Question 3 The Bank of Canada is interested in studying the relationship between mortgage rates and median home prices. The data is provided below Year interest rate (%) 1988 10.30 1989 10.30 1990 10.10 1991 9.30 1992 8.40 1993 7.30 1994 8.40 1995 7.90 1996 7.60 1997 7.60 1998 6.90 1999 7.40 2000 8.10 2001 7.00 2002 6.50 2003 5.80 2004 5.80 2005 5.80 2006 6.40 2007 6.30 2008 6.00 2009 5.00 2010 4.70 2011 4.40 2012 3.60 2013 4.00 2014 4.10 2015 3.80 2016 3.60 2017 4.00 Median home price $183,800 $183,200 $174,900 $173,500 $172,900 $173,200 $173,200 $169,700 $174,500 $177,900 $188,100 $203,200 $230,200 $258,200 $309,800 $329,800 $431,000 $515,000 $537,000 $496,000 $352,000 $232,000 $291,700 $262,900 $299,200 $321,200 $373,500 $358,100 $382,500 $402,900 a) Estimate a simple linear regression model and find the value of the parameters for the estimation of mortgage rates and the median home price b) Interpret the intercept and the slope coefficients c) State the correlation coefficient and the coefficient of determination. Interpret the coefficient of determination d) Confirm the intercept, slope and correlation coefficient by computing them without SPSS e) At the 5% significance level, determine if the model is useful. In responding, construct and test any appropriate hypothesis.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Question 3

The Bank of Canada is interested in studying the relationship between mortgage rates and median home prices. The data is provided below

Year interest rate (%)

1988 10.30
1989 10.30
1990 10.10
1991 9.30
1992 8.40
1993 7.30
1994 8.40
1995 7.90
1996 7.60
1997 7.60
1998 6.90
1999 7.40
2000 8.10
2001 7.00
2002 6.50
2003 5.80
2004 5.80
2005 5.80
2006 6.40
2007 6.30
2008 6.00
2009 5.00
2010 4.70
2011 4.40
2012 3.60
2013 4.00
2014 4.10
2015 3.80
2016 3.60
2017 4.00

Median home price

$183,800 $183,200 $174,900 $173,500 $172,900 $173,200 $173,200 $169,700 $174,500 $177,900 $188,100 $203,200 $230,200 $258,200 $309,800 $329,800 $431,000 $515,000 $537,000 $496,000 $352,000 $232,000 $291,700 $262,900 $299,200 $321,200 $373,500 $358,100 $382,500 $402,900

a) Estimate a simple linear regression model and find the value of the parameters for the estimation of mortgage rates and the median home price
b) Interpret the intercept and the slope coefficients

c) State the correlation coefficient and the coefficient of determination. Interpret the

coefficient of determination

d) Confirm the intercept, slope and correlation coefficient by computing them without SPSS
e) At the 5% significance level, determine if the model is useful. In responding, construct and test any appropriate hypothesis.

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