Interpret the coefficient for the size of the apartment. Find the correlation coefficient between Price and Lot Size.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Part c and d

Q1) A real estate consultant is considering developing a series of price models for
residential houses in different areas of the province of Ontario, in Canada. The
dataset, provided by the Windsor and Essex County Board, covers residential home
sales in Windsor. To develop the model, the consultant performs a linear regression to
estimate the price (in Canadian dollars) as a linear function of the size of the
apartment (in square feet) and obtains the following Excel result.
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.53580413
0.28708607
0.28577556
41101.9362
546
ANOVA
df
MS
Significance F
1 3.70082E+11 3.7008E+11 219.065461 6.74643E-42
Regression
Residual
Total
544 9.19017E+11 1689369158
545
1.2891E+12
Coefficients Standard Error
62171.5874 4537.036582 13.7031268 6.2969E-37 53259.33066 71083.8441
t Stat
P-value
Lower 95%
Upper 95%
Intercept
LOTSIZE
12.0187669
0.81203165 14.8008601 6.7464E-42 10.42366523 13.6138685
a) Write the regression equation.
b) Predict the price for LOTSIZE = 4000. Round your answer to two decimal places.
c) Interpret the coefficient for the size of the apartment.
d) Find the correlation coefficient between Price and Lot Size. Round your answer to
three
decimals.
Transcribed Image Text:Q1) A real estate consultant is considering developing a series of price models for residential houses in different areas of the province of Ontario, in Canada. The dataset, provided by the Windsor and Essex County Board, covers residential home sales in Windsor. To develop the model, the consultant performs a linear regression to estimate the price (in Canadian dollars) as a linear function of the size of the apartment (in square feet) and obtains the following Excel result. SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.53580413 0.28708607 0.28577556 41101.9362 546 ANOVA df MS Significance F 1 3.70082E+11 3.7008E+11 219.065461 6.74643E-42 Regression Residual Total 544 9.19017E+11 1689369158 545 1.2891E+12 Coefficients Standard Error 62171.5874 4537.036582 13.7031268 6.2969E-37 53259.33066 71083.8441 t Stat P-value Lower 95% Upper 95% Intercept LOTSIZE 12.0187669 0.81203165 14.8008601 6.7464E-42 10.42366523 13.6138685 a) Write the regression equation. b) Predict the price for LOTSIZE = 4000. Round your answer to two decimal places. c) Interpret the coefficient for the size of the apartment. d) Find the correlation coefficient between Price and Lot Size. Round your answer to three decimals.
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