and NBER James Poterba MIT and NBER * We are grateful to Jeffrey Brown, Perre-Andre

More information

Recurrence. 1 Definitions and main statements

Recurrence. 1 Definitions and main statements Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.

More information

The Greedy Method. Introduction. 0/1 Knapsack Problem

The Greedy Method. Introduction. 0/1 Knapsack Problem The Greedy Method Introducton We have completed data structures. We now are gong to look at algorthm desgn methods. Often we are lookng at optmzaton problems whose performance s exponental. For an optmzaton

More information

Rotation Kinematics, Moment of Inertia, and Torque

Rotation Kinematics, Moment of Inertia, and Torque Rotaton Knematcs, Moment of Inerta, and Torque Mathematcally, rotaton of a rgd body about a fxed axs s analogous to a lnear moton n one dmenson. Although the physcal quanttes nvolved n rotaton are qute

More information

Types of Injuries. (20 minutes) LEARNING OBJECTIVES MATERIALS NEEDED

Types of Injuries. (20 minutes) LEARNING OBJECTIVES MATERIALS NEEDED U N I T 3 Types of Injures (20 mnutes) PURPOSE: To help coaches learn how to recognze the man types of acute and chronc njures. LEARNING OBJECTIVES In ths unt, coaches wll learn how most njures occur,

More information

Binomial Link Functions. Lori Murray, Phil Munz

Binomial Link Functions. Lori Murray, Phil Munz Bnomal Lnk Functons Lor Murray, Phl Munz Bnomal Lnk Functons Logt Lnk functon: ( p) p ln 1 p Probt Lnk functon: ( p) 1 ( p) Complentary Log Log functon: ( p) ln( ln(1 p)) Motvatng Example A researcher

More information

total A A reag total A A r eag

total A A reag total A A r eag hapter 5 Standardzng nalytcal Methods hapter Overvew 5 nalytcal Standards 5B albratng the Sgnal (S total ) 5 Determnng the Senstvty (k ) 5D Lnear Regresson and albraton urves 5E ompensatng for the Reagent

More information

L10: Linear discriminants analysis

L10: Linear discriminants analysis L0: Lnear dscrmnants analyss Lnear dscrmnant analyss, two classes Lnear dscrmnant analyss, C classes LDA vs. PCA Lmtatons of LDA Varants of LDA Other dmensonalty reducton methods CSCE 666 Pattern Analyss

More information

Texas Instruments 30X IIS Calculator

Texas Instruments 30X IIS Calculator Texas Instruments 30X IIS Calculator Keystrokes for the TI-30X IIS are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the

More information

Shielding Equations and Buildup Factors Explained

Shielding Equations and Buildup Factors Explained Sheldng Equatons and uldup Factors Explaned Gamma Exposure Fluence Rate Equatons For an explanaton of the fluence rate equatons used n the unshelded and shelded calculatons, vst ths US Health Physcs Socety

More information

Portfolio Loss Distribution

Portfolio Loss Distribution Portfolo Loss Dstrbuton Rsky assets n loan ortfolo hghly llqud assets hold-to-maturty n the bank s balance sheet Outstandngs The orton of the bank asset that has already been extended to borrowers. Commtment

More information

Transition Matrix Models of Consumer Credit Ratings

Transition Matrix Models of Consumer Credit Ratings Transton Matrx Models of Consumer Credt Ratngs Abstract Although the corporate credt rsk lterature has many studes modellng the change n the credt rsk of corporate bonds over tme, there s far less analyss

More information

Support Vector Machines

Support Vector Machines Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.

More information

International University of Japan Public Management & Policy Analysis Program

International University of Japan Public Management & Policy Analysis Program Internatonal Unversty of Japan Publc Management & Polcy Analyss Program Practcal Gudes To Panel Data Modelng: A Step by Step Analyss Usng Stata * Hun Myoung Park, Ph.D. kucc65@uj.ac.jp 1. Introducton.

