07exLR - ISOM111 Business Statistics Exercise for Tutorial Set 7 Linear Regression and Correlation 1 Many variables influence the sales of homes One of

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.