ECON 2220 A Winter 2024

PLEASE BE SURE TO READ THE DOCUMENT ENTITLED “GENERAL ASSIGNMENT GUIDELINES” BEFORE YOU BEGIN THIS ASSIGNMENT. ALL REFERENCES ARE TO THE 7th EDITION OF STUDENMUND. ASSIGNMENTS SHOULD BE SUBMITTED THROUGH BRIGHTSPACE EITHER ON OR BEFORE THE DUE DATE.

IF IN DOUBT, PROVIDE MORE DETAIL IN YOUR ANSWERS, RATHER THAN LESS.

NOTE: If a statistical table does not give an entry for the appropriate number(s) of degrees of freedom, then use the closest number(s) of degrees of freedom available.

1. Consider the simple linear regression model

yi  = β0  + β1xi  + E i             i  = 1, 2, … , 5

and the data set

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 estimateβ(̂)0  [equation (2.5)]

c) RSS [one of the equations in Footnote 3 on p. 38]

d) R2  [equation (2.14)]

e)R(̅)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 historical data set A1Q2.xls (available in Brightspace), where the data are drawn from a survey of US respondents, aged between 26 and 32 in 2011, and the variables are defined as follows:

FEMALE = 1 if the respondent is female, = 0 otherwise

H = height of respondent (in inches)

W2004 = weight of respondent in 2004 (in pounds)

W2011 = weight of respondent in 2011 (in pounds)

a) Calculate summary statistics for all four of the variables 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 four variables from the STATA output in part a).

c) Use STATA to run the regression of W2004 on H and then copy and paste your STATA output into your assignment.

d) Write down the values of the two estimated parameters and then carefully interpret these values.

e) Write down the r2  value and then carefully interpret this value.

f) Repeat part c), but using ONLY the observations for the female respondents. Note that one way to isolate the observations for the female respondents would be to use the following command:

reg Y X if FEMALE == 1

Obviously, I amusing the variables Y and X in the above syntax for illustrative purposes. You need to adapt the code, accordingly.

g) Write down the values of the two estimated parameters and then carefully interpret these values.

h) Why do the values of the two estimated parameters in part d) differ from those obtained in part g)? Explain carefully.

3. Continuing on from Question 2: