A real estate agency collects the data concerning • y = sales
price of a house (in thousands of dollars) • x1 = home size (in
hundreds of square feet) • x2 = rating (an overall “niceness
rating” for the house expressed on a scale from 1 [worst] to 10
[best], and provided by the real estate agency) The agency wishes
to develop a regression model that can be used to predict the sales
prices of future houses it will list.
X1
X2
Y
Home Size
Rating
Sales Price
23
5
180.0
11
2
98.1
20
9
173.1
17
3
136.5
15
8
141.0
21
4
165.9
24
7
193.5
13
6
127.8
19
7
163.5
25
2
172.5
a) Interpret the equation parameters b0, b1, and b2
b) Interpret R 2 and RĚ„ 2 . Show how RĚ„ 2 has been
calculated from R 2 and other relevant quantities.
c. Overall Test of the Model
• Write the hypothesis statement to test the significance of the
overall regression relationship or that your model is
effective.
• Calculate the F(model) statistic by using the explained and
unexplained variations (as shown on the output) and other relevant
quantities. Find F(model) on the output to check your answer
(within rounding).
• Use the F(model) statistic and the appropriate critical value
(from the F-table) to test your hypothesis by setting α equal to
.05. • Find the p-value related to F(model) on the output. Using
the p-value, test the significance of the linear regression model
by setting α =.05.
• What do you conclude?
d. Testing the Significance of Independent Variables
• For every parameter use the t statistic and appropriate
critical values (from t-table) to test the significance of the
independent variable xj by setting α equal to .05:
H0: βj = 0 versus Ha: βj ≠0
• Which independent variables are significantly related to y at
α = .05?
• For every parameter find the p-value for testing H0: βj = 0
versus Ha: βj ≠0 on the output. Using the p-value, determine
whether we can reject H0 by setting α equal to .05.
• What do you conclude about the significance of the independent
variables in the model?