# CHAPTER 7 THE TWO-VARIABLE REGRESSION MODEL: HYPOTHESIS TESTING

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 CHAPTER 7 THE TWO-VARIABLE REGRESSION MODEL: HYPOTHESIS TESTING QUESTIONS 7.1. (a) In the regresson contet, the method of least squares estmates the regresson parameters n such a way that the sum of the squared dfference between the actual Y values (.e., the values of the dependent varable) and the estmated Y values s as small as possble. (b) The estmators of the regresson parameters obtaned by the method of least squares. (c) An estmator beng a random varable, ts varance, lke the varance of any random varable, measures the spread of the estmated values around the mean value of the estmator. (d) The (postve) square root value of the varance of an estmator. (e) Equal varance. (f) Unequal varance. (g) Correlaton between successve values of a random varable. (h) In the regresson contet, TSS s the sum of squared dfference between the ndvdual and the mean value of the dependent varable Y, namely, ( Y Y ). () ESS s the part of the TSS that s eplaned by the eplanatory varable(s). (j) RSS s the part of the TSS that s not eplaned by the eplanatory varable(s), the X varable(s). (k) It measures the proporton of the total varaton n Y eplaned by the eplanatory varables. In short, t s the rato of ESS to TSS. (l) It s the standard devaton of the Y values about the estmated regresson lne. 44

2 (m) BLUE means best lnear unbased estmator, that s, a lnear estmator that s unbased and has the least varance n the class of all such lnear unbased estmators. (n) A statstcal procedure of testng statstcal hypotheses. (o) A test of sgnfcance based on the t dstrbuton. (p) In a one-taled test, the alternatve hypothess s one-sded. For eample: H 0 : μ μ 0 aganst H 1 : μ > μ0 or μ < μ 0, where μ s the mean value. (q) In a two-taled test, the alternatve hypothess s two-sded. (r) It s a short-hand for the statement: reject the null hypothess. 7.. (a) False. It mnmzes the sum of resduals squared, that s, t mnmzes e. (b) True. (c) True. (d) False. The OLS does not requre any probablstc assumpton about the error term n estmatng the parameters. (e) True. The OLS estmators are lnear functons of u and wll follow the normal dstrbuton f t s assumed that u are normally dstrbuted. Recall that any lnear functon of a normally dstrbuted varable s tself normally dstrbuted. (f) False. It s ESS / TSS. (g) False. We should reject the null hypothess. (h) True. The numerator of both coeffcents nvolves the covarance between Y and X, whch can be postve or negatve. () Uncertan. The p value s the eact level of sgnfcance of a computed test statstc, whch may be dfferent from an arbtrarly chosen level of sgnfcance, α (a) t (b) se( b ) (c) 0 and 1 (d) -1 and +1 (e) ESS (f) ESS (g) the standard error of the estmate (h)( Y ) b + e Y () 45

3 7.4. The answers to the mssng numbers are n boes: Ŷ X r se ( ) ( ) n 0 t ( ) (18.73) The crtcal t value at the 5% level for 18 d.f. s.101 (two-taled) and (one-taled). Snce the estmated t value of far eceeds ether of these crtcal values, we reject the null hypothess. A two-taled test s approprate because no a pror theoretcal consderatons are known regardng the sgn of the coeffcent r y e ) / y ( ŷ / y b / y, followng Equatons (7.34) and (7.35) In provng the last equalty, note that follows by substtuton. ŷ b y y. Then the result 7.6. e n Y n Y b X ) n b X 0. See also Problem 6.. ( PROBLEMS 7.7. (a) The d.f. here are 14. Therefore, the 5% crtcal t value s.145. So, the 95% confdence nterval s: 3.4 ±.145(1.634) (-0.649, ) (b) The precedng nterval does nclude B. Therefore, do not reject the null hypothess. (c) t 3.4 / Snce car sales are epected to be postvely related to real dsposable ncome, the null and alternatve hypotheses should be: : B 0 and : B 0. Therefore, an one-taled t test s H0 H1 > approprate n ths case. The 5% one-taled t value for 14 d.f. s Snce the computed t value of eceeds the crtcal value, reject the null hypothess (one- and two tal tests sometmes gve dfferent results). 46

