# Premaster Statistics Tutorial 4 Full solutions

Save this PDF as:

Size: px
Start display at page:

Download "Premaster Statistics Tutorial 4 Full solutions"

## Transcription

1 Premaster Statistics Tutorial 4 Full solutions Regression analysis Q1 (based on Doane & Seward, 4/E, 12.7) a. Interpret the slope of the fitted regression = 125, b. What is the prediction for if = 2,000? c. Would the intercept be meaningful if this regression applies to home sales in a certain subdivision, different form the one used to find the regression equation? A1 a. Increasing the size of a home by 1 square foot increases the price by \$150. b. = \$125,000 + (\$150 2,000) = \$425,000. c. The intercept might be interpreted as the value of the lot without a home. But the range of values for does not include zero so it would be dangerous to extrapolate for = 0. Extra Observe the somewhat confusing habit in economic literarure of writing regression equations in the form = 125, , where is a variable, not a unit. Q2 (based on Doane & Seward, 4/E, 12.13) The regression equation = was estimated from a sample of 34 cities in the eastern United States. Both variables are in thousands of dollars. is the median selling price of homes in the city, and is median family income for the city. a. Interpret the slope. b. Is the intercept meaningful? Explain. c. Make a prediction of when = 50 and also when = 100. d. Given: = What is the meaning of that? (Data are from Money Magazine 32, no. 1 [January 2004], pp ) A2 a. Increasing the median income by \$1,000 raises the median home price by \$2,610; b. If median income is zero, then the model suggests that median home price is \$51,300; c. \$181,800 and \$312,300; d. 34% of the variance of is explained by the model. Sol a. Increasing the median income by \$1,000 raises the median home price by \$2,610. b. If median income is zero, then the model suggests that median home price is \$51,300. While it does not seem logical that the median family income for any city is zero, it is unclear what the lower bound would be. c. prediction HomePrice = \$ (2.61 \$50) = \$181.8 (in \$1000) or \$181,800 prediction Homeprice = \$ (2.61 \$100) = \$312.3 (in \$1000) or \$312,300 d. 34% of the variance of is explained by the model. That is quite low. And it might be due to chance: perhaps a lucky sample. Fortunately, the latter can be judged by statistical significance. The model is significant if the slope is significantly different from zero: this seems to be the case looking at the -value (see later). Q3 (based on Doane & Seward, 4/E, 12.26) A regression was performed using data on 16 randomly selected charities in The variables were = expenses (millions of dollars) and = revenue (millions of dollars). a. Write the fitted regression equation. b. Construct a 95 percent confidence interval for the slope. c. Perform a right-tailed test for zero slope at =.05. State the hypotheses clearly. (Data are from Forbes 172, no. 12, p. 248, and PM_STAT 1 Tutorial 4

2 SUMMARY OUTPUT Regression Statistics Multiple R 0, R Square 0, Adjusted R Square 0, Standard Error 14, Observations 16 ANOVA df SS MS F Significance F Regression , , , ,07289E-08 Residual , ,13245 Total Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 7, ,0403 Revenue 0,9467 0,0936 A3 a. = ; b ; c. reject Sol a. Define : expenses (\$1,000,000); : revenue (\$1,000,000) a. = b. For a 95% confidence level use ;. =2.145 The 95% confidence interval is ±( ) or c. Use our 5-steps procedure: Model ( step 0 ): = + + where ~ (0, ) (i) : 0 versus : >0 ( =0.05) (ii) Sample statistic: ; reject for large values. (iii) Distribution test statistic under : = ~ Assumptions: see model (iv) Calculated test statistic: =. = Critical value: = ;. =1.761 (v) Because >, reject. There is evidence that the slope is positive; increased revenue is correlated with increased expenses. Q4 Use a linear regression model to explain the height (Dutch: lengte ) of female premaster students ( ) in terms of their shoe size (Dutch: schoenmaat ). Below you find some computer output, based on a random sample of these students. PM_STAT 2 Tutorial 4

