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 R0.90
R Square0.81
Adjusted R Square0.79
Standard Error13.10
Observations45


ANOVA

dfSSMSFSignificance F
Regression428340.237085.0641.311.07E-13
Residual406860.06171.50

Total4435200.29




CoefficientsStandard Errort StatP-valueLower 95%Upper 95%
Intercept21.569.172.350.023.0340.09
AGE-0.270.09-2.890.01-0.46-0.08
SIZE0.050.017.415.00E-090.040.06
BEDROOMS-10.694.64-2.300.03-20.07-1.30
ROOMS3.752.191.710.09-0.688.18

please answer both parts

The descriptive statistics of the data is given below:


PRICEAGESIZEBEDROOMSROOMS
Mean75.7231.911,498.602.936.22
Median71.00261,48636
Minimum34.00941613
Maximum152.501023,600510


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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