4 7.8. (a) The slope coeffcent of means that durng the perod a percentage pont ncrease n the market rate of return lead to about 1.06 percent ponts ncrease n the mean return on the IBM stock. In the same perod, f the market rate of return were zero, the average rate of return on the stock would have been about 0.73 percent, whch may not make economc sense. (b) About 47 percent of the varaton n the mean return on the IBM stock was eplaned by the (varaton) n the market return. (c) : B 1, : B 1. Hence: H0 H1 > ( ) t For 38 d.f, ths t value s not statstcally sgnfcant at the 5% level on the bass of the one-taled t test. Thus, durng the study perod, the beta coeffcent of IBM was not statstcally dfferent from unty, suggestng that the IBM stock was not volatle or aggressve (a) b 1 1.; b (b) se( b 1 ) ; se( b ) (c) r (d) 95% CI for B 1 : to % CI for B : 0.48 to (e) Reject H 0, snce the precedng CI does not nclude B (a) The answers to the mssng numbers are n boes: GNP t M 1 t r se ( ) (0.197) t ( ) ( ) (b) : B 0, : B 0. The null hypothess can be rejected. H0 H1 > (c) No partcular economc meanng can be attached to t. (d) Gˆ NP (55) 3,676 bllon. 47

5 7.11. (a) Negatve. (b) Yes. Here, n 14 (14 presdental electons startng n 198 and endng n 1980) and therefore d.f. 1. The computed t value of -.67 s statstcally sgnfcant at the fve percent level (one-taled test). (c) Probably. But n the 1984 electons the personal popularty of Ronald Reagan was an mportant factor. (d) Snce t b / se( b ) under the null hypothess that the true B s zero, b se( b ). In the present eample these standard errors are and t , respectvely (a) It could be negatve or postve. As more output s produced as a result of ncreased capacty, prce ncreases (.e., nflaton) wll slow down. However, f capacty utlzaton s at ts optmal value, and f demand pressures contnue, nflaton may actually rse. (b) The output n EVews format s as follows: Dependent Varable: INFLATION Sample: Varable Coeffcent Std. Error t-statstc Prob. C CAPACITY R-squared (c) The estmated slope coeffcent s negatve but also statstcally nsgnfcant, for the estmated p value s qute hgh. (d) Yes t s, for under the null hypothess that the true slope coeffcent s 1, the estmated t value s (1) t The probablty of obtanng such a t value s practcally zero. (e) To get ths, solve C 0, whch gves C 19.14, whch may be called the natural rate of capacty utlzaton. 48

6 Note: The results of the above regresson are vrtually nsgnfcant. Plus, the natural rate of capacty utlzaton that was found to be may be problematc because the measure of capacty utlzaton does not eceed 100. The reason for the regresson breakdown s the fact that the data nclude the decade of the 1970s wth ts hgh rates of nflaton and the md 1970s stagflaton. Runnng the regresson over a perod that ecludes the 1970s, say , wll produce more reasonable and statstcally sgnfcant results. In fact, f the regresson covers the perod, the reader can easly verfy that the natural rate of capacty utlzaton s appromately (a) The EVews regresson results are as follows: Dependent Varable: CAPACITY Sample: Varable Coeffcent Std. Error t-statstc Prob. C INFLATION R-squared Note: Ths regresson s also nsgnfcant for the reason dscussed above. (b) Multplyng the two slope coeffcents, we obtan the value of whch s equal to the R value obtaned from ether equaton. Ths result s not surprsng n vew of Problem 6.1. (c) By way of another eample, let Y salary and X qualfcatons for a group of men and women. As Maddala notes, the drect regresson wll answer the queston whether men and women wth the same X value get the same Y value. The reverse regresson wll answer the questons whether men and women wth the same Y value wll have the same X value. Reverse regresson s advocated for wage dscrmnaton cases. (d) No (a) Postve. (b) and (c) The scattergram wll show that the relatonshp between the two s generally postve, although there are a few outlers. 49

7 (d) The regresson results are as follows: Ŷ t se ( ) (0.1154) (e) 99% CI: B t (0.039) (3.6406) X t r Snce the precedng nterval does not nclude zero, we can reject the null hypothess (a) The regresson results are: MA T ˆ HMt MATHFM t se (0.6353) (0.0455) t (8.579) ( ) r (b) Reject the null hypothess, snce the computed t value of far eceeds the crtcal value even at the level of sgnfcance. (c) MAˆ THM (d) CI: ( , ) (a) The regresson results are as follows: VE R ˆ BMt VERBFM t se (11.658) (0.068) t (1.713) (5.1018) r (b) Reject the null hypothess, snce the computed t value s very hgh. (c) VEˆ RBM (d) CI: ( , ) (a) There s a postve relatonshp between real return on the stock prce nde ths year and the dvdend prce rato last year: Per unt ncrease n the latter, the mean real return goes up by 5.6 percentage ponts. The ntercept has no vable economc meanng. (b) If the precedng results are accepted, t has serous mplcatons for the effcent market hypothess of modern fnance. 50

