FIN570 Spring 2024
Assignment # 4
Due on Friday 3/ 1 midnight
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 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 $5800? Compare (10) and (8), which is wider? Why?
2. There are 4 data sets on page 51 in Week-6 file. Each data set has one response variable (y)
and one explanatory variable (x). For each of the four data sets,
(1) Create scatterplots to replicate page 52 of the Week-6 slide file.
(2) Run a simple regression.
(3) Comment on the intercept and slope estimates for the four data sets.
[Hint: to save some time, you can copy the paste the following lines to input the data in R/RStudio:
x = c(10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5)
x1 = c(rep(8, 10), 19)
y1 = c(8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68)
y2 = c(9.14, 8.14, 8.74, 8.77, 9.26, 8.1, 6.13, 3.1, 9.13, 7.26, 4.74)
y3 = c(7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73)
y4 = c(6.58, 5.76, 7.71, 8.84, 8.47, 7.04, 5.25, 5.56, 7.91, 6.89, 12.5)
3. PSBE 12.34 Stocks and bonds. How is the flow of investors’ money into stock mutual funds related to the flow of money into bond mutual funds? Data file “flow.csv” shows the net new money flowing into stock and bond mutual funds in the years 1984 to 2017, in millions of
dollars. “Net” means that funds flowing out are subtracted from those flowing in. If more money leaves than arrives, the net flow will be negative. [Hint: you can use the following R commands to load the data in (a):
flow.data=read.csv(file.choose())
For part (c), use the next R commands to generate a subset of the original data,
flow_new=subset(flow.data, Year <= 2007)
model2 = lm(flow_new$Bond_funds~flow_new$Stock_funds)
(a) Make a scatterplot with cash flow into stock funds as the explanatory variable. Find the least-squares line for predicting net bond investments from net stock investments. What do the data suggest?
(b) Is there statistically significant evidence of some straight-line relationship between the flows of cash into bond funds and stock funds? (State the hypotheses, give a test statistic and its P-value, and state your conclusion.)
(c) Generate a plot of the residuals versus year. Describe any unusual patterns you see in this plot.
(d) Given the 2008 financial crisis and its lingering effects, remove the data for the years after 2007 and refit the remaining years. Is there statistically significant evidence of a straight-line relationship?
(e) Compare the least-squares regression lines and regression standard errors using all the years and using only the years before 2008.
(f) How would you report these results in a paper? In other words, how would you handle the difference in relationship before and after 2008?