Description

• PRICE: selling price of house in thousands of dollars
• BDR: number of bedrooms
• FLR: floor space in sq. ft.
• FP: number of fireplaces
• RMS: number of rooms ST: storm windows (1 if present, 0 if
• absent)
• LOT: front footage of lot in feet
• TAX: annual taxes
• BTH: number of bathrooms
• CON: construction (0 if frame, 1 if brick)
• GAR: garage size (0=no garage, 1=one-car garage, etc.)
• CDN: condition (1=”needs work”, 0 otherwise)
• L1: location (L1=1 if property is in zone A, L1=0 otherwise)
• L2: location (L2=1 if property is in zone B, L2=0 otherwise)
Based on some prior analysis, we have the following R output: Call:
lm(formula = Price FLR + RMS + BDR + BTH + ST + GAR + FP +LOT, data = house)
Coefficients:
Estimate Std.Error tvalue Pr(> |t|)
(Intercept) 18.64 5.24 3.56 0.0024 ∗∗
FLR 0.02 0.003 5.43 4.49e − 05 ∗ ∗ ∗
RMS 3.90 1.62 2.42 0.0272 ∗
BDR −7.70 1.83 −4.21 0.0006 ∗ ∗ ∗
BTH 2.37 2.56 0.93 0.3662
ST 10.82 2.30 4.70 0.0002 ∗ ∗ ∗
GAR 1.77 1.40 1.26 0.2243
FP 6.91 3.08 2.24 0.0387 ∗
LOT 0.26 0.14
1 1.95 0.0678 .
Multiple R-Squared: 0.9044, Adjusted R-squared: 0.8595 F-statistic: 20.11 on 8 and 17 DF, p-value: 3.147e-07
(1) Based on the R output, what would be the regression model you suggest?
(2) Write down the full model and reduced model associated with the following test and draw a conclusion based on this test (Note: This is a row obtained from the R output):
GAR 1.77 1.40 1.26 0.2243
(3) Write down the null hypothesis and alternative hypothesis associated with the F-statistic and what is the conclusion based on the test.
(4) The house for selling has 750 square feet of space, 5 rooms, 2 bedrooms, 1.5 baths, storm windows, a 1-car garage, 1 fireplace and a 25 front-foot lot. Analyze the housing price data. Based on this dataset, what can you tell this person about how much he could expect to get for the house? Please report your fitted model and also construct a confidence interval for the prediction (Hint: You can try different variable selection methods to find the final model).
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