Question

SUMMARY OUTPUT 0.865 0.748 Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.726 5.195 50 ANOVA df SS MS F Significance F 0.0000 3605.7736 1201.9245 Regression Residual Total 1214.2264 26.3962 49 4820 P-value 0.7798 Intercept Income Coefficients Standard Error -1.6335 5.8078 0.4485 0.1137 4.2615 0.8062 -0.6517 0.4319 t Stat -0.281 3.9545 0.0003 Size 5.286 0.0001 0.1383 School -1.509

Answer 1

1) 0.748

The proportion of variablility explained is given by the value of R square and hence in can be observed that the value of R square in the output is 0.748.

2) 24.88

The regression equation is given by

$\hat{house}=-1.6335+0.4485*income+4.2615*size-0.6517*school$

In this example

income=40 (in thousand of dollars)

size=4

school=13

So

$\hat{house}=-1.6335+0.4485*40+4.2615*4-0.6517*13$

  $=24.8804 \approx 24.88$

3) -5.40

Here

income=100

size=10

school=16

$\hat{house}=-1.6335+0.4485*100+4.2615*10-0.6517*16$

$=75.4043$

So the residual is

$res=original-estimated=70-75.4043=-5.4043 \approx-5.40$

4) 3.9545

From the table it can be observed that the value of the t-statistic is 3.9545.

Do comment if you have any doubt.

Thank you !!!