1. The data in the table below are the outputs of a random sample of present home sales in your neighborhood that your boss has asked you to use to calculate the relationship between the selling price of the house and the number of square feet in it.
Observation Number Sale Price (in thousands) Square Feet (in hundreds)
1 280 20.3
2 328 30.0
3 281 21.5
4 293 25.4
5 263 14.5
6 291 22.3
7 320 31.0
8 256 37.2
9 311 27.1
10 352 30.2
11 288 21.2
12 356 37.2
13 293 23.0
14 272 26.7
15 308 26.5
a. First plot the data, with number of square feet on the “X” axis and the price of the house on the “Y” axis. Describe why housing price is the dependent variable and square feet is the independent variable.
b. What is the estimated regression line? What does the coefficient of square feet represent?
c. Is the sample size large enough for the estimated coefficient of square feet to be statistically significant at the 5% level?
d. What is the coefficient of determination (R2)?
e. Carry out an F-test, again at the 5% level.
2. You are given the following regression results computing the demand for widgets based on time series data for the past 40 months.
Qt = 2.5 – 0.3 x Pt + 12 x Mt
Where Qt represents quantity of widgets sold per period t, Pt represents the price of widgets during period t, and Mt represents average household income of customers during period t.
You are also given the following information about regression results
R2 = 0.75 F-statistic = 23 Durbin-Watson (d) statistic = 0.66
standard deviation of constant = 0.52; standard deviation of P = 0.16
standard deviation of M = 2.0
a. Which of the independent variables are statistically significant at the 5% level?
b. could you reject the null hypothesis that price does not affected quantity demanded? Could you reject the null hypothesis that income does not affect quantity demanded?
c. What proportion of total variation in Q is explained by the regression equation?
d. Is the F-statistic significant at the 5% level? What is the meaning of the F-statistic and F test?