3 Predicted values for: Lengtecm 95% Confidence Interval 95% Prediction Interval Schoenmaat Predicted lower upper lower upper A4 Sol a. Determine the theoretical and the estimated model belonging to the given output. b. It is claimed that the slope in this model is larger than 2. Test this hypothesis ( =1%). c. Is this a useful model in order to predict the height of female premaster students? (Perhaps you have seen a footprint in the snow; is it useful (using this model) to predict the height of the person concerned?) d. You see a footprint of size 38 in the snow and looking up you see in the distance a (female) premaster student just walking away. Give a relevant 95% interval for the height of this (female) premaster student. e. The next day you see another footprint of size 38. Give a relevant 95% interval for the average height of all (female) premaster students with shoe size 38. f. Calculate a 90% confidence interval for the constant in the regression model. a. Theoretical model: = + +, with ~ (0, ); Estimated model: = + = ; b. reject ; c. not very useful; d , ; e , ; f , a. Theoretical model: = + +, with ~ (0, ). = height in cm, = shoe size (may be stated for individual observations with or without the subscript ). Estimated model: = + = b. Use the 5 steps procedure! step 0 (model): see a. (i) : 2; : >2; =1% (ii) Sample statistic: ; reject for large values (iii) Distribution test statistic under : = ~ = ( =91) Assumptions: see model. We do not really need normality because is so large. (iv) Calculated test statistic: =. = PM_STAT 3 Tutorial 4

4 Critical value: = ;. = using Excel. With the table, you may take a conservative value ;. = value: (using Excel) (v) Decision: do reject, because -value smaller than 1% or because >. Conclude that the slope is larger than 2. c. It is a statistically significant model, so the question about practically relevant is meaningful. We have = which is quite low. It would have quite limited value in predicting the height of a thief if the police found a footprint in the snow. d. This is individual prediction : e. This is mean prediction : f. ± ;. =51.386±( ), so (Excel: ;. = ) Q5 A consumer products company wants to measure the effectiveness of different types of advertising media in the promotion of its products. Specifically, the company is interested in the effectiveness of radio advertising and newspaper advertising (including the cost of discount coupons). A sample of 22 cities with approximately equal populations is selected for study during a test period of one month. Each city is allocated a specific expenditure level both for radio advertising and for newspaper advertising. The sales of the product (in thousands of dollars) and also the levels of media expenditure (in thousands of dollars) during the test month are recorded, with the following results: SPSS results: PM_STAT 4 Tutorial 4

7 A2 Sol Q3 following three teams and state whether or not the leverage would be considered high. Given: =999,603 and =2004. a. The Golden State Warriors attempted 2,382 free throws. b. The New Jersey Nets attempted 2,125 free throws. c. The New York Knicks attempted 1,620 free throws. a. Yes; b. No; c. Yes a. h= +( ) = +( ) =0.18. The value of = =0.14, so this observation has a high leverage statistic. b. h= +( ) = +( ) =0.05. The value of = =0.14, so this observation does not have a high leverage statistic. c. h= +( ) = +( ) =0.18. See a. A consumer products company wants to measure the effectiveness of different types of advertising media in the promotion of its products. Specifically, the company is interested in the effectiveness of radio advertising and newspaper advertising (including the cost of discount coupons). A sample of 22 cities with approximately equal populations is selected for study during a test period of one month. Each city is allocated a specific expenditure level both for radio advertising and for newspaper advertising. The sales of the product (in thousands of dollars) and also the levels of media expenditure (in thousands of dollars) during the test month are recorded, with the following results: SPSS output is given below: PM_STAT 7 Tutorial 4

8 a. State the multiple regression equation (description of the the model including assumptions and the estimated model). b. Interpret the meaning of the slopes, and, in this problem. c. Interpret the meaning of the regression coefficient,. d. Which type of advertising is more effective? Explain. e. Determine whether there is a significant relationship between sales and the two independent variables (radio advertising and newspaper advertising) at the 0.05 level of significance. f. Interpret the meaning of the -value. g. Compute the coefficient of multiple determination,, and interpret its meaning. h. Find the adjusted and interpret its meaning. i. Perform a residual analysis on your results. PM_STAT 8 Tutorial 4

