SELF-TEST: SIMPLE REGRESSION

Size: px
Start display at page:

Download "SELF-TEST: SIMPLE REGRESSION"

Transcription

1 ECO 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 used to get an answer and be able to interpret the answers. 1. What are the assumptions involved in simple linear regression? 2. What line does the method of least squares actually find? 3. What information might we get from a scatter plot of y against x? 4. Describe how to use Excel to create a scatter diagram. 5. Describe how to use Excel to calculate a regression line. 6. The regression equation of starting salary on GPA for a sample of recent graduates of RCCC is salary = * GPA. Randy just graduated with a GPA of 2.6; what starting salary would the regression equation predict for him? 7. For a cross-section of companies, a marketing analyst regressed sales on advertising expenditures, resulting in the following Excel output: SUMMARY OUTPUT Regression Statistics Multiple R 0.9 R Square 0.81 Adjusted R Square 0.80 Standard Error 100 Observations 45 ANOVA df SS MS F Significance F Regression Residual Total Coefficients Standard Error t Stat P-value Intercept E -06 Advertising a) Write out the regression equation, showing sales as a function of advertising expenditures. b) Give a point prediction for sales for a company whose advertising expenditures equal $7,000. c) Give a 95% confidence interval for the average sales level for a company spending $2,000 on advertising. Assume the mean advertising expenditure = $4,000. d) Give a 95% confidence interval for a specific value of y for a company spending $2,000 on advertising with x = $4,000. e) Explain why the intervals in c. and d. are not the same.

2 Stats II, Regression, page 2 8. What shape do confidence intervals for y values at given x values have? What does this imply about predicted values far from the mean value of x? 9. Say whether the following statement is true or false and explain your answer: If a regression equation has a high r 2, statisticians see no problem with making extrapolations well beyond the observed range of x and y values. 10. What does the coefficient of correlation measure? How is it related to a regression line? 11. Find the coefficient of correlation between x and y: x y To test whether a correlation between x and y is significant, we should test the null hypothesis with alternative hypothesis ; the test statistic is a with d.f. 13. Describe three different ways to find the correlation coefficient using Excel. 14. Comment on the following: Among the industrial nations, there is a negative correlation between average medical expenditures and life expectancy; this proves that medical care causes people to live shorter lives. 15. r 2 is called the ; it is interpreted as giving the in y which is by variation in x. 16. Generally speaking, what does r-squared tell us about a regression equation? 17. ART's engineers regressed production costs on output and found the regression equation: cost = * output. In the regression results, s y.x = 1800 and s b = 0.6; the regression was based on a sample of 40 days output and costs. Give a 98% confidence interval for β Using the data of the preceding question, formulate and conduct an appropriate test for the significance of the regression coefficient. 19. The following Excel output was generated by regressing percentage rates of inflation on percentage rates of increase in the money supply: SUMMARY OUTPUT Regression Statistics Multiple R 0.7 R Square 0.49 Adjusted R Square 0.46 Standard Error 1 Observations 62 ANOVA df SS MS F Significance F Regression Residual Total Coefficients Standard Error t Stat P-value Intercept X Variable