8 7.18 (a) The EVews regresson output s as follows: Dependent Varable: AVGHWAGE Sample: 1 13 Varable Coeffcent Std. Error t-statstc Prob. C YEARSSCH R-squared (b) On the bass of the t test ths hypothess can be easly rejected, for the computed t value s hghly sgnfcant; ts p value s practcally zero (c) Here t Ths t value s also hghly sgnfcant, leadng to the concluson that the educaton coeffcent s statstcally dfferent from 1. The p value of obtanng the computed t value s (two-tal test) Note: Ths Problem s an etenson of Problem (a) Based on the regresson, we need to calculate new varables based on the real GDP (RGDP) and the unemployment rate (UNRATE). These calculatons, based on the data n Table 6-1, are as follows: CHUNRATE Change n UNRATE UNRATE UNRATE(-1) PCTCRGDP % Change n RGDP [RGDP / RGDP(-1)]* Usng EVews, the regresson results are: Dependent Varable: PCTCRGDP Sample (adjusted): Varable Coeffcent Std. Error t-statstc Prob. C CHUNRATE R-squared Note: The sample s adjusted to start n 1971 nstead of the ntal observaton of 1970 because we are calculatng percentage changes (RGDP) and changes (UNRATE): Ths causes the loss of the frst observaton. 51

9 (b) Yes, for the estmated slope coeffcent has a t value of whose p value s practcally zero. (c) The ntercept term s also statstcally sgnfcant. The nterpretaton here s that f the change n the unemployment rate were zero, the growth n the real GDP wll be about 3.%, whch may be called the long-term, or steady-state, rate of growth of GDP The regresson results, usng EVews, are: Dependent Varable: SP500 Sample: Varable Coeffcent Std. Error t-statstc Prob. C /MTB R-squared As these results show, the slope coeffcent s statstcally sgnfcant at about the % level, but the ntercept s not. Any mnor dfferences wth the regresson shown n the tet are solely due to roundng The EVews regresson results for (6.7) are as follows: Dependent Varable: PRICE Sample: 1 3 Varable Coeffcent Std. Error t-statstc Prob. C AGE R-squared The estmated slope coeffcent s hghly statstcally sgnfcant, for the p value of obtanng a t statstc of or greater under the null hypothess of a zero true populaton slope coeffcent s practcally zero. In contrast, the estmated ntercept coeffcent s statstcally nsgnfcant snce ts p value s relatvely hgh. Lkewse, the EVews results of regresson (6.8) are: (Regresson output s shown n the followng page) 5

10 Dependent Varable: PRICE Sample: 1 3 Varable Coeffcent Std. Error t-statstc Prob. C NOBIDDERS R-squared Here both the coeffcents are ndvdually statstcally sgnfcant, as ther p values are qute low. 7.. Note: The regresson results presented here are dentcal to those of Problem (a) The results, usng EVews, are as follows: Dependent Varable: ASP Sample: 1 47 Varable Coeffcent Std. Error t-statstc Prob. C GPA R-squared As these results suggest, GPA has a postve mpact on ASP, and t s statstcally very sgnfcant, as the p value of the estmated coeffcent s very small. (b) The results for GMAT are as follows: Dependent Varable: ASP Sample: 1 47 Varable Coeffcent Std. Error t-statstc Prob. C GMAT R-squared These results show that GMAT has a postve and statstcally sgnfcant mpact on ASP. (c) The results for annual tuton are as follows: (Regresson output s shown n the followng page) 53

