Question

A real estate developer wishes to study the relationship between the size of home a client will purchase (in square feet) and other variables. Possible independent variables include the family income, family size, whether there is a senior adult parent living with the family (1 for yes, O for no), and the total years of education beyond high school for the husband and wife. The sample information is reported below. Family Size Senior Parent Education Family Square Feet 2,300 2,300 3,400 3,360 3,000 2,900 4,100 2,250 4,200 2,800 mino Income (0005) 60.8 68.4 104.5 89.3 72.2 113 125.4 83.6 133 NOVO mmt nun menm 95 ON Click here for the Excel Data File a. Develop an appropriate multiple regression equation using stepwise regression. (Use Excel data analysis and enter number of family members first, then their income and delete any insignificant variables. Leave no cells blank - be certain to enter "O" wherever required. R and R2 adj are in percent values. Round your answers to 3 decimal places.) 1 2 Step Constant Family Size t-statistic p-value Income t-statistic p-value R-Sq R-Sq(adj)

Answer 1

Answer:

a)

Step	1	2
Constant	1222.258	614.163
Family Size	515.484	319.173
t-statistic	5.149	3.317
p-value	0.001	0.013
Income		13.896
t-statistic		3.008
p-value		0.020
S	352.524	248.917
R-Sq	0.768	0.899
R-Sq(adj)	0.739	0.870

Explanation:

1. Size of a home vs the number of a family member

The regression analysis is done in excel by following steps

Step 1: Write the data values in excel. The screenshot is shown below,

Nm Square Feet Family Size 2200 2300 3400 2260

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

DATA REVIEW Data Analysis ? X Гок HE INSERT PAGE LAYOUT FORMULAS AL ZA X - Data Analysis Analysis Tools Fourier Analysis Histogram Moving Average Random Number Generation Rank and Percentile Regression Sampling t-Test: Paired Two Sample for Means t-Test: Two-Sample Assuming Equal Variances t-Test: Two-Sample Assuming Unequal Variances Cancel Help 36.6

Step 3: Select Input Y Range: 'Square Feet' column, Input X Range: 'Family Size' column then OK. The screenshot is shown below,

C D E F G A B 1 Square Feet Family Size 22001 2300 31 Regression Input Input Y Range: OK Cancel Input X Range: SAS1:SAS11 $B$1:$BS111 Constant is Zero 95 % Help Labels Confidence Level: Output options O Output Range: New Worksheet Ply:

The result is obtained. The screenshot is shown below,

F G H I SUMMARY OUTPUT 3 Regression Statistics 4 Multiple R 0.876476 5 R Square 0.768209 6 Adjusted R Squa 0.739236 7 Standard Error 352.5243 8 Observations 10 10 ANOVA 11 df 12 Regression 13 Residual 14 Total SSMS gnificance F 1 3294973 3294973 26.51391 0.000875 8 994187.1 124273.4 94289160 17 Intercept 18 Family Size Coefficientandard Err Stat P-value Lower 95%Upper 95% 1222.258 377.244 3.239966 0.011878 352.3317 2092.184 515.4839 100.1102 5.149166 0.000875 284.6294 746.3384

Conclusion:

The p-value for the variable Family size is 0.000875 which is less than 0.05 at a 5% significance level which means the independent variable fits the model significantly.

2. Size of a home vs the number of a family member and Income

Now add the variable Income and follow the similar steps as above. The screenshot of the result is shown below.

D SUMMARY OUTPUT Regression Statistics 4 Multiple R 0 .948093 5 R Square 0.89888 Adjusted R Square 0.869989 7 Standard Error 248.917 8 Observations 10 10 ANOVA df SSMSF gnificance F 2 3855442 1927721 31.1125 0.000329 7 433717.8 61959.69 9 4289160 12 Regression 13 Residual 14 Total 15 16 17 Intercept 18 Family Size 19 Income Coefficientsandard Errt Stat P-value Lower 95%Upper 95% 614.1632 334.4141 1.836535 0.108897 176.601 1404.927 319.1731 96.21383 3.317331 0.012812 91.66358 546.6827 13.89573 4.620191 3.007608 0.019729 2.97071 24.82074

Conclusion:

The p-value for the variable Family size is 0.0128 which is less than 0.05 at a 5% significance level which means the independent variable Family size fits the model significantly.

The p-value for the variable Income is 0.0197 which is less than 0.05 at a 5% significance level which means the independent variable income fits the model significantly.

b)

Answer: The significant variables in the final model are Income and Education

Explanation: Now adding a new independent variable Senior Parent in model 2.

The screenshot of the result is shown below,

B C D E F 1 SUMMARY OUTPUT Regression Statistics 4 Multiple R 0.951828 5 R Square 0.905977 6 Adjusted R Square 0.858966 7 Standard Error 259.2547 8 Observations 10 ANOVA df 12 Regression 13 Residual Total SS 3 3885882 6 403278 9 4289160 MS F gnificance F 1295294 19.27148 0.001753 67213 17 Intercept 18 Family Size 19 Income 20 Senior Parent Coefficientandard Err Stat P-value Lower 95%Upper 95%d 680.6283 362.0346 1.880009 0.109154 -205.238 1566.495 311.8171 100.804 3.093299 0.021298 65.15845 558.4757 13.85969 4.812368 2.880014 0.028057 2.084246 25.63513 -121.911 181.1538 -0.67297 0.526024 -565.178 321.3567

Conclusion:

	P-value
Family Size	0.021298	<	0.05	Significant
Income	0.028057	<	0.05	Significant
Senior Parent	0.526024	>	0.05	Not Significant

The independent variable Senior Parent is not significant in the model. Hence not included in the next step.

Now adding a new independent variable Education.

The screenshot of the result is shown below,

B C D E F G A 1 SUMMARY OUTPUT 3 Regression Statistics 4 Multiple R 0 .977698 5 R Square 0.955893 6 Adjusted R Squar 0.93384 7 Standard Error 177.5677 8 Observations 10 ONS 10 ANOVA 12 Regression 13 Residual 14 Total df SSMS F gnificance F 3 4099978 1366659 43.34435 0.000185 6 189181.7 31530.28 9 4289160 17 Intercept 18 Family Size 19 Income 20 Education Coefficientsandard Errt Stat P-value Lower 95%Upper 95%0! 909.5253 261.0716 3.483815 0.013082 270.706 1548.345 179.7043 84.96385 2.115067 0.078819 -28.1948 387.6033 19.70218 3.899986 5.051859 0.002329 10.15926 29.2451 -67.1924 24.1275 -2.78489 0.031791 -126.23 -8.1545

Conclusion:

	P-value
Family Size	0.078819	>	0.05	Not Significant
Income	0.002329	<	0.05	Significant
Education	0.031791	<	0.05	Significant

The independent variable Family Size is not significant in the model. Hence not included in the final model.

Final model with independent variable Income and Education

The screenshot of the result is shown below,

B C D E 1 SUMMARY OUTPUT Regression Statistics 4 Multiple R 0.960733 5 R Square 0.923008 6 Adjusted R Square 0.90101 7 Standard Error 217.2006 8 Observations 10 ANOVA df 12 Regression 13 Residual 14 Total SS 2 3958927 7 330232.7 9 4289160 MS F gnificance F 1979464 41.95903 0.000127 47176.1 17 Intercept 18 Income 19 Education Coefficientandard Errt Stat P-value Lower 95%Upper 95% 1102.445 299.2184 3.684417 0.007814 394.9064 1809.984 26.12177 2.995625 8.719973 5.24E-05 19.03824 33.20529 -97.2719 23.84086 -4.08005 0.004689 -153.647 -40.8973

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