3 Stats II, Regression, page 3 a) What is the simple correlation coefficient between prices and money? b) In a t test of H 0 : ρ = 0, what is the calculated value of t? c) In a t test of H 0 : β 1 = 0, what is the calculated value of t? At α = 0.01, what should we do with the null hypothesis? d) In an ANOVA test of this regression equation, what is the critical value of F for α = 0.025? (Use FINV to find the critical value.) e) What is the calculated value of F in an ANOVA test? Should we accept or reject the null hypothesis of no linear relation between money and inflation? 20. In a regression ANOVA table, how are the following terms defined? Regression sum of squares; residual sum of squares; total sum of squares. What does each represent? 21. In a regression of managers' salaries on firm size, researchers estimated the equation salary = * sales, where sales were measured in millions of dollars. Observation number 42 works at a firm with annual sales of 8 million dollars, and he makes $53,000 a year. What is the residual for observation 42? 22. How could a graph of the residuals from a regression equation help in determining whether ε is normally distributed? 23. How might you use a histogram of the residuals from a regression equation? A CPA has gathered the following data for a sample of twelve corporations: Observation # Long-Term Assets Long-Term Debt (N) Suppose that we wish to know whether acquiring long-term assets is done primarily by acquiring long-term debt. a) Designating assets as y and debt as x, use your spreadsheet to find the regression equation of assets on debt; state this equation in algebraic notation. b) What does the x coefficient tell you about the relation between assets and debt? c) What is the correlation between assets and debt? Use a t test to find whether we can consider this significant. d) Use an appropriate t test to test whether the slope of the regression line can be considered different from 0; set your significance level at 5%. e) At 1% significance, use ANOVA to test H 0 : there is no significant linear relation between assets and debt. f) Make a point prediction of assets for a corporation which has 25 million dollars of long term debt. g) Give a 95% prediction interval for the assets of a corporation with 25 million dollars of debt. h) Give a 95% confidence interval for the average of all corporations that have 25 million dollars of debt. i) Compute and interpret the residual for observation #9. j) Give a 90% confidence interval for the value of β. 25. What would you look for in a residual plot that would be a clue to the presence of each of the following conditions? a) non-normality of the residuals b) heteroscedasticity c) non-linearity of the relation between x and y

4 Stats II, Regression, page 4 d) autocorrelation 26. In the ANOVA table, the regression sum of squares is defined as SSR = Σ( ŷ y) 2 ; explain why that represents the variation in y which is explained by variation in x. 27. The residual sum of squares, or error sum of squares, is defined as SSE = Σ(y ŷ ) 2 ; explain why this term represents the variation in y which is NOT explained by variation in x r 2 2 ( y yˆ) is defined as r = 1. Explain how this definition leads to the interpretation usually given of 2 ( y y) r What condition is indicated by each of the following residual plots? A. B. C. D.

5 SELF TEST: MULTIPLE REGRESSION 1. Marketing researchers at ART, Inc., have regressed their sales on Gross Domestic Product and their own advertising expenditures with the following result: Sales = 400, ,000 GDP A a) What could we predict ART's sales to be if GDP = 6.5 trillion and advertising expenditures = 20 million? b) If GDP rose to 6.8 trillion, by how much would we expect sales to change? c) ART wishes to increase its unit sales by 21,000; by how much will they need to increase their advertising budget? 2. Why is the use of adjusted R 2 preferred to the use of plain R 2 in multiple regression? What is it we're adjusting for? 3. When is it important to use adjusted R 2? When is it not important? 4. R 2 can be thought of as the proportion of in y which is by in the x's. State the definition of R 2 and explain why that definition leads to this interpretation. 5. In performing a t test on a coefficient from multiple regression, what null and alternative hypotheses are we testing? The following Excel output is for questions 6 to 12: SUMMARY OUTPUT Regression Statistics Multiple R R Square 0.6 Adjusted R Square 0.52 Standard Error Observations 16 ANOVA df SS MS F Significance F Regression Residual Total Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept X Variable X Variable X Variable What is the regression equation? 7. How many degrees of freedom are there in the t Stats? 8. According to the t ratios, which of the regression coefficients would be significant at the 5% level? Which at the 10% level? 9. What is the F ratio? What null hypothesis would be tested with this value? At α = 0.01, can we reject the null hypothesis? Can we reject at α = 0.05?

