Question

A company has recorded data on a sample of real estate listings from Waltham, MA. The variables are:

PRICE -- List price, thousands of dollars
SQFT -- Square footage
BEDS -- Number of bedrooms
BATHS -- Number of bathrooms
HWY -- A dummy variable (1 = close to highways; 0 = far from highways).

Use Excel's Regression tool to answer the following questions:

PRICE	SQFT	BEDS	BATHS	HWY
713	2400	3	3	0
645	2524	3	2	1
625	2732	4	2.5	1
585	1947	3	1.5	0
583	2224	3	2.5	0
540	1488	3	1.5	0
511	1752	3	1.5	0
463	1714	3	2	1
435	1500	3	1.5	1
402	1152	3	1	1
380	1272	3	1	1
368	1272	3	1	1
356	1431	2	2	1
330	1465	3	1	0
308	850	1	1	0

Fill in Multiple Blanks. For all numerical answers, show two (2) digits to the right of the decimal point, for example, 1.00, 1.20, 1.22. Apply the appropriate rounding rule if necessary. Hint: You can use the “Format Cell” option in the Regression output so that it shows two digits after the decimal point. Excel will automatically round the values up or down, if necessary.

1. The estimated regression line is (enter the estimated coefficients in the appropriate space):

PRICEhat = Blank 1 + Blank 2 SQFT + Blank 3 BEDS + Blank 4 BATHS + Blank 5 HWY

2. On average, a house with 4 bedrooms will be Blank 6 thousand dollars Blank 7 (cheaper, more expensive) than a house with 2 bedrooms, ceteris paribus.

3. On average, a house located close to highways will be Blank 8 thousand dollars Blank 9 (cheaper, more expensive) than a house located far from highways, ceteris paribus.

4. Predict PRICE for a house with square footage of 1960, 2 bedrooms and 2.5 bathrooms, which is located far from highways. PRICEhat = Blank 10 (in thousands of dollars).

5. At 90% confidence, SQFT Blank 11 (is, is not) significantly related to PRICE.

6. At 90% confidence, BEDS Blank 12 (is, is not) significantly related to PRICE.

7. At 90% confidence, BATHS Blank 13 (is, is not) significantly related to PRICE.

8. At 90% confidence, HWY Blank 14 (is, is not) significantly related to PRICE.

9. True or false? At 90% confidence, a significant relationship exists between PRICE and the set of all the independent variables included in the regression model (SQFT, BEDS, BATHS, and HWY). Blank 15 (true, false).

10. True or false? About 85% of the variability in PRICE is explained by the set of all the independent variables included in the regression model (SQFT, BEDS, BATHS, and HWY), and about 15% of the variability in PRICE is explained by the other factors not included in the regression. Blank 16 (true, false).

Answer 1

The regression output is:

	R²	0.848
	Adjusted R²	0.788
	R	0.921
	Std. Error	58.681
	n	15
	k	4
	Dep. Var.	PRICE
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,92,572.1786	4	48,143.0446	13.98	.0004
Residual	34,434.7548	10	3,443.4755
Total	2,27,006.9333	14
Regression output					confidence interval
variables	coefficients	std. error	t (df=10)	p-value	95% lower	95% upper
Intercept	115.21
SQFT	0.16	0.0712	2.184	.0539	-0.0031	0.3140
BEDS	23.27	36.9245	0.630	.5427	-59.0021	105.5435
BATHS	36.37	49.0941	0.741	.4759	-73.0200	145.7568
HWY	-49.07	32.1388	-1.527	.1578	-120.6843	22.5352
Predicted values for: PRICE
					95% Confidence Interval		95% Prediction Interval
SQFT	BEDS	BATHS	HWY	Predicted	lower	upper	lower	upper	Leverage
1,960	2	2.5	0	557.35	469.771	644.931	399.979	714.722	0.449

1. The estimated regression line is (enter the estimated coefficients in the appropriate space):

PRICEhat = 115.21 + 0.16 SQFT + 23.27 BEDS + 36.37 BATHS - 49.07 HWY

2. On average, a house with 4 bedrooms will be 46.54 thousand dollars more expensive than a house with 2 bedrooms, ceteris paribus.

3. On average, a house located close to highways will be 49.07 thousand dollars cheaper than a house located far from highways, ceteris paribus.

4. Predict PRICE for a house with square footage of 1960, 2 bedrooms and 2.5 bathrooms, which is located far from highways. PRICEhat = Blank 10 (in thousands of dollars).
PRICEhat = 557.35 (in thousands of dollars)

5. At 90% confidence, SQFT Blank 11 is significantly related to PRICE.

6. At 90% confidence, BEDS is not significantly related to PRICE.

7. At 90% confidence, BATHS is not significantly related to PRICE.

8. At 90% confidence, HWY is not significantly related to PRICE.

9. True or false? At 90% confidence, a significant relationship exists between PRICE and the set of all the independent variables included in the regression model (SQFT, BEDS, BATHS, and HWY). true

10. True or false? About 85% of the variability in PRICE is explained by the set of all the independent variables included in the regression model (SQFT, BEDS, BATHS, and HWY), and about 15% of the variability in PRICE is explained by the other factors not included in the regression. true