9 j. If appropriate, perform the Durbin-Watson test using =0.05. k. Are the regression assumptions valid for these data? l. Construct a 95% confidence interval estimate of the population slope between sales and radio advertising. m. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis of these results, indicate the independent variables to include in this model, using statistical significance as the only criterion. n. Test : 10 against : >10 (or is there evidence that the slope coefficient for Radio is more than 10?) o. Is there serious collinearity? p. Some might argue that there is a pattern in the residuals, suggesting a quadratic relation between sales and both advertising variables. We computed the variables and and included these variables in the regression model. State the model and the estimated model. Compare the two models. PM_STAT 9 Tutorial 4

12 variables ( ). Both VIFs are equal because we have only two explanatory variables in this model. p. Model: = , ~ (0, ), =Sales, =Radio Advertising, =Newspaper Advertising Note =0.907, considerably larger than =0.789 in smaller model. Not all variables are significant anymore, perhaps due to the substantial multicollinearity (VIFs are 13.4, 9.1, 13.4 and 9.45, all considerably larger than 5). You perhaps could eliminate the variables and (the linear, non-significant terms, and you end up with the model below, which is very good. q. The skewness and kurtosis statistics look fine, well between 1 and 1. There is no sign of heteroscedasticity. PM_STAT 12 Tutorial 4

### 1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years

### SELF-TEST: SIMPLE REGRESSION

ECO 22000 McRAE SELF-TEST: SIMPLE REGRESSION Note: Those questions indicated with an (N) are unlikely to appear in this form on an in-class examination, but you should be able to describe the procedures

### 12/31/2016. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2

PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 Understand when to use multiple Understand the multiple equation and what the coefficients represent Understand different methods

### , then the form of the model is given by: which comprises a deterministic component involving the three regression coefficients (

Multiple regression Introduction Multiple regression is a logical extension of the principles of simple linear regression to situations in which there are several predictor variables. For instance if we

### Multiple Regression in SPSS STAT 314

Multiple Regression in SPSS STAT 314 I. The accompanying data is on y = profit margin of savings and loan companies in a given year, x 1 = net revenues in that year, and x 2 = number of savings and loan

### Using SPSS for Multiple Regression. UDP 520 Lab 7 Lin Lin December 4 th, 2007

Using SPSS for Multiple Regression UDP 520 Lab 7 Lin Lin December 4 th, 2007 Step 1 Define Research Question What factors are associated with BMI? Predict BMI. Step 2 Conceptualizing Problem (Theory) Individual

### Module 5: Multiple Regression Analysis

Using Statistical Data Using to Make Statistical Decisions: Data Multiple to Make Regression Decisions Analysis Page 1 Module 5: Multiple Regression Analysis Tom Ilvento, University of Delaware, College

### e = random error, assumed to be normally distributed with mean 0 and standard deviation σ

1 Linear Regression 1.1 Simple Linear Regression Model The linear regression model is applied if we want to model a numeric response variable and its dependency on at least one numeric factor variable.

### " Y. Notation and Equations for Regression Lecture 11/4. Notation:

Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through

### , has mean A) 0.3. B) the smaller of 0.8 and 0.5. C) 0.15. D) which cannot be determined without knowing the sample results.

