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Assignment 2

ECO 562

Due: Sunday 3/23 11:59pm on D2L

[5 Points]

1. Suppose that you are interested in determining the effect of adding a bedroom on the price of your house with sales data (Hprice.xlsx). Using GPT 4o/4.5, es mate the naïve regression [provide the link to full chat below]:

price = 𝑚 ∗ bedrooms + 𝑏 + �̃� (1)

Link:

a. [0.5 Points] Using GPT 4o/4.5, test for heteroscedas city and linearity of the regression (1). If there are viola ons to either assump on, fix it in the chat provided above. If there are no issues, proceed to part b.

b. [0.5 Points] What is the interpreta on of the es mated values of 𝑚 and 𝑏, including the p-values? [No AI allowed]

c. [0.5 Points] Why did we test for viola ons of OLS before interpre ng the es mated coefficients 𝑚 and 𝑏? [No AI allowed]

d. [0.5 Points] What does it mean for 𝑚 to be unbiased? [No AI allowed]

e. [0.5 Points] Why might the square footage of the house be an omi ed variable from the regression (1)? In other words, if the only objec ve is to determine the effect of adding one more bedroom on the price of the house, why would the square footage need to be included in the regression for the es mates to be unbiased? [No AI allowed]

Using GPT 4o/4.5, es mate the regression below [es mate should be in the same chat as the link above]:

price = 𝑚 ∗ bedrooms + 𝑚 ∗ square footage + 𝑏 + 𝑒 (2)

f. [0.5 Points] Using GPT 4o/4.5, test for heteroscedas city and linearity of the regression (2). If there are viola ons to either assump on, fix it in the chat link provided above. If there are no issues, proceed to part g.

g. [0.5 Points] What is the interpreta on of the es mates 𝑚 and 𝑚 , including the p- values? [No AI Allowed]

h. [0.5 Points] How does 𝑚 and 𝑚 compare? Why does including square footage in the

regression affect the marginal effect of the number of bedrooms posi vely/nega vely? [No AI Allowed]

2. To demonstrate the weakness of measure 𝑅 as a measure of goodness-of-fit in the context of regression analysis, consider Random Numbers.xlsx.

ChatGPT Link:

a. [0.25 Points] Using GPT 4o/4.5, create a correla on table and matrix of Y and X1, X2,…, X50. What is the intrinsic rela onship between Y and the 50 X’s? [Hint: the spreadsheet is called ‘Random Numbers’]

b. [0.25 Points] Ask GPT 4o/4.5 to es mate the regressions (copy and paste the quoted below into the chat):

“Es mate the regressions

Y=m1*X1+b+e

Y=m1*X1+ m2*X2+b+e

Y=m1*X1+ m2*X2+ m3*X3+b+e

…

Y=m1*X1+ m2*X2+ m3*X3+…+ m50*X50+b+e

For each regression, collected the r-squared. Plot the es mated r-square as a func on of the number of uncorrelated independent variables.”

Describe the plot created with this prompt.

c. [0.5 Points] How does this exercise relate to the concept of a Kitchen Sink Regression?