6 Stats II, Regression, page Suppose x 1 = 6, x 2 = 0, and x 3 = 2; what is ŷ? 11. Observation #8 had x 1 = 8, x 2 = 2, and x 3 = 4; for that observation, y = 108. What is the residual for this observation? 12. Find a 95% confidence interval for ß 1, the coefficient on variable X What is a dummy variable? 14. A marketing researcher has created a dummy variable for "Owns own home." John lives in an apartment; what value will this dummy have for him? Mary is paying off the mortgage on her condominium; what value will this dummy have for her? 15. In a regression of monthly entertainment expenditures on several things, the dummy of q. 14 had the value $21. Explain the meaning of this number. 16. What is multicollinearity? How can we detect it? 17. What are the effects in regression analyses of multicollinearity? 18. Suppose the relation between x and y is not linear: how could you detect this nonlinearity? 19. (N) A researcher wishes to be able to predict the number of movies attended in a year's time on the basis of four explanatory variables: age, education, income, and sex. A sample of ten people yields the following data: No. of Movies Age Education Income Sex Dummy (Male = 1) a) Using your spreadsheet, find the regression equation and write it out in algebraic notation. b) Explain what each of the regression X coefficients means. c) Using an appropriate t test, at 5% significance test H 0 : β i = 0 for i = 1 to 4. d) What is the adjusted R 2? How would we interpret that number? Why is there so much difference in this case between R 2 and adjusted R 2? e) Using ANOVA state and test the appropriate null hypothesis to test whether there is a significant linear relation among these variables. f) Predict how many movies will be seen by a 37 year-old female high-school graduate whose family income is $43,000 a year. g) State the 95% confidence interval for each X coefficient. h) Calculate a 98% confidence interval for β 2 i) Find the residual for the first observation (25 movies, age 18 and so on). j) In examining the residual plots generated by the Excel, do you detect any problems or violations of the regression assumptions? k) Does there appear to be significant multicollinearity among the X variables? How do you know that?

7 Stats II, Regression, page 7 Selected Answers: Simple Regression:: 6. 17, a a. sales = adv b b c. 3 reject c ± d d ± e. 9, reject $7, ± a. nothing in particular 18. H 0 : β = 0; t = 3.33; p-value b. autocorrelation = c. non-linearity d. heteroscedasticity 24. a. y-hat = X b. for each one-dollar increase in debt, assets increase 94 cents c. 0.71; since p value = , we can reject at 1% significance the hypothesis that population correlation = 0. d. for α = 0.05, critical t = < calculated 3.219, so reject the null that β = 0. (Alternatively, since p < 0.05, reject.) e. Critical F = < , so reject null and conclude there is a significant relation. (Alternatively, in ANOVA table p < 0.01, so reject null.) f g ± h ± 6.72 i j β Multiple Regression: ,000; +1,200; $3 million 6. ŷ = 20+10x 1 +5x 2 +3x β 2 and β 3 at 5%; all at 10% 9. F=6; with 3,12 d.f. F.01 =5.95, so reject H O at 1% and 5% ± ; homeowners typically spend $21 a month less on entertainment 19. a. movies = x age 1.30 x educ x inc 2.28 x male b. movies attended falls by.93 for each year age increases, falls by 1.3 for each extra year of education, and increases by about 0.1 for each extra thousand dollars of family income; other things being equal males attend 2.28 fewer movies a year than females c. reject H 0 for β 1 since p = 0.024; fail to reject for i = 2-4 since all p values > 0.05 d. Adj. R 2 = 0.77; these four variables explain 77% of the observed variation in movie attendance. e. H 0 : β 1 = β 2 = β 3 = β 4 = 0 vs. H 1 : at least one equality not true F = with p value = 0.018, so at 2% significance we reject null and conclude there is a significant linear relation with at least one of the x variables. f. y-hat = g. see output Lower 95% Upper 95% h ± 4.86 i. since y-hat = 26.72, residual = 1.72 j. no k. yes; education is highly correlated with income and sex with age; use Data Analysis Correlation tool

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

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

More information

SIMPLE REGRESSION ANALYSIS

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

More information

Chapter 9. Section Correlation

Chapter 9. Section Correlation Chapter 9 Section 9.1 - Correlation Objectives: Introduce linear correlation, independent and dependent variables, and the types of correlation Find a correlation coefficient Test a population correlation

More information

Regression step-by-step using Microsoft Excel

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

More information

Premaster Statistics Tutorial 4 Full solutions

Premaster Statistics Tutorial 4 Full solutions 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 = 125,000 + 150. b. What is the prediction for

More information

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

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

More information

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

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.

