The interest rate for a 30-year conventional mortgage and the median number of months homes were listed for sale are given in the table below. The data represent the values for April of each year. (Source: economagic.com.)
Year Interest, x Months, y
1991 9.49 7.3
1992 8.85 7.2
1993 7.47 6.1
1994 8.32 5.1
1995 8.32 4.8
1996 7.93 5.7
1997 8.14 4.6
1998 7.14 5.9
1999 6.92 4.6
2000 8.15 5
2001 7.08 5.3
2002 6.99 4.3
2003 5.81 4.7
2004 5.83 4.3
2005 5.86 4.4
2006 6.51 3.9
2007 6.18 5.8
2008 5.92 7.9
1. Draw a scatter diagram of the data, treating the interest rate as the explanatory variable.
2. Compute the linear correlation coefficient between the interest rate and the median number of months homes were listed for sale.
3. Is there a linear relation between the interest rate and the median number of months homes are listed for sale? That is, is the correlation statistically significant? (Compare your correlation to Table II.)
4. Delete the observation for the year 2008. Repeat problems (1) through (3).
5. Does it seem that the data for the year 2008 is inconsistent with the data for the other years? If so, can you speculate on the cause of this irregularity?
6. Continue to work without the data from 2008. Find the least squares regression line treating the interest rate as the explanatory variable and the median number of months as the response variable.
7. Interpret the slope and intercept, if appropriate.
8. Predict the median number of months required to sell a home if the interest rate is 5.92%. (This is the interest rate in 2008.)