Question

Using the data provided from the excel file entitled homes_asst1, estimate a sample regression function of a linear form to predict the sale price of a home using the acreage for the respective home. Present the results of the regression by pasting the excel output into your document, and then answer the questions below.

1. What is the value of the intercept a?
2. What is the value of the slope b?
3. What is the sale price for a home with 1.39 acres? Calculate the sample residual for this observation. Show your work.
4. Interpret the value of the R-squared for the regression model.

e. Which other 2 variable(s) in the data set, or just in general, do you think would also be a good predictor for the sale price of a home? Explain in a sentence or two.

Homes data to use for solving the problem:

Selling Price	Acres
400000	2.27
370000	0.75
382500	1
300000	0.43
305000	3.6
320000	1.7
321000	0.81
445000	2
377500	1.5
460000	1.09
265000	1.6
299000	0.42
385000	0.89
430000	4.79
214900	0.25
475000	11.58
280000	0.46
457000	1.84
210000	0.94
272500	1.39
268000	0.83
300000	0.57
477000	1.1
292000	0.52
379000	1
295000	0.9
499000	5.98
292000	2.93
305000	0.33
520000	1.53
308000	0.63
316000	2
355500	0.44
225000	0.62
270000	0.68
253000	0.68
310000	1.69
300000	0.83
295000	2.9
478000	2.14

Answer 1

	Coeff	SE	t-stat	lower t0.025(38)	upper t0.975(38)	Stand Coeff	p-value	VIF
b	-2.1395	1.2216	-1.7513	-4.6125	0.3336	0.000	0.08796
X1	0.00001118	0.000003467	3.2239	0.000004158	0.00001819	0.4634	0.002599	1.0000

Linear regression equation:

Y = -2.1395 + 0.00001118 X₁

a) The value of the intercept a = -2.1395

b) The value of the slope b = 0.00001118

c) The sale price for a home with 1.39 acres is

Y = -2.1395 + 0.00001118 X₁

Y = -2.1395 + 0.00001118(1.39)

Y = -2.14

Source	DF	Sum of Squares	Mean Square	F Statistic	P-value
Regression (between ŷiand yi)	1	33.7494	33.7494	10.3932	0.002599
Residual (between yiand ŷi)	38	123.3953	3.2472
Total(between yiand yi)	39	157.1447	4.0294

d)

R square (R²) equals 0.2148. It means that the predictors (X_i) explain 21.5% of the variance of Y.
Adjusted R square equals 0.1941.
The coefficient of multiple correlation (R) equals 0.4634. It means that there is a moderate direct relationship between the predicted data (ŷ) and the observed data (y).

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