More information

Regression Analysis: A Complete Example

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

More information

Regression, least squares

Regression, least squares Regression, least squares Joe Felsenstein Department of Genome Sciences and Department of Biology Regression, least squares p.1/24 Fitting a straight line X Two distinct cases: The X values are chosen

More information

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 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

More information

Chapter 7: Simple linear regression Learning Objectives

Chapter 7: Simple linear regression Learning Objectives Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) -

More information

REGRESSION LINES IN STATA

REGRESSION LINES IN STATA REGRESSION LINES IN STATA THOMAS ELLIOTT 1. Introduction to Regression Regression analysis is about eploring linear relationships between a dependent variable and one or more independent variables. Regression

More information

2013 MBA Jump Start Program. Statistics Module Part 3

2013 MBA Jump Start Program. Statistics Module Part 3 2013 MBA Jump Start Program Module 1: Statistics Thomas Gilbert Part 3 Statistics Module Part 3 Hypothesis Testing (Inference) Regressions 2 1 Making an Investment Decision A researcher in your firm just

More information

Module 5: Multiple Regression Analysis

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

More information

Statistics 112 Regression Cheatsheet Section 1B - Ryan Rosario

Statistics 112 Regression Cheatsheet Section 1B - Ryan Rosario Statistics 112 Regression Cheatsheet Section 1B - Ryan Rosario I have found that the best way to practice regression is by brute force That is, given nothing but a dataset and your mind, compute everything

More information

CHAPTER 13 SIMPLE LINEAR REGRESSION. Opening Example. Simple Regression. Linear Regression

CHAPTER 13 SIMPLE LINEAR REGRESSION. Opening Example. Simple Regression. Linear Regression Opening Example CHAPTER 13 SIMPLE LINEAR REGREION SIMPLE LINEAR REGREION! Simple Regression! Linear Regression Simple Regression Definition A regression model is a mathematical equation that descries the

More information

NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )

NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( ) Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates

More information

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

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

More information

Using Minitab for Regression Analysis: An extended example

Using Minitab for Regression Analysis: An extended example Using Minitab for Regression Analysis: An extended example The following example uses data from another text on fertilizer application and crop yield, and is intended to show how Minitab can be used to

More information

Multiple Linear Regression

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

More information

Regression Analysis. Data Calculations Output

Regression Analysis. Data Calculations Output Regression Analysis In an attempt to find answers to questions such as those posed above, empirical labour economists use a useful tool called regression analysis. Regression analysis is essentially a

More information

Chapter 13 Introduction to Linear Regression and Correlation Analysis

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

More information

Regression Analysis (Spring, 2000)

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

More information

Lesson Lesson Outline Outline

Lesson Lesson Outline Outline Lesson 15 Linear Regression Lesson 15 Outline Review correlation analysis Dependent and Independent variables Least Squares Regression line Calculating l the slope Calculating the Intercept Residuals and

More information

August 2012 EXAMINATIONS Solution Part I

August 2012 EXAMINATIONS Solution Part I August 01 EXAMINATIONS Solution Part I (1) In a random sample of 600 eligible voters, the probability that less than 38% will be in favour of this policy is closest to (B) () In a large random sample,

More information

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 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

More information

Introduction to Stata

Introduction to Stata Introduction to Stata September 23, 2014 Stata is one of a few statistical analysis programs that social scientists use. Stata is in the mid-range of how easy it is to use. Other options include SPSS,

More information

Yiming Peng, Department of Statistics. February 12, 2013

Yiming Peng, Department of Statistics. February 12, 2013 Regression Analysis Using JMP Yiming Peng, Department of Statistics February 12, 2013 2 Presentation and Data http://www.lisa.stat.vt.edu Short Courses Regression Analysis Using JMP Download Data to Desktop

