Average price per square foot of floor area in new one-family houses sold. Price per square foot of floor area excludes value of improved lot Source: The National Association of Home Builders Year 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Price per square foot $55.18 $57.41 $60.21 $62.45 $64.38 $66.81 $67.83 $67.70 $70.43 $71.93 $75.68 $79.21 $85.13 $90.63 $91.99
Instead of working on portions of the scatter plots, we want to approximate the data by a line we can use to predict prices in the future. The line that will best fit the given data is called the linear regression. The approximation will be acceptable whether the determina- tion coefficient R (r**2) is close to 1 or the correlation coefficient r is close to -1 or +1.
a) using your entered data to find the equation y = ax + b of the best line through the data points and give the values of coefficients a and b, and of the determination coefficient R or correlation coefficient r.
b. Use Excel to plot the scatter plot and the regression line on the same graph.
c. Is the linear regression a visually good approximation of the data? Sustain your argument by a mathematical proof.
d. use the linear regression to predict the price per square foot area in 2009
e. In what year will the price per square foot be greater than $199?