1
ISOM111 Business Statistics
Exercise for Tutorial Set 7
Linear Regression and Correlation
1.
Many variables influence the sales of homes.
One of these is the interest rate charged for mortgage loans.
The table below shows the number of homes sold annually and the annual mortgage rate from 1989 to 1998 in
a city.
Year
Home sold (in 1,000)
Interest rate (in %)
1989
321
12.2
1990
356
10.0
1991
352
10.1
1992
359
10.3
1993
334
10.2
1994
321
10.0
1995
322
9.2
1996
352
8.4
1997
380
7.3
1998
394
8.5
a)
State the dependent variable and the independent variable in this question.
b)
Find the estimated linear regression equation of the number of homes sold on the interest rate.
c)
Interpret the meaning of the Y intercept of this regression.
Explain briefly whether you think it is meaningful to interpret.
d)
Compute the standard error of the estimate.
e)
Calculate the sample correlation coefficient between X and Y.
f)
Do the data provide sufficient evidence to indicate that mortgage interest rates contribute information for
the prediction of annual sales of homes?
Use significance level = 10%.
g)
Market analysts predict the mortgage interest rate to be 9.5% and 11.0% in 1999 and 2000 respectively.
Estimate the number of homes sold for the year 1999 and 2000 under the assumption that the analysts’
forecasts are accurate.
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 Fall '08
 HU
 Regression Analysis, Interest Rates, Interest, Interest Rate, Sales, regression model

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