statistics, econ
ECON 3060/3090 Packet 3
Name and Section:
Answer the questions in the spaces provided on the question sheets. You may refer to any tables and software at any time. Your grade will be based on a combination of completeness and randomly selected problems to grade. The packet is due at the beginning of class on Monday, November 26th. You are allowed to work with your fellow students, but DO NOT JUST
COPY WORK FROM EACH OTHER.
1. You are conducting a study on the real estate market in Los Angeles county. According to the data you collected, you generated a sample regression line of
ŷ = 347 + .257x1 − .192x2 + 241x3
y is the price of a home in thousands of dollars x1 is the size of the home in square feet x2 is the age of the home in years x3 is a dummy variable that is equal to 1 if the house is in Beverly Hills city limits, 0 otherwise.
(a) Interpret the coefficient of x1.
(b) Interpret the coefficient of the dummy variable, x3.
(c) The p-value of the t-test statistic for the test H0 : β3 = 0 against H1 : β3 6= 0 is equal to .20182. Would you reject or fail to reject the null hypothesis at the α = .05 significance level? Does this line up with your perception of the price of a home in Beverly Hills vs. other parts of Los Angeles county?
(d) The 95% confidence interval for β2 is (−.2, .08). Would you reject or fail to reject the null hypothesis for the test H0 : β2 = 0 against H1 : β2 6= 0 at the α = .05 significance level? Why?
2. The following data represents a regression of systolic blood pressure (in mmHg) on the explanatory variables weight (lbs), age (years), a dummy variable that is equal to 1 if the patient suffers from Type 2 diabetes and 0 otherwise, and a dummy variable that is equal to 1 if the patient’s biological sex is male and 0 otherwise.
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(a) Find and interpret the R2.
(b) According to the F test for overall significance at the 5% level, would you reject or fail to reject the null hypothesis? Why?
(c) Which of the explanatory variables are statistically significant at the 5% level? Why?
(d) If you were seeking to improve the model, what, if any, variables would you delete from the regression? Why?
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3. For this question, refer to the data set labeled ”MovieData” on Moodle. Using the Data Analysis tool in Excel, run a regression where:
y is the box office receipts, in millions of dollars x1 is the production cost in millions of dollars x2 is the promotional cost in millions of dollars x3 is the box office receipts of the director’s first film in millions of dollars x4 is a dummy variable that equals 1 if the movie had a female director, 0 otherwise
(a) Write the equation of the sample regression line.
(b) Is there a good interpretation for b0 in this model? Why or why not?
(c) Find and interpret b2.
(d) Find and interpret the adjusted R2.
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(e) Which of these variables are statistically significant at the 5% significance level? Why?
(f) Write the 95% confidence interval for β2
(g) Write the 95% confidence interval for β4
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