10.27 Research and development obligations. The National Science Foundation collects data on the research and development obligations for science and engineering to universities and colleges in the United States.10 Here are the data for the years 2006, 2008, 2010, and 2012:

Year2006200820102012
Spending (billions of dollars)31.035.239.441.7

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

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

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

  3. (c) For each of the four years, find the residual. Use these residuals to calculate the estimated model standard error s.

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

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