More information

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

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

More information

1.5 Oneway Analysis of Variance

1.5 Oneway Analysis of Variance Statistics: Rosie Cornish. 200. 1.5 Oneway Analysis of Variance 1 Introduction Oneway analysis of variance (ANOVA) is used to compare several means. This method is often used in scientific or medical experiments

More information

Lecture 5 Hypothesis Testing in Multiple Linear Regression

Lecture 5 Hypothesis Testing in Multiple Linear Regression Lecture 5 Hypothesis Testing in Multiple Linear Regression BIOST 515 January 20, 2004 Types of tests 1 Overall test Test for addition of a single variable Test for addition of a group of variables Overall

More information

Statistical Significance and Bivariate Tests

Statistical Significance and Bivariate Tests Statistical Significance and Bivariate Tests BUS 735: Business Decision Making and Research 1 1.1 Goals Goals Specific goals: Re-familiarize ourselves with basic statistics ideas: sampling distributions,

More information

Using JMP with a Specific

Using JMP with a Specific 1 Using JMP with a Specific Example of Regression Ying Liu 10/21/ 2009 Objectives 2 Exploratory data analysis Simple liner regression Polynomial regression How to fit a multiple regression model How to

More information

, 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.

, 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

More information

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 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

More information

MULTIPLE REGRESSION EXAMPLE

MULTIPLE REGRESSION EXAMPLE MULTIPLE REGRESSION EXAMPLE For a sample of n = 166 college students, the following variables were measured: Y = height X 1 = mother s height ( momheight ) X 2 = father s height ( dadheight ) X 3 = 1 if

More information

Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.

Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics. Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing

More information

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. 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

More information

Outline. Correlation & Regression, III. Review. Relationship between r and regression

Outline. Correlation & Regression, III. Review. Relationship between r and regression Outline Correlation & Regression, III 9.07 4/6/004 Relationship between correlation and regression, along with notes on the correlation coefficient Effect size, and the meaning of r Other kinds of correlation

More information

Final Exam Practice Problem Answers

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

More information

2. What is the general linear model to be used to model linear trend? (Write out the model) = + + + or

2. What is the general linear model to be used to model linear trend? (Write out the model) = + + + or Simple and Multiple Regression Analysis Example: Explore the relationships among Month, Adv.$ and Sales $: 1. Prepare a scatter plot of these data. The scatter plots for Adv.$ versus Sales, and Month versus

More information

STAT 350 Practice Final Exam Solution (Spring 2015)

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

More information

Simple Regression Theory II 2010 Samuel L. Baker

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

More information

Answer: C. The strength of a correlation does not change if units change by a linear transformation such as: Fahrenheit = 32 + (5/9) * Centigrade

Answer: C. The strength of a correlation does not change if units change by a linear transformation such as: Fahrenheit = 32 + (5/9) * Centigrade Statistics Quiz Correlation and Regression -- ANSWERS 1. Temperature and air pollution are known to be correlated. We collect data from two laboratories, in Boston and Montreal. Boston makes their measurements

More information

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 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,

More information

Inferential Statistics

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

More information

Prediction and Confidence Intervals in Regression

Prediction and Confidence Intervals in Regression Fall Semester, 2001 Statistics 621 Lecture 3 Robert Stine 1 Prediction and Confidence Intervals in Regression Preliminaries Teaching assistants See them in Room 3009 SH-DH. Hours are detailed in the syllabus.

More information

Chapter 5 Analysis of variance SPSS Analysis of variance

Chapter 5 Analysis of variance SPSS Analysis of variance Chapter 5 Analysis of variance SPSS Analysis of variance Data file used: gss.sav How to get there: Analyze Compare Means One-way ANOVA To test the null hypothesis that several population means are equal,

More information

5. Multiple regression

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

More information

Simple Linear Regression in SPSS STAT 314

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,

More information

Outline. Topic 4 - Analysis of Variance Approach to Regression. Partitioning Sums of Squares. Total Sum of Squares. Partitioning sums of squares

