Question
A realtor wishes to investigate what type of homes would attract residents in a neighborhood. The realtor collected sample data that contains the following information
A realtor wishes to investigate what type of homes would attract residents in a neighborhood. The realtor collected sample data that contains the following information about some single-family houses recently sold in the neighborhood.
y = price in $1,000s (PRICE)
x1 = age of the house in years (AGE)
x2 = size of the house in square feet (SIZE)
x3 = number of bedrooms (BEDROOMS)
x4 = number of rooms (ROOMS)
The realtor conducted a regression analysis using the following model:
y = β0 + β1 x1 + β2 x2 + β3 x3 + β4 x4 + ε
A portion of the regression results from Excel is shown below.
Regression Statistics | |
---|---|
Multiple R | 0.90 |
R Square | 0.81 |
Adjusted R Square | 0.79 |
Standard Error | 13.10 |
Observations | 45 |
ANOVA | |||||
---|---|---|---|---|---|
df | SS | MS | F | Significance F | |
Regression | 4 | 28340.23 | 7085.06 | 41.31 | 1.07E-13 |
Residual | 40 | 6860.06 | 171.50 | ||
Total | 44 | 35200.29 |
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
---|---|---|---|---|---|---|
Intercept | 21.56 | 9.17 | 2.35 | 0.02 | 3.03 | 40.09 |
AGE | -0.27 | 0.09 | -2.89 | 0.01 | -0.46 | -0.08 |
SIZE | 0.05 | 0.01 | 7.41 | 5.00E-09 | 0.04 | 0.06 |
BEDROOMS | -10.69 | 4.64 | -2.30 | 0.03 | -20.07 | -1.30 |
ROOMS | 3.75 | 2.19 | 1.71 | 0.09 | -0.68 | 8.18 |
please answer both parts
The descriptive statistics of the data is given below:
PRICE | AGE | SIZE | BEDROOMS | ROOMS | |
Mean | 75.72 | 31.91 | 1,498.60 | 2.93 | 6.22 |
Median | 71.00 | 26 | 1,486 | 3 | 6 |
Minimum | 34.00 | 9 | 416 | 1 | 3 |
Maximum | 152.50 | 102 | 3,600 | 5 | 10 |
Consider a house in the neighborhood that is 10 years old and has 2,400 square feet, 4 bedrooms, and 8 rooms. Based on the regression output, the predicted selling price of this house is __________.
For houses with a given square footage and a number of bedrooms, if the number of rooms stays the same, then for every one-year older in age of the house, the average price is expected to drop by $ __________.
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