More information

Characterization of Assembly. Variation Analysis Methods. A Thesis. Presented to the. Department of Mechanical Engineering. Brigham Young University

Characterization of Assembly. Variation Analysis Methods. A Thesis. Presented to the. Department of Mechanical Engineering. Brigham Young University Characterzaton of Assembly Varaton Analyss Methods A Thess Presented to the Department of Mechancal Engneerng Brgham Young Unversty In Partal Fulfllment of the Requrements for the Degree Master of Scence

More information

Meta-Analysis of Hazard Ratios

Meta-Analysis of Hazard Ratios NCSS Statstcal Softare Chapter 458 Meta-Analyss of Hazard Ratos Introducton Ths module performs a meta-analyss on a set of to-group, tme to event (survval), studes n hch some data may be censored. These

More information

Student Performance in Online Quizzes as a Function of Time in Undergraduate Financial Management Courses

Student Performance in Online Quizzes as a Function of Time in Undergraduate Financial Management Courses Student Performance n Onlne Quzzes as a Functon of Tme n Undergraduate Fnancal Management Courses Olver Schnusenberg The Unversty of North Florda ABSTRACT An nterestng research queston n lght of recent

More information

Stress test for measuring insurance risks in non-life insurance

Stress test for measuring insurance risks in non-life insurance PROMEMORIA Datum June 01 Fnansnspektonen Författare Bengt von Bahr, Younes Elonq and Erk Elvers Stress test for measurng nsurance rsks n non-lfe nsurance Summary Ths memo descrbes stress testng of nsurance

More information

21 Vectors: The Cross Product & Torque

21 Vectors: The Cross Product & Torque 21 Vectors: The Cross Product & Torque Do not use our left hand when applng ether the rght-hand rule for the cross product of two vectors dscussed n ths chapter or the rght-hand rule for somethng curl

More information

Institute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic

Institute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange

More information

Instructions for Analyzing Data from CAHPS Surveys:

Instructions for Analyzing Data from CAHPS Surveys: Instructons for Analyzng Data from CAHPS Surveys: Usng the CAHPS Analyss Program Verson 4.1 Purpose of ths Document...1 The CAHPS Analyss Program...1 Computng Requrements...1 Pre-Analyss Decsons...2 What

More information

Heterogeneous Paths Through College: Detailed Patterns and Relationships with Graduation and Earnings

Heterogeneous Paths Through College: Detailed Patterns and Relationships with Graduation and Earnings Heterogeneous Paths Through College: Detaled Patterns and Relatonshps wth Graduaton and Earnngs Rodney J. Andrews The Unversty of Texas at Dallas and the Texas Schools Project Jng L The Unversty of Tulsa

More information

ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C White Emerson Process Management

ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C White Emerson Process Management ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C Whte Emerson Process Management Abstract Energy prces have exhbted sgnfcant volatlty n recent years. For example, natural gas prces

More information

Calculating the high frequency transmission line parameters of power cables

Calculating the high frequency transmission line parameters of power cables < ' Calculatng the hgh frequency transmsson lne parameters of power cables Authors: Dr. John Dcknson, Laboratory Servces Manager, N 0 RW E B Communcatons Mr. Peter J. Ncholson, Project Assgnment Manager,

More information

MATLAB Workshop 15 - Linear Regression in MATLAB

MATLAB Workshop 15 - Linear Regression in MATLAB MATLAB: Workshop 15 - Lnear Regresson n MATLAB page 1 MATLAB Workshop 15 - Lnear Regresson n MATLAB Objectves: Learn how to obtan the coeffcents of a straght-lne ft to data, dsplay the resultng equaton

More information

How To Understand The Results Of The German Meris Cloud And Water Vapour Product

How To Understand The Results Of The German Meris Cloud And Water Vapour Product Ttel: Project: Doc. No.: MERIS level 3 cloud and water vapour products MAPP MAPP-ATBD-ClWVL3 Issue: 1 Revson: 0 Date: 9.12.1998 Functon Name Organsaton Sgnature Date Author: Bennartz FUB Preusker FUB Schüller

