Research and development spending. The National Science Foundation collects data on the research and development spending by universities and colleges in the United States.3 Here are the data for the years 2003 to 2007:

Year: 2003 2004 2005 2006 2007 Spending (billions of dollars): 40.1 43.3 45.8 47.7 49.4

(a) Make a scatterplot that shows the increase in research and development spending over time. Does the pattern suggest that the spending is increasing linearly over time?

(b) Find the equation of the least-squares regression line for predicting spending from year. Add this line to your scatterplot.

(c) For each of the five years find the residual. Use these residuals to calculate the standard error s. (Do these calculations with a calculator.)

(d) Write the regression model for this setting. What are your estimates of the unknown parameters in this model?

(e) Use your least-squares equation to predict research and development spending for the year 2001. The actual spending for that year was $32.8 billion. Add this point to your plot and comment on why your equation performed so poorly.