Research and development spending. The National Science

Chapter , Problem 10.7

(choose chapter or problem)

Research and development spending. The National Science Foundation collects data on the research and development spending by universities and colleges in the United States. 8 Here are the data for the years 2003, 2006, and 2009:

\(\begin{array}{l|ccc}
\hline \text { Year } & 2003 & 2006 & 2009 \\
\hline \text { Spending (billions of dollars) } & 40.1 & 47.8 & 54.9 \\
\hline
\end{array}\)

Do the following by hand or with a calculator and verify your results with a software package.

(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 three years, find the residual. Use these residuals to calculate the standard error s.

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

(e) Compute a 95% confidence interval for the slope and summarize what this interval tells you about the increase in spending over time.