BA 275 Review Problems - Week 9 (11/20/06-11/24/06) CD Lessons: 69, 70, 16-20 Textbook: pp. 520-528, 111-124, 133-141 An SRS of size 100 is taken from a population having proportion 0.8 of successes. An

### Multiple Regression Analysis in Minitab 1

Multiple Regression Analysis in Minitab 1 Suppose we are interested in how the exercise and body mass index affect the blood pressure. A random sample of 10 males 50 years of age is selected and their

### Simple Linear Regression

Inference for Regression Simple Linear Regression IPS Chapter 10.1 2009 W.H. Freeman and Company Objectives (IPS Chapter 10.1) Simple linear regression Statistical model for linear regression Estimating

### Final Exam Practice Problem Answers

Final Exam Practice Problem Answers The following data set consists of data gathered from 77 popular breakfast cereals. The variables in the data set are as follows: Brand: The brand name of the cereal

### A. Karpinski

Chapter 3 Multiple Linear Regression Page 1. Overview of multiple regression 3-2 2. Considering relationships among variables 3-3 3. Extending the simple regression model to multiple predictors 3-4 4.

### Week TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500 6 8480

1) The S & P/TSX Composite Index is based on common stock prices of a group of Canadian stocks. The weekly close level of the TSX for 6 weeks are shown: Week TSX Index 1 8480 2 8470 3 8475 4 8510 5 8500

### 12/31/2016. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2

PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 Understand linear regression with a single predictor Understand how we assess the fit of a regression model Total Sum of Squares

### Interpreting Multiple Regression

Fall Semester, 2001 Statistics 621 Lecture 5 Robert Stine 1 Preliminaries Interpreting Multiple Regression Project and assignments Hope to have some further information on project soon. Due date for Assignment

### Supplement 13A: Partial F Test

Supplement 13A: Partial F Test Purpose of the Partial F Test For a given regression model, could some of the predictors be eliminated without sacrificing too much in the way of fit? Conversely, would it

### Regression step-by-step using Microsoft Excel

Step 1: Regression step-by-step using Microsoft Excel Notes prepared by Pamela Peterson Drake, James Madison University Type the data into the spreadsheet The example used throughout this How to is a regression

### Residuals. Residuals = ª Department of ISM, University of Alabama, ST 260, M23 Residuals & Minitab. ^ e i = y i - y i

A continuation of regression analysis Lesson Objectives Continue to build on regression analysis. Learn how residual plots help identify problems with the analysis. M23-1 M23-2 Example 1: continued Case

### Regression. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Class: Date: Regression Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Given the least squares regression line y8 = 5 2x: a. the relationship between

### 1. The parameters to be estimated in the simple linear regression model Y=α+βx+ε ε~n(0,σ) are: a) α, β, σ b) α, β, ε c) a, b, s d) ε, 0, σ

STA 3024 Practice Problems Exam 2 NOTE: These are just Practice Problems. This is NOT meant to look just like the test, and it is NOT the only thing that you should study. Make sure you know all the material

### Simple Linear Regression in SPSS STAT 314

Simple Linear Regression in SPSS STAT 314 1. Ten Corvettes between 1 and 6 years old were randomly selected from last year s sales records in Virginia Beach, Virginia. The following data were obtained,

### ST 311 Evening Problem Session Solutions Week 11

1. p. 175, Question 32 (Modules 10.1-10.4) [Learning Objectives J1, J3, J9, J11-14, J17] Since 1980, average mortgage rates have fluctuated from a low of under 6% to a high of over 14%. Is there a relationship

### CHAPTER 2 AND 10: Least Squares Regression

CHAPTER 2 AND 0: Least Squares Regression In chapter 2 and 0 we will be looking at the relationship between two quantitative variables measured on the same individual. General Procedure:. Make a scatterplot

### Simple linear regression

Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between

### E205 Final: Version B

Name: Class: Date: E205 Final: Version B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of a local nightclub has recently surveyed a random

### Name: Student ID#: Serial #:

STAT 22 Business Statistics II- Term3 KING FAHD UNIVERSITY OF PETROLEUM & MINERALS Department Of Mathematics & Statistics DHAHRAN, SAUDI ARABIA STAT 22: BUSINESS STATISTICS II Third Exam July, 202 9:20

### CHAPTER 9: SERIAL CORRELATION

Serial correlation (or autocorrelation) is the violation of Assumption 4 (observations of the error term are uncorrelated with each other). Pure Serial Correlation This type of correlation tends to be

### Homework 8 Solutions

Math 17, Section 2 Spring 2011 Homework 8 Solutions Assignment Chapter 7: 7.36, 7.40 Chapter 8: 8.14, 8.16, 8.28, 8.36 (a-d), 8.38, 8.62 Chapter 9: 9.4, 9.14 Chapter 7 7.36] a) A scatterplot is given below.