11 Dependent Varable: ASP Sample: 1 47 Varable Coeffcent Std. Error t-statstc Prob. C TUITION R-squared Tuton (perhaps reflectng the qualty of educaton) has a postve and statstcally sgnfcant mpact on ASP. Incdentally, t can also be shown that the mpact of recruter ratng has a postve and hghly sgnfcant mpact on ASP, as t can be seen from the followng EVews output: Dependent Varable: ASP Sample: 1 47 Varable Coeffcent Std. Error t-statstc Prob. C RATING R-squared The regresson results of ependture on mported goods (Y) and personal dsposable ncome (X), usng EVews, are as follows: Dependent Varable: Y Sample: Varable Coeffcent Std. Error t-statstc Prob. C X R-squared These results suggest that personal dsposable ncome has a very sgnfcant postve mpact on ependture on mported goods, an unsurprsng fndng. The p value for the slope s vrtually zero, and the null hypothess s therefore rejected If we let w, we can wrte b w Y, that s, b s a lnear estmator,.e., a lnear functon of the Y values. Note that we are treatng 54

12 55 X as non-stochastc. Follow smlar steps to show that 1 b s also a lnear functon of the Y values. Now: ) ( u X B B Y y b u X B B + u B Ths s n vew of the fact that 0 ( X ) X and 1 X. Therefore, ) ( B u B E b E + Note: ) ( 1 u E u E, snce s a constant and snce X and u are uncorrelated by OLS assumpton. Follow smlar steps to prove that 1 b s also unbased Squarng Equaton (7.33) and summng, we obtan: + + e b e b y + e b snce 0 e.

### The covariance is the two variable analog to the variance. The formula for the covariance between two variables is

Regresson Lectures So far we have talked only about statstcs that descrbe one varable. What we are gong to be dscussng for much of the remander of the course s relatonshps between two or more varables.

### 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.

### 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

### 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

### 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

### 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

### x f(x) 1 0.25 1 0.75 x 1 0 1 1 0.04 0.01 0.20 1 0.12 0.03 0.60

BIVARIATE DISTRIBUTIONS Let be a varable that assumes the values { 1,,..., n }. Then, a functon that epresses the relatve frequenc of these values s called a unvarate frequenc functon. It must be true

### The Analysis of Covariance. ERSH 8310 Keppel and Wickens Chapter 15

The Analyss of Covarance ERSH 830 Keppel and Wckens Chapter 5 Today s Class Intal Consderatons Covarance and Lnear Regresson The Lnear Regresson Equaton TheAnalyss of Covarance Assumptons Underlyng the

### PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 12

14 The Ch-squared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304-C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed

### Analysis of Covariance

Chapter 551 Analyss of Covarance Introducton A common tas n research s to compare the averages of two or more populatons (groups). We mght want to compare the ncome level of two regons, the ntrogen content

### CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES

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

### Inequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.

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.

### 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

### Study on CET4 Marks in China s Graded English Teaching

Study on CET4 Marks n Chna s Graded Englsh Teachng CHE We College of Foregn Studes, Shandong Insttute of Busness and Technology, P.R.Chna, 264005 Abstract: Ths paper deploys Logt model, and decomposes

### 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

### 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

### 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

### Examples of Multiple Linear Regression Models

ECON *: Examples of Multple Regresson Models Examples of Multple Lnear Regresson Models Data: Stata tutoral data set n text fle autoraw or autotxt Sample data: A cross-sectonal sample of 7 cars sold n

### 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

### H 1 : at least one is not zero

Chapter 6 More Multple Regresson Model The F-test Jont Hypothess Tests Consder the lnear regresson equaton: () y = β + βx + βx + β4x4 + e for =,,..., N The t-statstc gve a test of sgnfcance of an ndvdual

### 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

### 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.

### 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

### MULTIPLE LINEAR REGRESSION IN MINITAB

MULTIPLE LINEAR REGRESSION IN MINITAB Ths document shows a complcated Mntab multple regresson. It ncludes descrptons of the Mntab commands, and the Mntab output s heavly annotated. Comments n { } are used

### Week 4 Lecture: Paired-Sample Hypothesis Tests (Chapter 9)

Week 4 Lecture: Pare-Sample Hypothess Tests (Chapter 9) The two-sample proceures escrbe last week only apply when the two samples are nepenent. However, you may want to perform a hypothess tests to ata

### 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

### Lecture 14: Implementing CAPM

Lecture 14: Implementng CAPM Queston: So, how do I apply the CAPM? Current readng: Brealey and Myers, Chapter 9 Reader, Chapter 15 M. Spegel and R. Stanton, 2000 1 Key Results So Far All nvestors should

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

### Linear Regression Analysis for STARDEX

Lnear Regresson Analss for STARDEX Malcolm Halock, Clmatc Research Unt The followng document s an overvew of lnear regresson methods for reference b members of STARDEX. Whle t ams to cover the most common

