The data in the table below are the results of a random sample of recent home sales in your neighborhood that your boss has asked you to use to estimate 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. Explain 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. Perform an F-test, again at the 5% level.