Question

Part 1

An important problem in real estate is determining how to price homes to be sold. There are so many factors—size, age, and style of the home; number of bedrooms and bathrooms; size of the lot; and so on—which makes setting a price a challenging task. In this project, we will try to help realtors in this task by determining how different characteristics of homes relate to home prices, identifying the key variables in pricing, and building multiple-variable regression models to predict prices based on property characteristics. Our analysis will be based on the Mount Pleasant Real Estate Data (available on stat.hawkeslearning.com). This data set includes information about 195 properties for sale in three communities in the suburban town of Mount Pleasant, South Carolina, in 2017. Consider the following variables associated with each property.

x1= number of bedrooms	x5=age
x2=number of bathrooms	x6=fenced yard
x3=number of stories	x7=golf course?
X4=square footage	x8=number of fireplaces

1. Perform a hypothesis test to determine if the model is useful for predicting home values at a significance level of α = 0.05. State the followings:

1. Determine the null and alternative hypotheses.                                   (2 Points)
2. What is the value of the test statistics (F statistics)?                                           (2 Points)

65.04884

3. Determine the P-value.                                                                 (2 Points)
4. Make a decision to reject or fail to reject H₀.                                          (2 Points)
5. State the conclusion in terms of the original question.                     (2 Points)

2. Are any variables not useful predictors of home price at a significance level of α = 0.05? State the P-values of these variables. Intuitively, what does this mean with respect to pricing properties? (Show your results)                                                    (8 Points)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.858306
R Square	0.73669
Adjusted R Square	0.725364
Standard Error	94030.87
Observations	195
ANOVA
	df	SS	MS	F	Significance F
Regression	8	4.6E+12	5.75E+11	65.04884	7.3335E-50
Residual	186	1.64E+12	8.84E+09
Total	194	6.25E+12

Answer 1