Question 15 Questions 15 through 19 refer to the following : The following data

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Question 15

Questions 15 through 19 refer to the following:

The following data are from www.realtor.com and represent a random sample of real estate listings for single family homes in the Millbrook, AL area. The least squares regression equation relating price (Y) to square feet (X) is as follows:

Listing Price ($1000s)

Square Feet

72.9

1,456

91.5

1,399

99.0

1,472

108.9

1,493

121.9

1,617

142.9

1,832

169.0

1,756

179.9

1,962

195.9

2,140

232.9

2,580

269.0

2,853

299.9

3,310

?x = 23,870        ?x2 = 51,708,572

?y = 1,983.7       ?y2 = 386,472.13

?xy = 4,431,334

Source

SS

df

MS

F

Regression

Error

Total

Find the value of R2 for this set of data.

0.8989

0.4316

0.7412

0.6571

0.9521

Question 16

Find s, the standard error of the estimate.

14.093

29.618

16.753

9.345

3.731

Question 17

Find the value of the F statistic for determining whether a nonzero slope exists between listing price and square footage.

9.345

280.669

47.221

198.609

20.084

Question 18

Do these data provide evidence of a nonzero slope at the .01 significance level?

yes

no

zero

cannot be determined

egg salad

Question 19

Which of the following correctly describes the p-value for the F statistic in #17?

p-value < .01

.01 < p-value < .025

.025 < p-value < .05

.05 < p-value < .10

p-value > .10

Listing Price ($1000s)

Square Feet

72.9

1,456

91.5

1,399

99.0

1,472

108.9

1,493

121.9

1,617

142.9

1,832

169.0

1,756

179.9

1,962

195.9

2,140

232.9

2,580

269.0

2,853

299.9

3,310

Explanation / Answer

running regression analysis in MS-Excel, we get:

R^2 = 0.9521

16. 16.753

17. 198.609

18. no

19. p-value < .01

SUMMARY OUTPUT Regression Statistics Multiple R 0.975737353 R Square 0.952063381 Adjusted R Square 0.94726972 Standard Error 16.75317431 Observations 12 ANOVA df SS MS F Significance F Regression 1 55743.30067 55743.30067 198.6087902 6.35767E-08 Residual 10 2806.688496 280.6688496 Total 11 58549.98917 Coefficients Standard Error t Stat P-value Lower 99.0% Upper 99.0% Intercept -63.11632379 16.91465814 -3.731457252 0.003900988 -116.7234876 -9.509159988 X Variable 1 0.114834348 0.008148404 14.0928631 6.35767E-08 0.089009833 0.140658863

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