Outline. Topic 4 - Analysis of Variance Approach to Regression. Partitioning Sums of Squares. Total Sum of Squares. Partitioning sums of squares Topic 4 - Analysis of Variance Approach to Regression Outline Partitioning sums of squares Degrees of freedom Expected mean squares General linear test - Fall 2013 R 2 and the coefficient of correlation

More information

GLM I An Introduction to Generalized Linear Models

GLM I An Introduction to Generalized Linear Models GLM I An Introduction to Generalized Linear Models CAS Ratemaking and Product Management Seminar March 2009 Presented by: Tanya D. Havlicek, Actuarial Assistant 0 ANTITRUST Notice The Casualty Actuarial

More information

t-tests and F-tests in regression

t-tests and F-tests in regression t-tests and F-tests in regression Johan A. Elkink University College Dublin 5 April 2012 Johan A. Elkink (UCD) t and F-tests 5 April 2012 1 / 25 Outline 1 Simple linear regression Model Variance and R

More information

We extended the additive model in two variables to the interaction model by adding a third term to the equation.

We extended the additive model in two variables to the interaction model by adding a third term to the equation. Quadratic Models We extended the additive model in two variables to the interaction model by adding a third term to the equation. Similarly, we can extend the linear model in one variable to the quadratic

More information

Course Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics

Course Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics Course Text Business Statistics Lind, Douglas A., Marchal, William A. and Samuel A. Wathen. Basic Statistics for Business and Economics, 7th edition, McGraw-Hill/Irwin, 2010, ISBN: 9780077384470 [This

More information

Statistical Inference and t-tests

Statistical Inference and t-tests 1 Statistical Inference and t-tests Objectives Evaluate the difference between a sample mean and a target value using a one-sample t-test. Evaluate the difference between a sample mean and a target value

More information

Simple linear regression

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

More information

Causal Forecasting Models

Causal Forecasting Models CTL.SC1x -Supply Chain & Logistics Fundamentals Causal Forecasting Models MIT Center for Transportation & Logistics Causal Models Used when demand is correlated with some known and measurable environmental

More information

Univariate Regression

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

More information

DEPARTMENT OF ECONOMICS. Unit ECON 12122 Introduction to Econometrics. Notes 4 2. R and F tests

DEPARTMENT OF ECONOMICS. Unit ECON 12122 Introduction to Econometrics. Notes 4 2. R and F tests DEPARTMENT OF ECONOMICS Unit ECON 11 Introduction to Econometrics Notes 4 R and F tests These notes provide a summary of the lectures. They are not a complete account of the unit material. You should also

More information

Hedge Effectiveness Testing

Hedge Effectiveness Testing Hedge Effectiveness Testing Using Regression Analysis Ira G. Kawaller, Ph.D. Kawaller & Company, LLC Reva B. Steinberg BDO Seidman LLP When companies use derivative instruments to hedge economic exposures,

More information

Notes on Applied Linear Regression

Notes on Applied Linear Regression Notes on Applied Linear Regression Jamie DeCoster Department of Social Psychology Free University Amsterdam Van der Boechorststraat 1 1081 BT Amsterdam The Netherlands phone: +31 (0)20 444-8935 email:

More information

A Primer on Forecasting Business Performance

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.

More information

Interaction between quantitative predictors

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

More information

Descriptive Statistics

Descriptive Statistics Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize

More information

STA 4163 Lecture 10: Practice Problems

STA 4163 Lecture 10: Practice Problems STA 463 Lecture 0: Practice Problems Problem.0: A study was conducted to determine whether a student's final grade in STA406 is linearly related to his or her performance on the MATH ability test before

More information

MULTIPLE REGRESSION WITH CATEGORICAL DATA

MULTIPLE REGRESSION WITH CATEGORICAL DATA DEPARTMENT OF POLITICAL SCIENCE AND INTERNATIONAL RELATIONS Posc/Uapp 86 MULTIPLE REGRESSION WITH CATEGORICAL DATA I. AGENDA: A. Multiple regression with categorical variables. Coding schemes. Interpreting