### 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.

### 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

### 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

### 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

### ErrorPropagation.nb 1. Error Propagation

ErrorPropagaton.nb Error Propagaton Suppose that we make observatons of a quantty x that s subject to random fluctuatons or measurement errors. Our best estmate of the true value for ths quantty s then

### 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

### 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

### PRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIGIOUS AFFILIATION AND PARTICIPATION

PRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIIOUS AFFILIATION AND PARTICIPATION Danny Cohen-Zada Department of Economcs, Ben-uron Unversty, Beer-Sheva 84105, Israel Wllam Sander Department of Economcs, DePaul

### 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

### The Analysis of Outliers in Statistical Data

THALES Project No. xxxx The Analyss of Outlers n Statstcal Data Research Team Chrysses Caron, Assocate Professor (P.I.) Vaslk Karot, Doctoral canddate Polychrons Economou, Chrstna Perrakou, Postgraduate

### Time Series Analysis in Studies of AGN Variability. Bradley M. Peterson The Ohio State University

Tme Seres Analyss n Studes of AGN Varablty Bradley M. Peterson The Oho State Unversty 1 Lnear Correlaton Degree to whch two parameters are lnearly correlated can be expressed n terms of the lnear correlaton

### 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

### 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

### 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

### 4 Hypothesis testing in the multiple regression model

4 Hypothess testng n the multple regresson model Ezequel Urel Unversdad de Valenca Verson: 9-13 4.1 Hypothess testng: an overvew 1 4.1.1 Formulaton of the null hypothess and the alternatve hypothess 4.1.

### 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

### Criminal Justice System on Crime *

On the Impact of the NSW Crmnal Justce System on Crme * Dr Vasls Sarafds, Dscplne of Operatons Management and Econometrcs Unversty of Sydney * Ths presentaton s based on jont work wth Rchard Kelaher 1

### Testing GOF & Estimating Overdispersion

Testng GOF & Estmatng Overdsperson Your Most General Model Needs to Ft the Dataset It s mportant that the most general (complcated) model n your canddate model lst fts the data well. Ths model s a benchmark

### Understanding the Impact of Marketing Actions in Traditional Channels on the Internet: Evidence from a Large Scale Field Experiment

A research and educaton ntatve at the MT Sloan School of Management Understandng the mpact of Marketng Actons n Tradtonal Channels on the nternet: Evdence from a Large Scale Feld Experment Paper 216 Erc

### The Effects of Tax Rate Changes on Tax Bases and the Marginal Cost of Public Funds for Canadian Provincial Governments

The Effects of Tax Rate Changes on Tax Bases and the Margnal Cost of Publc Funds for Canadan Provncal Governments Bev Dahlby a and Ergete Ferede b a Department of Economcs, Unversty of Alberta, Edmonton,

### 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

### Although ordinary least-squares (OLS) regression

egresson through the Orgn Blackwell Oxford, TEST 0141-98X 003 5 31000 Orgnal Joseph Teachng G. UK Artcle Publshng Esenhauer through Statstcs the Ltd Trust Orgn 001 KEYWODS: Teachng; egresson; Analyss of

### 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.

### 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

### 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

### Evaluating the Effects of FUNDEF on Wages and Test Scores in Brazil *

Evaluatng the Effects of FUNDEF on Wages and Test Scores n Brazl * Naérco Menezes-Flho Elane Pazello Unversty of São Paulo Abstract In ths paper we nvestgate the effects of the 1998 reform n the fundng

### 1 Example 1: Axis-aligned rectangles

COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture # 6 Scrbe: Aaron Schld February 21, 2013 Last class, we dscussed an analogue for Occam s Razor for nfnte hypothess spaces that, n conjuncton

### The impact of hard discount control mechanism on the discount volatility of UK closed-end funds

Investment Management and Fnancal Innovatons, Volume 10, Issue 3, 2013 Ahmed F. Salhn (Egypt) The mpact of hard dscount control mechansm on the dscount volatlty of UK closed-end funds Abstract The mpact

### Lecture 9: Logit/Probit. Prof. Sharyn O Halloran Sustainable Development U9611 Econometrics II

Lecture 9: Logt/Probt Prof. Sharyn O Halloran Sustanable Development U96 Econometrcs II Revew of Lnear Estmaton So far, we know how to handle lnear estmaton models of the type: Y = β 0 + β *X + β 2 *X

