A sample containing years to maturity and yield (percent) for 40 corporate bonds are contained in the data file named CorporateBonds (Barron’s, April 2, 2012).
a. Develop a scatter chart of the data using years to maturity as the independent variable.
Does a simple linear regression model appear to be appropriate?
b. Develop an estimated quadratic regression equation with years to maturity and squared values of years to maturity as the independent variables. How much variation in the sample values of yield does this regression model explain? Is the overall regression relationship significant at a 0.05 level of significance? If so, then test the relationship between each of the independent variables and the dependent variable at a 0.05 level of significance. How would you interpret this model?
c. Create a plot of the linear and quadratic regression lines overlaid on the scatter chart of years to maturity and yield. Does this helps you better understand the difference in how the quadratic regression model and a simple linear regression model fit the sample data? Which model does this chart suggest provides a superior fit to the sample data?
d. What other independent variables could you include in your regression model to explain more variation in yield?