1. Public University Tuition. Data file tuition.txt shows the undergraduate tuition and required fees (in dollars) in 33 public universities in 2000 and in 2008. [Hint: please use the following R commands to load tuition.txt and attach the data, tuition = read.table(file.choose(), sep = "\t", header = T) attach(tuition)

(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) Produce residual plot, where the residuals are on the y-axis and the 2000 tuition amount on the x-axis. 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 1 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?

(8) The tuition at BusStat U was $5800 in 2000. What is its predicted tuition in 2008? Find the 95% prediction interval for its tuition amount in 2008.

(9) The tuition at Moneypit U was $8700 in 2000. What is its predicted tuition in 2008? Discuss the appropriateness of using the fitted equation to predict tuition for BusStat U and for Moneypit U.

(10) Find the 95% confidence interval for the mean tuition amount for a public university with 2000 tuition amount of $5800? Compare (10) and (8), which is wider? Why?

University Year2000 Year2008 PennState 7018 13706 Pittsburgh 7002 13642 Michigan 6926 11738 Rutgers 6333 11540 MichiganState 5432 10690 Maryland 5136 8005 Illinois 4994 12106 Minnesota 4877 10634 Missouri 4726 7386 Buffalo 4715 6385 Indiana 4405 8231 OhioState 4383 8679 Virginia 4335 9300 Cal-Davis 4072 9497 Cal-Berkeley 4047 7656 Cal-Irvine 3970 8046 Purdue 3872 7750 Cal-SanDiego 3848 8062 Oregon 3819 6435 Wisconsin 3791 7569 Washington 3761 6802 UCLA 3698 8310 Texas 3575 8532 Nebraska 3450 6584 Iowa 3204 6544 Colorado 3188 7278 IowaState 3132 5524 NorthCarolina 2768 5397 Kansas 2725 7042 Arizona 2348 5542 Florida 2256 3256 GeorgiaTech 3308 6040 TexasAM 3374 7844