More information

"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *

Research Note APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES * Iranan Journal of Scence & Technology, Transacton B, Engneerng, ol. 30, No. B6, 789-794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC

More information

Fixed income risk attribution

Fixed income risk attribution 5 Fxed ncome rsk attrbuton Chthra Krshnamurth RskMetrcs Group chthra.krshnamurth@rskmetrcs.com We compare the rsk of the actve portfolo wth that of the benchmark and segment the dfference between the two

More information

Traffic-light a stress test for life insurance provisions

Traffic-light a stress test for life insurance provisions MEMORANDUM Date 006-09-7 Authors Bengt von Bahr, Göran Ronge Traffc-lght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE-113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax

More information

HARVARD John M. Olin Center for Law, Economics, and Business

HARVARD John M. Olin Center for Law, Economics, and Business HARVARD John M. Oln Center for Law, Economcs, and Busness ISSN 1045-6333 ASYMMETRIC INFORMATION AND LEARNING IN THE AUTOMOBILE INSURANCE MARKET Alma Cohen Dscusson Paper No. 371 6/2002 Harvard Law School

More information

Social Nfluence and Its Models

Social Nfluence and Its Models Influence and Correlaton n Socal Networks Ars Anagnostopoulos Rav Kumar Mohammad Mahdan Yahoo! Research 701 Frst Ave. Sunnyvale, CA 94089. {ars,ravkumar,mahdan}@yahoo-nc.com ABSTRACT In many onlne socal

More information

HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA*

HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA* HOUSEHOLDS DEBT BURDEN: AN ANALYSIS BASED ON MICROECONOMIC DATA* Luísa Farnha** 1. INTRODUCTION The rapd growth n Portuguese households ndebtedness n the past few years ncreased the concerns that debt

More information

How To Find The Dsablty Frequency Of A Clam

How To Find The Dsablty Frequency Of A Clam 1 Predcton of Dsablty Frequences n Lfe Insurance Bernhard Köng 1, Fran Weber 1, Maro V. Wüthrch 2 Abstract: For the predcton of dsablty frequences, not only the observed, but also the ncurred but not yet

More information

Traditional versus Online Courses, Efforts, and Learning Performance

Traditional versus Online Courses, Efforts, and Learning Performance Tradtonal versus Onlne Courses, Efforts, and Learnng Performance Kuang-Cheng Tseng, Department of Internatonal Trade, Chung-Yuan Chrstan Unversty, Tawan Shan-Yng Chu, Department of Internatonal Trade,

More information

v a 1 b 1 i, a 2 b 2 i,..., a n b n i.

v a 1 b 1 i, a 2 b 2 i,..., a n b n i. SECTION 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS 455 8.4 COMPLEX VECTOR SPACES AND INNER PRODUCTS All the vector spaces we have studed thus far n the text are real vector spaces snce the scalars are

More information

Quantification of qualitative data: the case of the Central Bank of Armenia

Quantification of qualitative data: the case of the Central Bank of Armenia Quantfcaton of qualtatve data: the case of the Central Bank of Armena Martn Galstyan 1 and Vahe Movssyan 2 Overvew The effect of non-fnancal organsatons and consumers atttudes on economc actvty s a subject

More information

Part 1: quick summary 5. Part 2: understanding the basics of ANOVA 8

Part 1: quick summary 5. Part 2: understanding the basics of ANOVA 8 Statstcs Rudolf N. Cardnal Graduate-level statstcs for psychology and neuroscence NOV n practce, and complex NOV desgns Verson of May 4 Part : quck summary 5. Overvew of ths document 5. Background knowledge

More information

Conversion between the vector and raster data structures using Fuzzy Geographical Entities

Conversion between the vector and raster data structures using Fuzzy Geographical Entities Converson between the vector and raster data structures usng Fuzzy Geographcal Enttes Cdála Fonte Department of Mathematcs Faculty of Scences and Technology Unversty of Combra, Apartado 38, 3 454 Combra,

More information

Two Faces of Intra-Industry Information Transfers: Evidence from Management Earnings and Revenue Forecasts