More information

Correlation and Simple Linear Regression

Correlation and Simple Linear Regression Correlation and Simple Linear Regression We are often interested in studying the relationship among variables to determine whether they are associated with one another. When we think that changes in a

More information

The importance of graphing the data: Anscombe s regression examples

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

More information

Technology Step-by-Step Using StatCrunch

Technology Step-by-Step Using StatCrunch Technology Step-by-Step Using StatCrunch Section 1.3 Simple Random Sampling 1. Select Data, highlight Simulate Data, then highlight Discrete Uniform. 2. Fill in the following window with the appropriate

More information

Lectures 8, 9 & 10. Multiple Regression Analysis

Lectures 8, 9 & 10. Multiple Regression Analysis Lectures 8, 9 & 0. Multiple Regression Analysis In which you learn how to apply the principles and tests outlined in earlier lectures to more realistic models involving more than explanatory variable and

More information

Statistics 104 Final Project A Culture of Debt: A Study of Credit Card Spending in America TF: Kevin Rader Anonymous Students: LD, MH, IW, MY

Statistics 104 Final Project A Culture of Debt: A Study of Credit Card Spending in America TF: Kevin Rader Anonymous Students: LD, MH, IW, MY Statistics 104 Final Project A Culture of Debt: A Study of Credit Card Spending in America TF: Kevin Rader Anonymous Students: LD, MH, IW, MY ABSTRACT: This project attempted to determine the relationship

More information

Simple Regression and Correlation

Simple Regression and Correlation Simple Regression and Correlation Today, we are going to discuss a powerful statistical technique for examining whether or not two variables are related. Specifically, we are going to talk about the ideas

More information

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

 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

More information

SPSS Guide: Regression Analysis

SPSS Guide: Regression Analysis SPSS Guide: Regression Analysis I put this together to give you a step-by-step guide for replicating what we did in the computer lab. It should help you run the tests we covered. The best way to get familiar

More information

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

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

More information

Homework 8 Solutions

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.

More information

Unit 26 Estimation with Confidence Intervals

Unit 26 Estimation with Confidence Intervals Unit 26 Estimation with Confidence Intervals Objectives: To see how confidence intervals are used to estimate a population proportion, a population mean, a difference in population proportions, or a difference

More information

Predictor Coef StDev T P Constant 970667056 616256122 1.58 0.154 X 0.00293 0.06163 0.05 0.963. S = 0.5597 R-Sq = 0.0% R-Sq(adj) = 0.

Predictor Coef StDev T P Constant 970667056 616256122 1.58 0.154 X 0.00293 0.06163 0.05 0.963. S = 0.5597 R-Sq = 0.0% R-Sq(adj) = 0. Statistical analysis using Microsoft Excel Microsoft Excel spreadsheets have become somewhat of a standard for data storage, at least for smaller data sets. This, along with the program often being packaged

More information

Stats for Strategy Exam 1 In-Class Practice Questions DIRECTIONS

Stats for Strategy Exam 1 In-Class Practice Questions DIRECTIONS Stats for Strategy Exam 1 In-Class Practice Questions DIRECTIONS Choose the single best answer for each question. Discuss questions with classmates, TAs and Professor Whitten. Raise your hand to check

More information

International Statistical Institute, 56th Session, 2007: Phil Everson

International Statistical Institute, 56th Session, 2007: Phil Everson Teaching Regression using American Football Scores Everson, Phil Swarthmore College Department of Mathematics and Statistics 5 College Avenue Swarthmore, PA198, USA E-mail: peverso1@swarthmore.edu 1. Introduction

More information

MGT 267 PROJECT. Forecasting the United States Retail Sales of the Pharmacies and Drug Stores. Done by: Shunwei Wang & Mohammad Zainal

MGT 267 PROJECT. Forecasting the United States Retail Sales of the Pharmacies and Drug Stores. Done by: Shunwei Wang & Mohammad Zainal MGT 267 PROJECT Forecasting the United States Retail Sales of the Pharmacies and Drug Stores Done by: Shunwei Wang & Mohammad Zainal Dec. 2002 The retail sale (Million) ABSTRACT The present study aims

