Question 1: To determine how the number of housing starts is affected by mortgage rates (in percents), an economist recorded the mortgage rate and the number of housing starts in a large county for the past 10 years. The data are listed below. Rate 5.5 4.8 4.6 4.5 5.0 5.4 5.8 5.9 5.5 5.0
Starts 115 161 185 201 206 167 155 117 133 150
(a) State what are the explanatory and response variables.
(b) Make a scatterplot of the data.
(c) Briefly describe the direction, form, and strength of relationship between mortgage rate and number of housing starts.
d) Showing your work, find the equation of the least-squares regression line of the number of housing starts on the mortgage rate and graph it on your scatterplot.
e) Assess the fit of the least-squares regression line computed in part (d) by making and commenting on the residual plot.
f) By how much would you expect the number of housing starts to change for a one percent increase in the mortgage rate?
G How many housing starts would you predict for a year in which the mortgage rate is 5.2 percent? What would your answer be for a 1.0 percent mortgage rate and why might you not trust it?
(h) Showing your work, compute the sample correlation coefficient r between the mortgage rate and the number of housing starts, and interpret the value of r^2