Name(s) ECON 2370: Introduction to Economic Data Analysis Due date: Monday, March 18 (Mo-We section) Tuesday, March 19 (Tu-Th sections) PS# Class time: Spring 2016 Homework # 7 1. To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow. Construct an analysis of variance table. Use a 0.05 level of significance to test whether the temperature level has an effect on the mean yield of the process. 50 C 34 24 36 39 32 Temperature 60 C 30 31 34 23 27 1 70 C 23 28 28 30 31 2. To the Internal Revenue Service, the reasonableness of total itemized deductions depends on the taxpayer's adjusted gross income. Large deductions, which include charity and medical deductions, are more reasonable for taxpayers with large adjusted gross incomes. If a taxpayer claims larger than average itemized deductions for a given level of income, the chances of an IRS audit are increased. Data (in thousands of dollars) on adjusted gross income and the average or reasonable amount of itemized deductions follow. Adjusted Reasonable Gross Amount of Itemized Income Deductions 22 27 32 48 65 85 120 x ( x i ) y ( y i ) x y ( x i ) ( y i ) 2 x ( x i ) 9.6 9.6 10.1 11.1 13.5 17.7 25.5 a. Develop a scatter diagram for these data with adjusted gross income as the independent variable. (You can copy&paste it from Excel or plot it manually.) b. Use the least squares method to develop the estimated regression equation. c. Predict the reasonable level of total itemized deductions for a taxpayer with an adjusted gross income of $52,500. If this taxpayer claimed itemized deductions of $20,400, would the IRS agent's request for an audit appear justified? Explain. 2 Answer each of the following two questions in a paragraph rather than incomplete phrases for each of the items of the questions. Think of it as explaining it to someone rather than answering questions in homework. 1. A large car dealership with 20 locations nationwide is interested in implementing a training program to increase the sales of its workers. A human resources consulting firm offers a variety of training programs which vary in technique and duration. After evaluating all proposals, the owners have narrowed it down to three possible training programs but disagree on which one would be more effective. Consider you want to help in making an informed decision and propose a way to statistically test the effectiveness of the three training programs by collecting data from three different dealer locations: Houston, San Antonio and Dallas. Write one or two short paragraphs explaining the owners how you would do this. In your answer make sure to include the following. a. Briefly explain how you would organize the experiment to evaluate the effectiveness of the three different training programs. b. What test statistic would you use? c. What is the specific question you will be able to answer with your proposed method? d. What are the sample elements from which you will collect the data? e. What is the random variable to use as a measure of the effectiveness of the programs? f. What sample statistics you would need to calculate in order to be able to test this? 3 2. You work for a consulting firm which is hired by a local restaurant chain to evaluate 10 potential locations for their next restaurant (simply think of the locations as zip codes). Your firm will evaluate different aspects of each location but your team is in charge of making sales estimates for each one of them. Write one or two paragraphs explaining how you would use a linear regression equation to do this. In your answer make sure to include the following: a. Make a list of at least three variables that would be useful to predict the sales of a restaurant location. b. Choose one of the variables above to write a linear regression equation to estimate the sales of these locations. c. Clearly define your dependent and independent variables and how to measure them. (For example, in the car dealership exercise above you could measure sales in dollars or numbers of cars. Here I want you to be as clear as possible.) d. What is the expected sign of the slope coefficient and why do you expect that sign? e. How will you use the coefficient of determination to evaluate the estimated model? f. Give a hypothetical numerical example to show how the linear equation would be used to estimate the sales. 4