Two Faces of Intra-Industry Information Transfers: Evidence from Management Earnings and Revenue Forecasts Two Faces of Intra-Industry Informaton Transfers: Evdence from Management Earnngs and Revenue Forecasts Yongtae Km Leavey School of Busness Santa Clara Unversty Santa Clara, CA 95053-0380 TEL: (408) 554-4667,

More information

Analysis of Premium Liabilities for Australian Lines of Business

Analysis of Premium Liabilities for Australian Lines of Business Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton

More information

Logistic Regression. Steve Kroon

Logistic Regression. Steve Kroon Logstc Regresson Steve Kroon Course notes sectons: 24.3-24.4 Dsclamer: these notes do not explctly ndcate whether values are vectors or scalars, but expects the reader to dscern ths from the context. Scenaro

More information

Fuzzy Regression and the Term Structure of Interest Rates Revisited

Fuzzy Regression and the Term Structure of Interest Rates Revisited Fuzzy Regresson and the Term Structure of Interest Rates Revsted Arnold F. Shapro Penn State Unversty Smeal College of Busness, Unversty Park, PA 68, USA Phone: -84-865-396, Fax: -84-865-684, E-mal: afs@psu.edu

More information

Course outline. Financial Time Series Analysis. Overview. Data analysis. Predictive signal. Trading strategy

Course outline. Financial Time Series Analysis. Overview. Data analysis. Predictive signal. Trading strategy Fnancal Tme Seres Analyss Patrck McSharry patrck@mcsharry.net www.mcsharry.net Trnty Term 2014 Mathematcal Insttute Unversty of Oxford Course outlne 1. Data analyss, probablty, correlatons, vsualsaton

More information

The Effect of Mean Stress on Damage Predictions for Spectral Loading of Fiberglass Composite Coupons 1

The Effect of Mean Stress on Damage Predictions for Spectral Loading of Fiberglass Composite Coupons 1 EWEA, Specal Topc Conference 24: The Scence of Makng Torque from the Wnd, Delft, Aprl 9-2, 24, pp. 546-555. The Effect of Mean Stress on Damage Predctons for Spectral Loadng of Fberglass Composte Coupons

More information

Financial Instability and Life Insurance Demand + Mahito Okura *

Financial Instability and Life Insurance Demand + Mahito Okura * Fnancal Instablty and Lfe Insurance Demand + Mahto Okura * Norhro Kasuga ** Abstract Ths paper estmates prvate lfe nsurance and Kampo demand functons usng household-level data provded by the Postal Servces

More information

Financial Mathemetics

Financial Mathemetics Fnancal Mathemetcs 15 Mathematcs Grade 12 Teacher Gude Fnancal Maths Seres Overvew In ths seres we am to show how Mathematcs can be used to support personal fnancal decsons. In ths seres we jon Tebogo,

More information

Damage detection in composite laminates using coin-tap method

Damage detection in composite laminates using coin-tap method Damage detecton n composte lamnates usng con-tap method S.J. Km Korea Aerospace Research Insttute, 45 Eoeun-Dong, Youseong-Gu, 35-333 Daejeon, Republc of Korea yaeln@kar.re.kr 45 The con-tap test has the

More information

Hot and easy in Florida: The case of economics professors

Hot and easy in Florida: The case of economics professors Research n Hgher Educaton Journal Abstract Hot and easy n Florda: The case of economcs professors Olver Schnusenberg The Unversty of North Florda Cheryl Froehlch The Unversty of North Florda We nvestgate

More information

PRACTICE 1: MUTUAL FUNDS EVALUATION USING MATLAB.

PRACTICE 1: MUTUAL FUNDS EVALUATION USING MATLAB. PRACTICE 1: MUTUAL FUNDS EVALUATION USING MATLAB. INDEX 1. Load data usng the Edtor wndow and m-fle 2. Learnng to save results from the Edtor wndow. 3. Computng the Sharpe Rato 4. Obtanng the Treynor Rato

More information