### 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

### Passive Filters. References: Barbow (pp 265-275), Hayes & Horowitz (pp 32-60), Rizzoni (Chap. 6)

Passve Flters eferences: Barbow (pp 6575), Hayes & Horowtz (pp 360), zzon (Chap. 6) Frequencyselectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called

### The announcement effect on mean and variance for underwritten and non-underwritten SEOs

The announcement effect on mean and varance for underwrtten and non-underwrtten SEOs Bachelor Essay n Fnancal Economcs Department of Economcs Sprng 013 Marcus Wkner and Joel Anehem Ulvenäs Supervsor: Professor

### Wage inequality and returns to schooling in Europe: a semi-parametric approach using EU-SILC data

MPRA Munch Personal RePEc Archve Wage nequalty and returns to schoolng n Europe: a sem-parametrc approach usng EU-SILC data Marco Bagett and Sergo Sccchtano Unversty La Sapenza Rome, Mnstry of Economc

### BERNSTEIN POLYNOMIALS

On-Lne Geometrc Modelng Notes BERNSTEIN POLYNOMIALS Kenneth I. Joy Vsualzaton and Graphcs Research Group Department of Computer Scence Unversty of Calforna, Davs Overvew Polynomals are ncredbly useful

### ESTIMATING THE MARKET VALUE OF FRANKING CREDITS: EMPIRICAL EVIDENCE FROM AUSTRALIA

ESTIMATING THE MARKET VALUE OF FRANKING CREDITS: EMPIRICAL EVIDENCE FROM AUSTRALIA Duc Vo Beauden Gellard Stefan Mero Economc Regulaton Authorty 469 Wellngton Street, Perth, WA 6000, Australa Phone: (08)

### High Correlation between Net Promoter Score and the Development of Consumers' Willingness to Pay (Empirical Evidence from European Mobile Markets)

Hgh Correlaton between et Promoter Score and the Development of Consumers' Wllngness to Pay (Emprcal Evdence from European Moble Marets Ths paper shows that the correlaton between the et Promoter Score

### Gender differences in revealed risk taking: evidence from mutual fund investors

Economcs Letters 76 (2002) 151 158 www.elsever.com/ locate/ econbase Gender dfferences n revealed rsk takng: evdence from mutual fund nvestors a b c, * Peggy D. Dwyer, James H. Glkeson, John A. Lst a Unversty

### Lecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.

Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook

### 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

### The DAX and the Dollar: The Economic Exchange Rate Exposure of German Corporations

The DAX and the Dollar: The Economc Exchange Rate Exposure of German Corporatons Martn Glaum *, Marko Brunner **, Holger Hmmel *** Ths paper examnes the economc exposure of German corporatons to changes

### The Eastern Caribbean Currency Union: Would a Fiscal Insurance Mechanism Mitigate National Income Shocks?

WP/12/17 The Eastern Carbbean Currency Unon: Would a Fscal Insurance Mechansm Mtgate Natonal Income Shocks? Antono Lemus and Paul Cashn 2012 Internatonal Monetary Fund WP/12/17 IMF Workng Paper Mddle East

### ! # %& ( ) +,../ 0 1 2 3 4 0 4 # 5##&.6 7% 8 # 0 4 2 #...

! # %& ( ) +,../ 0 1 2 3 4 0 4 # 5##&.6 7% 8 # 0 4 2 #... 9 Sheffeld Economc Research Paper Seres SERP Number: 2011010 ISSN 1749-8368 Sarah Brown, Aurora Ortz-Núñez and Karl Taylor Educatonal loans and

### Forecasting and Stress Testing Credit Card Default using Dynamic Models

Forecastng and Stress Testng Credt Card Default usng Dynamc Models Tony Bellott and Jonathan Crook Credt Research Centre Unversty of Ednburgh Busness School Verson 4.5 Abstract Typcally models of credt

### The Mathematical Derivation of Least Squares

Pscholog 885 Prof. Federco The Mathematcal Dervaton of Least Squares Back when the powers that e forced ou to learn matr algera and calculus, I et ou all asked ourself the age-old queston: When the hell

### WORKING PAPER. C.D. Howe Institute. The Effects of Tax Rate Changes on Tax Bases and the Marginal Cost of Public Funds for Provincial Governments

