RailTrailsHouseValues.xlsx has a number of variables relating to a set of houses
ID: 3152254 • Letter: R
Question
RailTrailsHouseValues.xlsx has a number of variables relating to a set of houses in two towns in Western Massachusetts. The worksheet Var Defs in this spreadsheet gives the variable definitions. We want to predict price2014, the Zillow estimated house price in 2014. The Zip variable is numeric but actually represents a category so an indicator variable has been created to represent this variable.
a) What is the regression equation?
b) Interpret the coefficients of the regression equation.
c) Predict price2014 for a house with 1800 square feet.
d) House number 35 happens to have 1800 square feet but price2014 for this house is different from what you
calculated in part c. Is this surprising? Why or why not?
e) What is the coefficient of determination and what does it tell you?
f) What is the standard error of the estimate?
g) Say you want to run a test to determine if the slope of the regression line is truly different from 0. Specify
the test. What is the p-value for this test? Would you reject the null hypothesis at = .01?
Explanation / Answer
From Excel
a) The regression equation is
y=a+bx
from excel
The fitted regression equation is
y=43.77 +159.17 (Square feet)
b)
Intercept=43.77
and Slope=159.17
C)
Predict price2014 for a house with 1800 square feet.
when x=1800
now y=43.77 +159.17 (Square feet)
y=43.77 +159.17 (1800)
y=286549.77
e)
From excel
coefficient of determination = 0.643
f) standard error=66.61
SUMMARY OUTPUT Regression Statistics Multiple R 0.801669232 R Square 0.642673558 Adjusted R Square 0.639170357 Standard Error 66.61057414 Observations 104 ANOVA df SS MS F Significance F Regression 1 813976.3793 813976.4 183.4533 1.57E-24 Residual 102 452570.7959 4436.969 Total 103 1266547.175 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 43.77115824 19.53218673 2.240976 0.027195 5.029158 82.51316 5.029158 82.51316 squarefeet 159.1689474 11.75156264 13.54449 1.57E-24 135.8598 182.4781 135.8598 182.4781Related Questions
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