Question

Show your work. Carry out all calculations to at least 3 significant digits.

A real estate study was conducted in the school district of Alhambra to determine what variables influenced the market value of a house (denoted by PRICE in $1,000s). Four possibly important variables – HOUSE (the house size in 1,000s of square feet), LOT (the lot size in 1,000s of square feet), BED (the number of bedrooms), BATH (the number of bathrooms), and AGE (the age of the house in years) – were examined. Listed in the table are data collected in 2003.

MAKE SURE TO ADD EXCEL STEPS:

HOUSE BED PRICE LOT BАTH AGE 1.152 3.959 315 3 2 88 6.500 1.177 319 2 1 71 349 1.087 6.503 3 1 89 6.520 1.338 360 3 15 79 6.724 380 1.485 2 1.5 75 389 1.646 5.920 3 2 46 6.247 424 1.652 4 2 49 1.680 6.300 1.5 425 4 43 438 1.700 6.400 3 2 39 1.5 450 1.768 6.300 4 38 2.105 7.200 458 4 2.5 43 2.150 7.300 468 4 3 46 2.000 7.155 488 4 36 2.321 8.250 498 3 40 2.400 8.100 505 4 2 25 2.525 8.250 4 3 35 515 535 2.570 8.300 28 4 9.640 545 2.571 4 33 3.016 8.948 550 4 13 The following regression model is to be fitted to the data: Bo BHOUSE + P2LOT BABATH + B5AGE + e. PRICE BBED

1. Report the regression results (including coefficient estimates, standard errors, and R 2).

2. The model has five different explanatory variables. Evaluate whether the coefficient on every explanatory variable (except for AGE) significantly differs from zero. Use α = 0.05 and 0.01.

3. Interpret the coefficient estimate of β3.

4. How would you test the significance of the age effect on a house’s market value? Conduct the test using α = 0.01.

5. Compute the adjusted R2 value from the R2 value.

6. Compute the fair market price (in $) of a 40 year old house in the same school district with a house size of 1,900 square feet, a lot size of 7,100 square feet, 3 bedrooms and 2 bathrooms.

Answer 1

	Coefficients	Standard Error	t Stat	P-value
?0	217.2183	49.311	4.405	0.0007
?1	23.6670	27.211	0.870	0.4002
?2	18.0645	5.692	3.174	0.0073
?3	20.3497	7.401	2.749	0.0166
?4	14.1973	9.447	1.503	0.1568
?5	-1.0468	0.382	-2.739	0.0169

Multiple R=0.987659648

R² =0.97547158

At 5% level of significance, coefficients ?₁ , ?₄ are not significantly different from zero since their respective p-values are more than 0.05. While, at 1% level of significance, all five slope coefficients are not significantly different from zero since, their respective p-values are greater than 0.01.

The coefficient ?₃ is significantly different from zero at 5% level of significance and its value is 20.3497. Therefore, one unit change in no. of bedrooms will result in 20.34 unit change in prices.

We will use t-test to test the significance of the age effect on a house’s market value. H₀: ?₃=0

t = ?₅- ?₅(H₀)/standard error = -1.0468-0/0.382=-2.739

Sine |t| calculated is 2.739 which is greater than t-critical (2.552) at 18 df at 1% level of significance. Therefore, we reject null hypothesis. Hence, the coefficient which measures (?₅) age effect on a house’s market value is significantly different from zero.

Adjusted R² =1 – (1-R²)*n-1/n-k = 1- (1-0.97547158)*19-1/19-6= 0.9659

Market price of the house = 217.2183 + 23.6670*1.900 + 18.0645*7.100 + 20.3497*3 + 14.1973*2 + (-1.0468)*40

                                                =217.2183 + 44.9673 + 128.25795 + 61.0491 + 28.3946 -41.872

                                                = 438.01525