Outcome 4: Multiple Regression: A real estate agency wishes to develop a regression model that can be used to predict th

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Outcome 4: Multiple Regression: A real estate agency wishes to
develop a regression model that can be used to predict the sales
prices of future homes it will list. In order to do so the agency
collects data on the following:
Y = Home Sale Price (in $1000)
X1 =
Home Size (in # of square feet)
X2 =
Rating [1-10] (an “overall niceness” rating for the house
expressed on a scale of
1 [worst] to 10 [best],
provided by the real estate agency)
1. Write the equation for linear regression [Y = b0
+ b1X1 + b2 X2 +
error] in terms of the variables and the estimated
coefficients.
2. Interpret the value of adjusted R2 for the
model. Comment on the goodness of fit of the model.
3. Use the coefficient estimates to describe the relationship
between Home Size and Sale Price of a house; Rating and Sale Price
(in the units given above).
4. Calculate the predicted sale price of a house with 2000
square feet and a rating of 8.
5. Conduct a test of hypothesis using a = 0.05, for
b1, and b Compare the model t-stats for each independent
variable against the critical t-value for a
2-sided test and determine if the variable is significant in
explaining home price
H0:
bj = 0
HA: bj ≠ 0
a. Sample size n =
; ii. Critical t-value or
z-value =
b. Use the t-stats from the Excel output to determine if you
should accept or reject the H0 for
b1, and b2.
(include the t-stats from the Excel output in your
answer)
c. What conclusions can you draw about the significance of Home
Size and Rating in determining the Sale Price of a home?
Explain.