(1) Plot the data with the 2000 tuition on the x-axis and 2008 tuition on the y-axis.
Describe the relationship. Are there any outliers or unusual values? Does a linear relationship between the tuition in 2000 and 2008 seem reasonable?
(2) Run the simple linear regression in R and write down the estimated least-squares
(LS) regression line. What are the LS intercept b0 and its standard error? What are the LS slope b1 and its standard error?
(3) Obtain the residuals and plot them versus the 2000 tuition amount. Is there anything unusual in the plot? [Alternatively, you can plot residuals against fitted 2008 tuition amount]
(4) Do the residuals appear to be approximately Normal? Explain.
(5) Give the null and alternative hypothesis for examining the relationship between 2000 and 2008 tuition amounts. Write down the test statistic and P-value for the hypothesis stated in (5). At 0.05 significance level, state your conclusion.
(6) Construct a 95% confidence interval for the slope β1 of the population regression line. What does this interval tell you?
(7) What percent of the variability in 2008 tuition is explained by a linear regression model using the 2000 tuition? What is the estimated correlation coefficient of the 2000 and the 2008 tuition?