The National Association of Realtors maintains a database consisting of sales information on homes sold in the United States. In order to investigate the sales prices for single-family homes, a multiplier linear regression model is estimated using data on a sample of 28 recently sold, single-family homes. The dependent variable is the sales price (in $1000). Data on the region of the country in which the home is located and the total number of homes sold in the region during the month the home sold are collected and to be used as the independent variables. In order to include the region of the country in the model, the following dummy variables are created.

X1=1 if the region is NW; 0 otherwise

X2=1 if the region is S; 0 otherwise

X3=1 if the region is W; 0 otherwise

The default category for the dummy variables is NE.

The regression results are shown below.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.89
R Square	0.80
Adjusted R Square	0.78
Standard Error	4.72
Observations	28
ANOVA
	df	SS	MS	F	Significance F
Regression	4	19176.33	4794.082	2.508483	0.069883
Residual	23	43956.4	1911.148
Total	27	63132.73
	Coefficients	Standard Error	t Stat	P-value
Intercept	144.91	62.55	2.32	0.03
Volume	1.51	0.63	2.40	0.03
X1	-87.35	29.31	-2.98	0.01
X2	-172.09	67.43	-2.55	0.02
X3	-54.49	29.06	-1.88	0.07

1. Comment how well the model fits the data. Make sure to discussion the criteria used and interpret it.
2. Interpret the coefficient for X3.
3. Predict the sales price for a single-family home in region W with 246 homes sold during the month the house was sold.