### 0.1 Multiple Regression Models

0.1 Multiple Regression Models We will introduce the multiple Regression model as a mean of relating one numerical response variable y to two or more independent (or predictor variables. We will see different

### Simple Linear Regression Chapter 11

Simple Linear Regression Chapter 11 Rationale Frequently decision-making situations require modeling of relationships among business variables. For instance, the amount of sale of a product may be related

### Regression Analysis: A Complete Example

Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty

### Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1. 1. Introduction p. 2. 2. Statistical Methods Used p. 5. 3. 10 and under Males p.

Sydney Roberts Predicting Age Group Swimmers 50 Freestyle Time 1 Table of Contents 1. Introduction p. 2 2. Statistical Methods Used p. 5 3. 10 and under Males p. 8 4. 11 and up Males p. 10 5. 10 and under

### Interaction between quantitative predictors

Interaction between quantitative predictors In a first-order model like the ones we have discussed, the association between E(y) and a predictor x j does not depend on the value of the other predictors

### STAT 350 Practice Final Exam Solution (Spring 2015)

PART 1: Multiple Choice Questions: 1) A study was conducted to compare five different training programs for improving endurance. Forty subjects were randomly divided into five groups of eight subjects

### Math 62 Statistics Sample Exam Questions

Math 62 Statistics Sample Exam Questions 1. (10) Explain the difference between the distribution of a population and the sampling distribution of a statistic, such as the mean, of a sample randomly selected

### Data and Regression Analysis. Lecturer: Prof. Duane S. Boning. Rev 10

Data and Regression Analysis Lecturer: Prof. Duane S. Boning Rev 10 1 Agenda 1. Comparison of Treatments (One Variable) Analysis of Variance (ANOVA) 2. Multivariate Analysis of Variance Model forms 3.

### The general form of the PROC GLM statement is

Linear Regression Analysis using PROC GLM Regression analysis is a statistical method of obtaining an equation that represents a linear relationship between two variables (simple linear regression), or

### Regression in SPSS. Workshop offered by the Mississippi Center for Supercomputing Research and the UM Office of Information Technology

Regression in SPSS Workshop offered by the Mississippi Center for Supercomputing Research and the UM Office of Information Technology John P. Bentley Department of Pharmacy Administration University of

### Statistics II Final Exam - January Use the University stationery to give your answers to the following questions.

Statistics II Final Exam - January 2012 Use the University stationery to give your answers to the following questions. Do not forget to write down your name and class group in each page. Indicate clearly

### Chapter 13 Introduction to Linear Regression and Correlation Analysis

Chapter 3 Student Lecture Notes 3- Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing

### Multiple Linear Regression

Multiple Linear Regression A regression with two or more explanatory variables is called a multiple regression. Rather than modeling the mean response as a straight line, as in simple regression, it is

### Chapter 10. Key Ideas Correlation, Correlation Coefficient (r),

Chapter 0 Key Ideas Correlation, Correlation Coefficient (r), Section 0-: Overview We have already explored the basics of describing single variable data sets. However, when two quantitative variables

### DEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9

DEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9 Analysis of covariance and multiple regression So far in this course,

### Statistics 100 Sample Final Questions (Note: These are mostly multiple choice, for extra practice. Your Final Exam will NOT have any multiple choice!

