Excel File is Attached

STATISTICAL ANALYSIS

Statistical Analysis

[Name of the Institute]

Question 4-22

Equations

Price = a1 + ß1 Area

Price = a2 + ß2 Bed

Price = a3 + ß3 Age

Result

SUMMARY OUTPUT OF Price = a1 + ß1 Area

Regression Statistics

Multiple R

0.803

R Square

0.645

Adjusted R Square

0.622

Standard Error

22069.14

Observations

17

ANOVA

 

df

SS

MS

F

Significance F

Regression

1

1.33E+10

1.33E+10

27.34216

0.000102

Residual

15

7.31E+09

4.87E+08

Total

16

2.06E+10

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

2367.261

22118.79

0.107025

0.916188

-44777.8

49512.34

-44777.8

49512.34

Area

46.60112

8.912098

5.228973

0.000102

27.60543

65.59681

27.60543

65.59681

SUMMARY OUTPUT OF Price = a2 + ß2 Bed

Regression Statistics

Multiple R

0.604196

R Square

0.365053

Adjusted R Square

0.322723

Standard Error

29545.75

Observations

17

ANOVA

 

df

SS

MS

F

Significance F

Regression

1

7.53E+09

7.53E+09

8.624012

0.010206

Residual

15

1.31E+10

8.73E+08

Total

16

2.06E+10

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

1923.469

39028.34

0.049284

0.961343

-81263.5

85110.41

-81263.5

85110.41

Bed

1923.469

12305.7

2.936667

0.010206

9908.767

62366.74

9908.767

62366.74

SUMMARY OUTPUT Price = a3 + ß3 Age

Regression Statistics

Multiple R

0.881338

R Square

0.776757

Adjusted R Square

0.761874

Standard Error

17519.23

Observations

17

ANOVA

 

df

SS

MS

F

Significance F

Regression

1

1.6E+10

1.6E+10

52.19143

2.95E-06

Residual

15

4.6E+09

3.07E+08

Total

16

2.06E+10

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

147670.9

6246.954

23.63886

2.77E-13

134355.8

160985.9

134355.8

160985.9

Age

-2424.16

335.5532

-7.22436

2.95E-06

-3139.37

-1708.94

-3139.37

-1708.94

Discussion

The equations to predict price of houses using the information about area, number of bedrooms and age of the house separately are shown above. F-statistic of first equation is significant depicting that the overall model is a good fit. On the other hand the value of adjusted R2 is not adequate enough. Typically, adjusted R2 greater than or equal to 0.8 is considered as an acceptable value showing that the dependent variable is explained by the independent variables in the regression equation. The coefficients estimated show that the average price of houses is $2367.26 irrespective the area. If a house is one square foot larger in the area then its price differ by an increase of $46.60. Values of t-statistic show that the coefficient estimated for the parameter ß1 is significant.

The second equation is also overall significant as depicted by the value of F statistic; however, value of adjusted R2 is very low. This shows that the explanatory variable included in the equation that is number of bedrooms is not enough to predict the price of the house. The obtained coefficients show that the average price of houses irrespective of the number of bedrooms is $1923.47 while if there is one more room in a house the price increases by $1923.47. According to the t statistics, the estimated relationship between price of a house and number of bedrooms is significant.

Although all the three equations are overall significant the third equation have the highest value of R2 which if approximated to one decimal place equals to 0.8 depicting that age of house is a stronger determinant of its price as compare to the area and the number of bedrooms. Estimated coefficients show that the average price of homes irrespective of age is $147670.9 while if a house is one year older than the price reduces by $2424.16. This coefficient of reduction is found to be statistically significant as depicted by the t statistic. Comparing the results of the above three regression equations, third equation is the best as only this equation have the larger value of adjusted R2.

Question 4-23

Equation

Price = a4 + ß4 Area + ?4 Bed

Result

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.804033

R Square

0.646469

Adjusted R Square

0.595964

Standard Error

22820.32

Observations

17

ANOVA

 

df

SS

MS

F

Significance F

Regression

2

1.33E+10

6.67E+09

12.80023

0.00069

Residual

14

7.29E+09

5.21E+08

Total

16

2.06E+10

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

5701.449

30165.65

0.189005

0.852802

-58997.4

70400.32

-58997.4

70400.32

Area

48.50544

14.53001

3.338293

0.004876

17.34167

79.66922

17.34167

79.66922

Bed

-2540.39

14985.9

-0.16952

0.867814

-34681.9

29601.17

-34681.9

29601.17

Discussion

In question 4-22, the three equations are simple regression models. The above equation is a multiple regression model as it includes more than one explanatory variable. F statistic shows overall significance of the model but adjusted R2 has lower value. One thing which is quite ...