Reference no: EM132426806

Assignment 

Question 1. Public University Tuition is 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?

Question 2. There are 4 data setsEach data set has one response variable (y) and one explanatory variable (x). For each of the four data sets,

• (1) Create scatterplots to replicate
•  (2) Run a simple regression.
•  (3) Comment on the intercept and slope estimates for the four data sets.