ECON 2220 E Fall 2023 Assignment 1

ECON 2220 E Fall 2023 Simon Power Assignment 1: Due October 16 PLEASE BE SURE TO READ THE DOCUMENT ENTITLED “GENERAL ASSIGNMENT GUIDELINES” BEFORE YOU BEGIN THIS ASSIGNMENT. ALL REFERENCES ARE TO THE 7 th EDITION OF STUDENMUND. ASSIGNMENTS SHOULD BE SUBMITTED THROUGH BRIGHTSPACE EITHER ON OR BEFORE THE DUE DATE. 1. Consider the simple linear regression model ? 𝑖 = 𝛽 0 + 𝛽 1 ? 𝑖 + 𝜖 𝑖 𝑖 = 1,2, … , 5 and the data set Y X 4 16 7 24 3 8 9 40 17 72 Calculate the following quantities using the equations indicated and a basic calculator. You may NOT use STATA (or any other computer software) for this exercise and you MUST show your detailed working, step-by-step, in each case. a) The OLS estimate 𝛽 ̂ 1 [equation (2.4)] b) The OLS estimate 𝛽 ̂ 0 [equation (2.5)] c) ??? [one of the equations in Footnote 3 on p. 38] d) ? 2 [equation (2.14)] e) ? ̅ 2 [equation (2.15)] And f) Explain how your answers to parts a) through e) would change, if at all, if the sample size being used in the analysis were to be doubled, through the simple expedient of repeating each one of the original observations in the sample. 2. Using the data set A1Q2.xlsx (available in Brightspace), where the variables are defined as follows: WEIGHT = weight of respondent (in pounds) HEIGHT = height of respondent (in inches)

2 This historical data set consists of data drawn from a survey of male US respondents, aged between 26 and 32. a) Calculate summary statistics for the HEIGHT variable using the STATA summarize command and then copy and paste your STATA output into your assignment. b) Briefly describe (in words) ALL of the information that can be gained about the HEIGHT variable from the STATA output in part a). c) Generate a new demeaned version of the HEIGHT variable and name it HEIGHTN. Note that one way to generate a demeaned version of a variable, say X, named XN would be to execute the following sequence of commands: sum X scalar a = r(mean) gen XN = X - a Now, use STATA to run the regression of WEIGHT on HEIGHTN and then copy and paste your STATA output into your assignment. d) Write down the values of the estimated parameters and then carefully interpret these values. e) Write down the ? 2 value and then carefully interpret this value. f) If you had used the original HEIGHT variable, rather than the new HEIGHTN variable, in the regression, would the ? 2 value have been any different? Carefully explain why or why not. g) Use STATA to generate the new variable BMI (Body Mass Index), where BMI is defined (in imperial units) as follows: 𝐵𝑀𝐼 = 703 × ( 𝑊?𝑖𝑔ℎ? 𝑖? ?????? (𝐻?𝑖𝑔ℎ? 𝑖? 𝑖??ℎ??) 2 ) and then calculate summary statistics for this new BMI variable. Copy and paste your STATA output into your assignment. h) Using appropriate STATA commands, determine and then report the number of respondents in the sample who fall into the following four BMI categories: Underweight (< 18.5), Normal Range (>= 18.5, but < 25), Overweight (>= 25, but < 30), Obese (>= 30). Be sure to copy and paste any relevant STATA output into your assignme nt. NOTE: The “count” command, together with appropriate “if” expressions, may prove useful. 3. Consider the used tractor prices example discussed in Section 7.7 on pp. 217-220. Note that the relevant TRACTOR7.dta dataset can be downloaded from the Studenmund website and that the variable definitions are given in Section 7.7. a) Using STATA, estimate a basic used tractor prices linear regression model, in which the variable saleprice is regressed on just the variable horsepower, and report your results in the standard format of equation (3.4). b) Re-estimate this model using STATA, but this time add both age and johndeere as additional explanatory variables, and report your results in the standard format of equation (3.4). c) Explain carefully why the value of the estimated parameter associated with the horsepower variable differs between parts a) and b).