Statistics 100 Sample Final Questions (Note: These are mostly multiple choice, for extra practice. Your Final Exam will NOT have any multiple choice!) Part A - Multiple Choice Indicate the best choice

### 4. Multiple Regression in Practice

30 Multiple Regression in Practice 4. Multiple Regression in Practice The preceding chapters have helped define the broad principles on which regression analysis is based. What features one should look

### Chapter Seven. Multiple regression An introduction to multiple regression Performing a multiple regression on SPSS

Chapter Seven Multiple regression An introduction to multiple regression Performing a multiple regression on SPSS Section : An introduction to multiple regression WHAT IS MULTIPLE REGRESSION? Multiple

### A Primer on Forecasting Business Performance

A Primer on Forecasting Business Performance There are two common approaches to forecasting: qualitative and quantitative. Qualitative forecasting methods are important when historical data is not available.

### where b is the slope of the line and a is the intercept i.e. where the line cuts the y axis.

Least Squares Introduction We have mentioned that one should not always conclude that because two variables are correlated that one variable is causing the other to behave a certain way. However, sometimes

### UCLA STAT 13 Statistical Methods - Final Exam Review Solutions Chapter 7 Sampling Distributions of Estimates

UCLA STAT 13 Statistical Methods - Final Exam Review Solutions Chapter 7 Sampling Distributions of Estimates 1. (a) (i) µ µ (ii) σ σ n is exactly Normally distributed. (c) (i) is approximately Normally

### Regression III: Dummy Variable Regression

Regression III: Dummy Variable Regression Tom Ilvento FREC 408 Linear Regression Assumptions about the error term Mean of Probability Distribution of the Error term is zero Probability Distribution of

### Answers Investigation 4

Applications 1. a. Median height is 15.7 cm. Order the 1 heights from shortest to tallest. Since 1 is even, average the two middle numbers, 15.6 cm and 15.8 cm. b. Median stride distance is 124.8 cm. Order

### Chapter 11: Two Variable Regression Analysis

Department of Mathematics Izmir University of Economics Week 14-15 2014-2015 In this chapter, we will focus on linear models and extend our analysis to relationships between variables, the definitions

### AP * Statistics Review. Linear Regression

AP * Statistics Review Linear Regression Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production

### Chapter 4 and 5 solutions

Chapter 4 and 5 solutions 4.4. Three different washing solutions are being compared to study their effectiveness in retarding bacteria growth in five gallon milk containers. The analysis is done in a laboratory,

### Simple Linear Regression Inference

Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation

### Collinearity of independent variables. Collinearity is a condition in which some of the independent variables are highly correlated.

Collinearity of independent variables Collinearity is a condition in which some of the independent variables are highly correlated. Why is this a problem? Collinearity tends to inflate the variance of

### Regression analysis in practice with GRETL

Regression analysis in practice with GRETL Prerequisites You will need the GNU econometrics software GRETL installed on your computer (http://gretl.sourceforge.net/), together with the sample files that

### MS&E 226: Small Data. Lecture 17: Additional topics in inference (v1) Ramesh Johari

MS&E 226: Small Data Lecture 17: Additional topics in inference (v1) Ramesh Johari ramesh.johari@stanford.edu 1 / 34 Warnings 2 / 34 Modeling assumptions: Regression Remember that most of the inference

### ACTM State Exam-Statistics

ACTM State Exam-Statistics For the 25 multiple-choice questions, make your answer choice and record it on the answer sheet provided. Once you have completed that section of the test, proceed to the tie-breaker

### Univariate Regression

Univariate Regression Correlation and Regression The regression line summarizes the linear relationship between 2 variables Correlation coefficient, r, measures strength of relationship: the closer r is

### 12.13 RESIDUAL ANALYSIS IN MULTIPLE REGRESSION (OPTIONAL)

12.13 Analysis in Multiple Regression (Optional) 1 Although Excel and MegaStat are emphasized in Business Statistics in Practice, Second Canadian Edition, some examples in the additional material on Connect

### Statistics for Management II-STAT 362-Final Review

Statistics for Management II-STAT 362-Final Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. The ability of an interval estimate to

### INCOME AND HAPPINESS 1. Income and Happiness

INCOME AND HAPPINESS 1 Income and Happiness Abstract Are wealthier people happier? The research study employed simple linear regression analysis to confirm the positive relationship between income and

