Question

 

Ann Perkins, a realtor in Brownsburg, Indiana, would like to use estimates from a multiple regression model to help prospective sellers determine a reasonable asking price for their homes. She believes that the following four factors influence the asking price (Price) of a house:

1. The square footage of the house (SQFT)
2. The number of bedrooms (Bed)
3. The number of bathrooms (Bath)
4. The lot size (LTSZ) in acres

She randomly collects online listings for 50 single-family homes. .

Requirements and associated point values:

Part 1 – Provide summary statistics (with Excel Data Analysis) by calculating the mean and standard deviation on the asking price, square footage, the number of bedrooms, the number of bathrooms, and the lot size. Explain each factor’s mean and standard deviation. What does each of these summary statistics tell us.

Part 2 – Estimate and interpret a multiple regression model where the asking price is the response variable and the other four factors are the explanatory variables.

The end result should be a Excel Regression Output

SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adj. R Square
Standard Error
Observations
ANOVA
	Df	SS	MS	F	Significance F
Regression
Residual
Total
	Coefficients	Standard Error	t Stat	P-value	Lower 95%		Upper 95%
Intercept
SQFT
Bed
Bath
LTSZ

Also provide the estimate model equation: Price =

Answer 1

part 1 )

	Price	SQFT	Bed	Bath	LTSZ
Mean	208789.320	2.598	3.560	2.490	0.818
Standard Deviation	79636.520	1.016	0.675	0.746	1.375

mean and standard deviation on each variable is above

you can generate by data-> data analysis -> descriptive statistics

check on summary statistics

for each variable

The statistical mean refers to the mean or average that is used to derive the central tendency of the data in question. It is determined by adding all the data points in a population and then dividing the total by the number of points.We derive the average and call as mean.

The standard deviation of a dataset gives you a measure of how spread out it is. On an average, it helps you ascertain how close each point is from the mean

for example average price is 208789.320

and sd of price is 79636.520

part 2)

using data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.91940202
R Square	0.845300074
Adjusted R Square	0.83154897
Standard Error	32685.04673
Observations	50
ANOVA
	df	SS	MS	F	Significance F
Regression	4	262682738715.9840	65670684678.9961	61.4714	0.0000
Residual	45	48074052582.8958	1068312279.6199
Total	49	310756791298.8800
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	23714.6259	25435.2663	0.9324	0.3561	-27514.6301
SQFT	44971.6764	6262.3653	7.1813	0.0000	32358.6252
Bed	-5028.7156	7921.0849	-0.6349	0.5287	-20982.5995
Bath	26142.4324	8917.5724	2.9316	0.0053	8181.5196
LTSZ	25725.1240	3437.0852	7.4846	0.0000	18802.4790