Use SPSS to answer the questions below. Interpret the output: running the test alone will not give you full credit.  Keep in mind the requirements spelled out at the beginning of this assignment as well for all hypothesis testing questions.

1. A researcher on real estate is interested in the relationship between the size of a home (in square feet) and the price of the home (in dollars per square foot). He collected data on 25 homes of similar style from a particular community on the west side of Edmonton. The data are given below. 

House     Size            Price      House    Size    Price

                 (sq. ft)     ($/sq ft.)                 (sq. ft)    ($/sq ft.)

 1         1180   266.78      14       1716        237.93

 2         1270   266.78     15       1600        245.78

 3         1260   269.05     16       1238        241.77

 4         1202   263.73     17        2260        214.52

 5         1422   256.61     18        2239        228.67

 6         1466   264.32     19        2181        233.38

 7         1731   254.88     20        2381        217.89

 8         1390   272.54     21        2224        237.77

 9         1830         245.36     22        1619        245.12

10         1992   225.40     23        1700        238.95

11         2099   223.87     24        2100        222.67

12         2413   221.76     25        1325        274.12

13       1600   239.67

a. Plot the data on a scatter plot and comment on the relationship between the two variables.

b. Use SPSS to find the strength of the linear relationship between the two variables. Interpret the value.

c. At alpha = 0.01, is there sufficient evidence to indicate that the smaller the house, the higher the price per square foot.

d. Assuming that there are no possible violations of regression assumptions, run a simple linear regression analysis. 

e. Plot histogram and normal probability plots for standardized residuals and verify the assumptions for simple regression. 

f. Examine the plots and comment on whether there appear to be a possible lack of fit of the linear model. 

g. Write the estimated regression equation to predict house price from square footage. 

h. Using your regression equation, predict the price of a 1200 square foot house. 

i. Would you use this regression equation to predict the house price of a 4000 square foot home? Explain. 

j. Would you use this regression equation to predict the house price of similar homes in Vancouver? Explain. 

k. What is the value of the coefficient of determination? What does that value tell you?

l. Find an estimate of σε. Interpret the value. 

m. Test the hypothesis H0:  β0 = 0 using a t-test with alpha = 0.05. 

n. Record the p value for this test. Is the p value one tailed or two tailed?

o. Test the hypothesis H0:  β1 = 0 using a t-test with alpha = 0.05.

p. Record the p value for this test. Is the p value one tailed or two tailed?

q. Use the AOV part of the regression output and explain how your result is the same as the one you got in part (o).