### Course Objective This course is designed to give you a basic understanding of how to run regressions in SPSS.

SPSS Regressions Social Science Research Lab American University, Washington, D.C. Web. www.american.edu/provost/ctrl/pclabs.cfm Tel. x3862 Email. SSRL@American.edu Course Objective This course is designed

### Using R for Linear Regression

Using R for Linear Regression In the following handout words and symbols in bold are R functions and words and symbols in italics are entries supplied by the user; underlined words and symbols are optional

### Simple Methods and Procedures Used in Forecasting

Simple Methods and Procedures Used in Forecasting The project prepared by : Sven Gingelmaier Michael Richter Under direction of the Maria Jadamus-Hacura What Is Forecasting? Prediction of future events

### Lecture 18 Linear Regression

Lecture 18 Statistics Unit Andrew Nunekpeku / Charles Jackson Fall 2011 Outline 1 1 Situation - used to model quantitative dependent variable using linear function of quantitative predictor(s). Situation

### SIMPLE REGRESSION ANALYSIS

SIMPLE REGRESSION ANALYSIS Introduction. Regression analysis is used when two or more variables are thought to be systematically connected by a linear relationship. In simple regression, we have only two

### 5. Multiple regression

5. Multiple regression QBUS6840 Predictive Analytics https://www.otexts.org/fpp/5 QBUS6840 Predictive Analytics 5. Multiple regression 2/39 Outline Introduction to multiple linear regression Some useful

### Inferential Statistics

Inferential Statistics Sampling and the normal distribution Z-scores Confidence levels and intervals Hypothesis testing Commonly used statistical methods Inferential Statistics Descriptive statistics are

### DO NOT TURN OVER UNTIL TOLD TO BEGIN

THIS PAPER IS NOT TO BE REMOVED FROM THE EXAMINATION HALLS University of London BSc Examination 2012 BA1040 (BBA0040) +Enc Business Administration Business Statistics Date tba: Time tba DO NOT TURN OVER

### EDUCATION AND VOCABULARY MULTIPLE REGRESSION IN ACTION

EDUCATION AND VOCABULARY MULTIPLE REGRESSION IN ACTION EDUCATION AND VOCABULARY 5-10 hours of input weekly is enough to pick up a new language (Schiff & Myers, 1988). Dutch children spend 5.5 hours/day

### Regression Analysis (Spring, 2000)

Regression Analysis (Spring, 2000) By Wonjae Purposes: a. Explaining the relationship between Y and X variables with a model (Explain a variable Y in terms of Xs) b. Estimating and testing the intensity

### 1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number

1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x - x) B. x 3 x C. 3x - x D. x - 3x 2) Write the following as an algebraic expression

### Elementary Statistics Sample Exam #3

Elementary Statistics Sample Exam #3 Instructions. No books or telephones. Only the supplied calculators are allowed. The exam is worth 100 points. 1. A chi square goodness of fit test is considered to

### 12-1 Multiple Linear Regression Models

12-1.1 Introduction Many applications of regression analysis involve situations in which there are more than one regressor variable. A regression model that contains more than one regressor variable is

### UNDERSTANDING MULTIPLE REGRESSION

UNDERSTANDING Multiple regression analysis (MRA) is any of several related statistical methods for evaluating the effects of more than one independent (or predictor) variable on a dependent (or outcome)

### X X X a) perfect linear correlation b) no correlation c) positive correlation (r = 1) (r = 0) (0 < r < 1)

CORRELATION AND REGRESSION / 47 CHAPTER EIGHT CORRELATION AND REGRESSION Correlation and regression are statistical methods that are commonly used in the medical literature to compare two or more variables.

