The following data give the selling price, square footage, number of bedrooms, a

Question

The following data give the selling price, square footage, number of bedrooms, and the age of the houses that have sold in a neighborhood in the past 6 months. Develop three regression models to predict the selling price based upon each of other the other factors individually. Which of these is the best?

Second part of question...

Using the above data and develop a regression model to predict selling price based on the square footage and number of bedrooms.  Use this to predict the selling price of a 2,000 square foot house with 3 bedrooms. Compare this model with the above models. Should the number of bedrooms be included in the model? Why or why not?

Selling Price($) Square Footage Bedrooms Age (Years) 84,000 1,670 2 30 79,000 1,339 2 25 91,500 1,712 3 30 120,000 1,840 3 40 127,500 2,300 3 18 132,500 2,234 3 30 145,000 2,311 3 19 164,000 2,377 3 7 155,000 2,736 4 10 168,000 2,500 3 1 172,500 2,500 4 3 174,000 2,479 3 3 175,000 2,400 3 1 177,500 3,124 4 0 184,000 2,500 3 2 195,500 4,062 4 10 195,000 2,854 3 3

Explanation / Answer

Using Excel's regression datapack:

Selling price = $26532.24 + 51.03*Square Footage

Selling price = $20331.63 + 41403.06* No. of Bedrooms

Selling price = $182504.7 - 2424.91 * Age

Using the model with the highest R square and adjusted R Square, one can see the best model is the 3rd one - Age of the house. Using p-value also, one can see that Age of the house has the lowest p-value, which means that it is the most significant of the variables.

Using both sq footage and no of bedrooms:

Selling price = 24202.38 + 49.70*Sq Footage + 1775.16*no of bedrooms

=24202.38+49.70*2000 + 1775.16*3 = $128,927.9

As can be seen in the descriptive stats, p-value of square footage is 0.0033 but that of bedrooms is very high 0.904. This means that bedrooms is an insignificant factor in deciding selling price. Hence, it can be excluded from the model.

SUMMARY OUTPUT Regression Statistics Multiple R 0.83664 R Square 0.699967 Adjusted R Square 0.679965 Standard Error 21360.3 Observations 17 ANOVA df SS MS F Significance F Regression 1 1.6E+10 1.6E+10 34.99449 2.83E-05 Residual 15 6.84E+09 4.56E+08 Total 16 2.28E+10 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 26532.24 21408.36 1.23934 0.234261 -19098.6 72163.07 -19098.6 72163.07 Square Footage 51.02721 8.625852 5.915614 2.83E-05 32.64164 69.41278 32.64164 69.41278

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