Question

**PLEASE SHOW EXPLAINATION FOR ANSWERS. **

This assignment extends the analysis of

house prices in Springfield (data in *House Prices.xlsx*) that was conducted in earlier assignments.

(a) Consider Model 1 from Individual Assignment 2. Use this regression model to test (at the 5% level of significance) if the average price of a house in the East neighborhood is less than the average pric e of a similar house in the North neighborhood.

Model 1 Output

· State the null and alternative hypotheses.

· State the *p*-value for this test.

· State the statistical conclusion.

· Communicate the results of the test in "plain English" within the context of the problem.

SUMMARY OUTPUT

*Regression Statistics*

Multiple R

0.930384625

R Square

0.86561555

Adjusted R Square

0.857776457

Standard Error

50660.95358

Observations

128

ANOVA

* *

*df*

*SS*

*MS*

*F*

*Significance F*

Regression

7

1.98383E+12

2.83404E+11

110.4229

3.17667E-49

Residual

120

3.07984E+11

2566532218

Total

127

2.29181E+12

* *

*Coefficients*

*Standard Error*

*t Stat*

*P-value*

*Lower 95%*

*Upper 95%*

*Lower 95.0%*

*Upper 95.0%*

Intercept

-12055.20512

44691.44115

-0.269743038

0.787821

-100541.1483

76430.74

-100541

76430.74

SqFt

274.4720171

28.71182947

9.559544697

1.93E-16

217.624593

331.3194

217.6246

331.3194

Bedrooms

24088.33576

7944.589907

3.032042691

0.002977

8358.600646

39818.07

8358.601

39818.07

Bathrooms

37363.03284

10792.47277

3.461952939

0.000744

15994.68785

58731.38

15994.69

58731.38

Offers

-40757.52654

5519.172415

-7.384717032

2.21E-11

-51685.10382

-29829.9

-51685.1

-29829.9

Brick Coded

85958.21519

10054.72173

8.549039696

4.7E-14

66050.56593

105865.9

66050.57

105865.9

East coded

-12020.22191

12314.42924

-0.976108732

0.330974

-36401.93479

12361.49

-36401.9

12361.49

west coded

99685.90872

15680.03715

6.357504628

3.86E-09

68640.52643

130731.3

68640.53

130731.3

(b) Consider Model 2 from Individual Assignment 2. Use this regression model to test (at the 5% level of significance) if the brick premium in the West exceeds the brick premium in the North.

Model 2 Output

· State the null and alternative hypotheses.

· State the *p*-value for this test.

· State the statistical conclusion.

· Communicate the results of the test in "plain English" within the context of the problem.

SUMMARY OUTPUT

*Regression Statistics*

Multiple R

0.934623672

R Square

0.873521408

Adjusted R Square

0.863874736

Standard Error

49562.93089

Observations

128

ANOVA

* *

*df*

*SS*

*MS*

*F*

*Significance F*

Regression

9

2.00195E+12

2.22E+11

90.55158

1.01432E-48

Residual

118

2.89865E+11

2.46E+09

Total

127

2.29181E+12

* *

*Coefficients*

*Standard Error*

*t Stat*

*P-value*

*Lower 95%*

*Upper 95%*

*Lower 95.0%*

Intercept

-89.79829617

44216.901

-0.00203

0.998383

-87651.3003

87471.704

-87651.3

SqFt

276.8302333

28.2262254

9.807554

5.74E-17

220.9346225

332.72584

220.9346

Bedrooms

26192.77172

7825.496458

3.347107

0.001096

10696.15825

41689.385

10696.16

Bathrooms

30094.14158

10894.6699

2.762281

0.00666

8519.729105

51668.554

8519.729

Offers

-41398.0651

5412.84349

-7.64812

6.05E-12

-52116.96885

-30679.161

-52117

Brick Coded

60960.29572

20572.89716

2.963136

0.003684

20220.35839

101700.23

20220.36

East coded

-8085.045065

13899.72344

-0.58167

0.561899

-35610.28167

19440.192

-35610.3

west coded

81298.35221

16849.02308

4.825108

4.23E-06

47932.69938

114664.01

47932.7

Brick*East

9080.366235

25423.74171

0.357161

0.721609

-41265.56394

59426.296

-41265.6

Brick*west

61854.24045

26704.64404

2.316235

0.022271

8971.774935

114736.71

8971.775

(c) Consider Model 2 from Individual Assignment 2. Use this regression model to test (at the 5% level of significance) if the average increase in price for a 1 square foot increase in floor area is less than $300 per square foot.

· State the null and alternative hypotheses.

· Compute the test statistic.

· Compute the *p*-value for this test.

State the Excel function (specifying all inputs) that will compute this probability.

· State the statistical conclusion.

· Communicate the results of the test in "plain English" within the context of the problem.