ASSIGNMENT #4 1. Use EXCEL file: RESIDENT to develop the multiple regression mod

Question

ASSIGNMENT #4 1. Use EXCEL file: RESIDENT to develop the multiple regression model to fit the following residential sales data in Eugene, Oregon: SALES SQUARE PRICE FEET TOTAL ATTACHED RESIDENCE # ($1,000) (100) BEDRMS BATHRMS ROOMS AGE GARAGE VIEW 90.3 25.6 3 15 96.0 25.0 101.4 25.0 2 105.9 26.8 3 111.3 22.1 3 112.5 27.5 114.0 25.0 4 115.2 24.0 117.0 31.0 4 129.0 21.0 4 165.0 40.0 8 18 12 13 9 25 1 18 22 10 9 12 (a) Show the EXCEL printout for this multiple regression problem. Give the least squares regression model for predicting the sales price (in $1,000) of residential sales in Eugene, Oregon. (b) Is this model useful in predicting the sales price at 90% confidence? (e) In the presence of the other variables in the model, which is the most significant predictor of the sales price? Which is the least significant? (d) Use the regression model to establish assessed valuations for each of the five Eugene residences. The data are given in the accompanying table. SQUARE TOTAL ATTACHED RESIDENCE FEET BEDRMS BATHRMS ROOMS AGE GARAGE VIEW 22.44 15.3 3 17.2 4 31.7 20.0 7 18 4 9 24

Explanation / Answer

a)Excel output after applying ‘REGRESSION’ from the Data Analysis Toolpack on the data :

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.983078977

R Square

0.966444275

Adjusted R Square

0.888147583

Standard Error

6.651021374

Observations

11

ANOVA

df

SS

MS

F

Significance F

Regression

7

3822.153562

546.0219

12.34336

0.031741806

Residual

3

132.7082559

44.23609

Total

10

3954.861818

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 90.0%

Upper 90.0%

Intercept

-54.29238494

25.38938455

-2.13839

0.122039

-135.092738

26.50797

-114.043

5.458064

Square feet

-2.515122948

1.490003365

-1.688

0.189995

-7.256978653

2.226733

-6.02164

0.991396

Bedrms

-16.53016064

8.033206349

-2.05773

0.131783

-42.09540851

9.035087

-35.4352

2.374893

Bathrms

34.00238415

23.12696363

1.470249

0.237848

-39.59793582

107.6027

-20.4238

88.42853

Total rooms

26.125135

5.384650857

4.851779

0.016712

8.988772776

43.2615

13.45309

38.79718

Age

-2.441682982

1.168651907

-2.08932

0.12786

-6.160854925

1.277489

-5.19195

0.30858

Attached garage

40.0234526

14.67822828

2.726722

0.07214

-6.689220762

86.73613

5.480247

74.56666

View

-5.841604525

8.587234703

-0.68027

0.545131

-33.17001788

21.48681

-26.0505

14.36728

Regression model :

Sales price = -54.29-2.51*Square feet-16.53*Bedrms+34*Bathrms+26.12*Total rooms-2.44*Age+40*Attached garage-5.84*View

b)Yes the model is useful in prediction as explained by the F-statistic which is greater than the significant F, implying that the regression model is useful.
Moreover, adjusted R-square is approximately 0.888 which implies that the 88.8% variability is explained by the regression model obtained which is quite a good amount explained.

c)The least significant variable is VIEW since its p-value is > 0.1 implying that the effect of this variable is not significant enough.
The most significant variable is TOTAL ROOMS whose p-value is the least.

d)

64.360486

22.4

4

2

7

18

1

1

93.866367

15.3

3

2

7

6

0

0

83.461908

17.2

4

1

7

4

1

0

61.86039

31.7

5

3

9

24

0

0

113.6137

20

4

2

8

11

1

1

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.983078977

R Square

0.966444275

Adjusted R Square

0.888147583

Standard Error

6.651021374

Observations

11

ANOVA

df

SS

MS

F

Significance F

Regression

7

3822.153562

546.0219

12.34336

0.031741806

Residual

3

132.7082559

44.23609

Total

10

3954.861818

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 90.0%

Upper 90.0%

Intercept

-54.29238494

25.38938455

-2.13839

0.122039

-135.092738

26.50797

-114.043

5.458064

Square feet

-2.515122948

1.490003365

-1.688

0.189995

-7.256978653

2.226733

-6.02164

0.991396

Bedrms

-16.53016064

8.033206349

-2.05773

0.131783

-42.09540851

9.035087

-35.4352

2.374893

Bathrms

34.00238415

23.12696363

1.470249

0.237848

-39.59793582

107.6027

-20.4238

88.42853

Total rooms

26.125135

5.384650857

4.851779

0.016712

8.988772776

43.2615

13.45309

38.79718

Age

-2.441682982

1.168651907

-2.08932

0.12786

-6.160854925

1.277489

-5.19195

0.30858

Attached garage

40.0234526

14.67822828

2.726722

0.07214

-6.689220762

86.73613

5.480247

74.56666

View

-5.841604525

8.587234703

-0.68027

0.545131

-33.17001788

21.48681

-26.0505

14.36728

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