Assignment #6 1. Public University Tuition [cf. PSBE]. Data file “tuition.txt” shows the undergraduate tuition and required fees (in dollars) in 33 public universities in 2000 and 2008. (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 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 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? (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?
2. There are 4 data sets on page 57 in file “Week 10.pdf”. Each data set has one response variable (y) and one explanatory variable (x). For each of the four data sets, (1) Create scatterplots to replicate page 58 of “Week 10.pdf”. (2) Run a simple regression. (3) Comment on the intercept and slope estimates for the four data sets. 3. From textbook, Question #10.30. Please use the data file “flow.csv” Assignment #6