### Correlation and Regression Analysis: SPSS

Correlation and Regression Analysis: SPSS Bivariate Analysis: Cyberloafing Predicted from Personality and Age These days many employees, during work hours, spend time on the Internet doing personal things,

### The scatterplot indicates a positive linear relationship between waist size and body fat percentage:

STAT E-150 Statistical Methods Multiple Regression Three percent of a man's body is essential fat, which is necessary for a healthy body. However, too much body fat can be dangerous. For men between the

### Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression

Unit 31 A Hypothesis Test about Correlation and Slope in a Simple Linear Regression Objectives: To perform a hypothesis test concerning the slope of a least squares line To recognize that testing for a

### HYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION

HYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION HOD 2990 10 November 2010 Lecture Background This is a lightning speed summary of introductory statistical methods for senior undergraduate

### Good luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:

Glo bal Leadership M BA BUSINESS STATISTICS FINAL EXAM Name: INSTRUCTIONS 1. Do not open this exam until instructed to do so. 2. Be sure to fill in your name before starting the exam. 3. You have two hours

### Factors affecting online sales

Factors affecting online sales Table of contents Summary... 1 Research questions... 1 The dataset... 2 Descriptive statistics: The exploratory stage... 3 Confidence intervals... 4 Hypothesis tests... 4

### Regression in ANOVA. James H. Steiger. Department of Psychology and Human Development Vanderbilt University

Regression in ANOVA James H. Steiger Department of Psychology and Human Development Vanderbilt University James H. Steiger (Vanderbilt University) 1 / 30 Regression in ANOVA 1 Introduction 2 Basic Linear

### The importance of graphing the data: Anscombe s regression examples

The importance of graphing the data: Anscombe s regression examples Bruce Weaver Northern Health Research Conference Nipissing University, North Bay May 30-31, 2008 B. Weaver, NHRC 2008 1 The Objective

### 1. ε is normally distributed with a mean of 0 2. the variance, σ 2, is constant 3. All pairs of error terms are uncorrelated

STAT E-150 Statistical Methods Residual Analysis; Data Transformations The validity of the inference methods (hypothesis testing, confidence intervals, and prediction intervals) depends on the error term,

### ABSORBENCY OF PAPER TOWELS

ABSORBENCY OF PAPER TOWELS 15. Brief Version of the Case Study 15.1 Problem Formulation 15.2 Selection of Factors 15.3 Obtaining Random Samples of Paper Towels 15.4 How will the Absorbency be measured?

### Practice 3 SPSS. Partially based on Notes from the University of Reading:

Practice 3 SPSS Partially based on Notes from the University of Reading: http://www.reading.ac.uk Simple Linear Regression A simple linear regression model is fitted when you want to investigate whether

### ECO220Y1Y Duration - 3 hours Examination Aids: Calculator

Page 1 of 16 UNIVERSITY OF TORONTO Faculty of Arts and Science APRIL 2011 EXAMINATIONS ECO220Y1Y Duration - 3 hours Examination Aids: Calculator Last Name: First Name: Student #: ENTER YOUR NAME AND STUDENT

### Statistics & Regression: Easier than SAS

ST003 Statistics & Regression: Easier than SAS Vincent Maffei, Anthem Blue Cross and Blue Shield, North Haven, CT Michael Davis, Bassett Consulting Services, Inc., North Haven, CT ABSTRACT In this paper

### Simple Regression Theory II 2010 Samuel L. Baker

SIMPLE REGRESSION THEORY II 1 Simple Regression Theory II 2010 Samuel L. Baker Assessing how good the regression equation is likely to be Assignment 1A gets into drawing inferences about how close the

### (d) True or false? When the number of treatments a=9, the number of blocks b=10, and the other parameters r =10 and k=9, it is a BIBD design.

PhD Qualifying exam Methodology Jan 2014 Solutions 1. True or false question - only circle "true " or "false" (a) True or false? F-statistic can be used for checking the equality of two population variances

### AP Statistics 2011 Scoring Guidelines

AP Statistics 2011 Scoring Guidelines The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in

### 13: Additional ANOVA Topics. Post hoc Comparisons

13: Additional ANOVA Topics Post hoc Comparisons ANOVA Assumptions Assessing Group Variances When Distributional Assumptions are Severely Violated Kruskal-Wallis Test Post hoc Comparisons In the prior