MARCH 211 C.D. Howe Insttute WORKING PAPER FISCAL AND TAX COMPETITIVENESS The Effects of Tax Rate Changes on Tax Bases and the Margnal Cost of Publc Funds for Provncal Governments Bev Dahlby Ergete Ferede

### An Analysis of the relationship between WTI term structure and oil market fundamentals in 2002-2009

MPRA Munch Personal RePEc Archve An Analyss of the relatonshp between WTI term structure and ol market fundamentals n 00-009 Mleno Cavalcante Petrobras S.A., Unversdade de Fortaleza. August 00 Onlne at

### 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

### Control Charts for Means (Simulation)

Chapter 290 Control Charts for Means (Smulaton) Introducton Ths procedure allows you to study the run length dstrbuton of Shewhart (Xbar), Cusum, FIR Cusum, and EWMA process control charts for means usng

### 5 Multiple regression analysis with qualitative information

5 Multple regresson analyss wth qualtatve nformaton Ezequel Urel Unversty of Valenca Verson: 9-13 5.1 Introducton of qualtatve nformaton n econometrc models. 1 5. A sngle dummy ndependent varable 5.3 Multple

### Online Appendix Supplemental Material for Market Microstructure Invariance: Empirical Hypotheses

Onlne Appendx Supplemental Materal for Market Mcrostructure Invarance: Emprcal Hypotheses Albert S. Kyle Unversty of Maryland akyle@rhsmth.umd.edu Anna A. Obzhaeva New Economc School aobzhaeva@nes.ru Table

### 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

### 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

### 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

### Multiple/Post Hoc Group Comparisons in ANOVA

Multple/Pot Hoc Group Comparon n ANOVA Note: We may ut go over th quckly n cla. The key thng to undertand that, when tryng to dentfy where dfference are between group, there are dfferent way of adutng

### New evidence of the impact of dividend taxation and on the identity of the marginal investor

New evdence of the mpact of dvdend taxaton and on the dentty of the margnal nvestor LEONIE BELL AND TIM JENKINSON * * Economcs Department, Oxford Unversty and Saïd Busness School, Oxford Unversty and CEPR

### IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS

IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,

### Chapter 15: Debt and Taxes

Chapter 15: Debt and Taxes-1 Chapter 15: Debt and Taxes I. Basc Ideas 1. Corporate Taxes => nterest expense s tax deductble => as debt ncreases, corporate taxes fall => ncentve to fund the frm wth debt

### A random variable is a variable whose value depends on the outcome of a random event/experiment.

Random varables and Probablty dstrbutons A random varable s a varable whose value depends on the outcome of a random event/experment. For example, the score on the roll of a de, the heght of a randomly

### 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

### Management Quality and Equity Issue Characteristics: A Comparison of SEOs and IPOs

Management Qualty and Equty Issue Characterstcs: A Comparson of SEOs and IPOs Thomas J. Chemmanur * Imants Paegls ** and Karen Smonyan *** Current verson: November 2009 (Accepted, Fnancal Management, February

### 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..

### Survival analysis methods in Insurance Applications in car insurance contracts

Survval analyss methods n Insurance Applcatons n car nsurance contracts Abder OULIDI 1 Jean-Mare MARION 2 Hervé GANACHAUD 3 Abstract In ths wor, we are nterested n survval models and ther applcatons on

### 1 De nitions and Censoring

De ntons and Censorng. Survval Analyss We begn by consderng smple analyses but we wll lead up to and take a look at regresson on explanatory factors., as n lnear regresson part A. The mportant d erence

### EDUCATION AND RELIGION

DUCATION AND RLIGION by dward L. Glaeser Harvard Unversty and NR and ruce I. Sacerdote 1 Dartmouth College and NR February 14, 2002 Abstract In the Unted States, relgous attendance rses sharply wth educaton

### Evidence of the unspanned stochastic volatility in crude-oil market

The Academy of Economc Studes The Faculty of Fnance, Insurance, Bankng and Stock Echange Doctoral School of Fnance and Bankng (DOFIN) Dssertaton Paper Evdence of the unspanned stochastc volatlty n crude-ol

### 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

### 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

### Chapter XX More advanced approaches to the analysis of survey data. Gad Nathan Hebrew University Jerusalem, Israel. Abstract

Household Sample Surveys n Developng and Transton Countres Chapter More advanced approaches to the analyss of survey data Gad Nathan Hebrew Unversty Jerusalem, Israel Abstract In the present chapter, we

### 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