Question

Solve 4-23 Please

4-22 The following data give the selling price, square footage, number of bedrooms, and age of 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 the other factors individually. Which of these is best? SELLING PRICE (S) SQUARE FOOTAGE BEDROOMS AGE (YEARS) 84,000 1,670 79,000 1,339 91,500 1,712 120,000 1,840 127.500 2,300 132.500 2,234 145.000 2,311 164.000 2,377 155,000 2,736 168,000 2,500 172,500 2,500 174.000 2,479 175.000 2,400 177.500 3,124 184.000 2,500 195,500 4,062 195.000 2,854 4-23 Use the data in Problem 4-22 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 three bedrooms. Compare this model with the models in Problem 4-22. Should the number of bedrooms be included in the model? Why or why not?

Answer 1

The regression output is:

	R²	0.698
	Adjusted R²	0.655
	R	0.835
	Std. Error	22146.755
	n	17
	k	2
	Dep. Var.	Selling Price ($)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	15,84,72,67,997.5409	2	7,92,36,33,998.7704	16.15	.0002
Residual	6,86,67,02,590.6944	14	49,04,78,756.4782
Total	22,71,39,70,588.2353	16
Regression output					confidence interval
variables	coefficients	std. error	t (df=14)	p-value	95% lower	95% upper
Intercept	24,824.3937
Square Footage	49.6254	14.1011	3.519	.0034	19.3814	79.8693
Bedrooms	1,602.2866	14,543.5756	0.110	.9138	-29,590.5807	32,795.1539
Predicted values for: Selling Price ($)
			95% Confidence Interval		95% Prediction Interval
Square Footage	Beedrooms	Predicted	lower	upper	lower	upper
2,000	3	1,28,882.029	1,13,765.831	1,43,998.227	79,034.705	1,78,729.352

The regression model is:

Selling Price = 24,824.3937 + 49.6254*Square Footage + 1,602.2866*Bedrooms

The predicted selling price of a 2,000 square feet house with three bedrooms is 1,28,882.029.

The number of beds is not a significant independent variable, therefore, it should not be included in the model.

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