More information

Section 14 Simple Linear Regression: Introduction to Least Squares Regression

Section 14 Simple Linear Regression: Introduction to Least Squares Regression Slide 1 Section 14 Simple Linear Regression: Introduction to Least Squares Regression There are several different measures of statistical association used for understanding the quantitative relationship

More information

Class 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1)

Class 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1) Spring 204 Class 9: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the

More information

IAPRI Quantitative Analysis Capacity Building Series. Multiple regression analysis & interpreting results

IAPRI Quantitative Analysis Capacity Building Series. Multiple regression analysis & interpreting results IAPRI Quantitative Analysis Capacity Building Series Multiple regression analysis & interpreting results How important is R-squared? R-squared Published in Agricultural Economics 0.45 Best article of the

More information

Simple Linear Regression Inference

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

More information

Hypothesis testing - Steps

Hypothesis testing - Steps Hypothesis testing - Steps Steps to do a two-tailed test of the hypothesis that β 1 0: 1. Set up the hypotheses: H 0 : β 1 = 0 H a : β 1 0. 2. Compute the test statistic: t = b 1 0 Std. error of b 1 =

More information

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

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

More information

Simple Methods and Procedures Used in Forecasting

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

More information

Linear Regression. Chapter 5. Prediction via Regression Line Number of new birds and Percent returning. Least Squares

Linear Regression. Chapter 5. Prediction via Regression Line Number of new birds and Percent returning. Least Squares Linear Regression Chapter 5 Regression Objective: To quantify the linear relationship between an explanatory variable (x) and response variable (y). We can then predict the average response for all subjects

More information

Recall this chart that showed how most of our course would be organized:

Recall this chart that showed how most of our course would be organized: Chapter 4 One-Way ANOVA Recall this chart that showed how most of our course would be organized: Explanatory Variable(s) Response Variable Methods Categorical Categorical Contingency Tables Categorical

More information

Moderation. Moderation

Moderation. Moderation Stats - Moderation Moderation A moderator is a variable that specifies conditions under which a given predictor is related to an outcome. The moderator explains when a DV and IV are related. Moderation

More information

2. Simple Linear Regression

2. Simple Linear Regression Research methods - II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according

More information

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

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.

More information

11. Analysis of Case-control Studies Logistic Regression

11. Analysis of Case-control Studies Logistic Regression Research methods II 113 11. Analysis of Case-control Studies Logistic Regression This chapter builds upon and further develops the concepts and strategies described in Ch.6 of Mother and Child Health:

More information

Multiple Regression: What Is It?

Multiple Regression: What Is It? Multiple Regression Multiple Regression: What Is It? Multiple regression is a collection of techniques in which there are multiple predictors of varying kinds and a single outcome We are interested in

More information

business statistics using Excel OXFORD UNIVERSITY PRESS Glyn Davis & Branko Pecar

business statistics using Excel OXFORD UNIVERSITY PRESS Glyn Davis & Branko Pecar business statistics using Excel Glyn Davis & Branko Pecar OXFORD UNIVERSITY PRESS Detailed contents Introduction to Microsoft Excel 2003 Overview Learning Objectives 1.1 Introduction to Microsoft Excel

More information

SIMPLE LINEAR CORRELATION. r can range from -1 to 1, and is independent of units of measurement. Correlation can be done on two dependent variables.

SIMPLE LINEAR CORRELATION. r can range from -1 to 1, and is independent of units of measurement. Correlation can be done on two dependent variables. SIMPLE LINEAR CORRELATION Simple linear correlation is a measure of the degree to which two variables vary together, or a measure of the intensity of the association between two variables. Correlation

More information

Inferences About Differences Between Means Edpsy 580

Inferences About Differences Between Means Edpsy 580 Inferences About Differences Between Means Edpsy 580 Carolyn J. Anderson Department of Educational Psychology University of Illinois at Urbana-Champaign Inferences About Differences Between Means Slide

More information

Good luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:

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

More information