Homework 1, Statistics 512, Spring 2005 s1

Homework 7, Statistics 112, Fall 2005

This homework is due Thursday, November 10th at the beginning of class.

1. Dielman, Problem 6.2, page 219-220. The data is in rd6.JMP .

2. In this problem, you will do a simulation study to get a feel for interpreting the normal quantile plot. Create a new data file in JMP by clicking File, then New, then Data Table.

Label the first column X. Create 100 rows by clicking Rows, Add Rows and then entering 100 in the How Many Rows to Add box.

(a) In this part, we will look at the normal quantile plot for random variables generated from the normal distribution. Right click on the X column, click Formula and then click Random (you need to scroll down in the Functions to see Random) and then click Random Normal. Click OK. This will create 100 normal random variables. Make a normal quantile plot of the X column and print the normal quantile plot. Right click on the X column again, click Formula and then click Apply and then click OK. This will generate a new set of 100 normal random variables. Make a normal quantile plot of the X column and print the plot.

(b) In this part, we will look at the normal quantile plot for random variables generated from the uniform distribution [the uniform distribution has a constant density on the interval (0,1)]. Right click on the X column, click Formula and then click Random and then click Random Uniform. Click OK. This will create 100 uniform random variables. Make a normal quantile plot of the X column and print the normal quantile plot. Right click on the X column again, click Formula and then click Apply and then click OK. This will generate a new set of 100 uniform random variables. Make a normal quantile plot of the X column and print the plot.

(c) Comment on the differences in appearance between the normal quantile plots for the normally distributed random variables from part (a) and the normal quantile plots for the uniformly distributed random variables from part (b).

3. Dielman, Problem 6.13, page 265. The data is in comprep6.JMP . Be sure to examine residual plots versus the explanatory variables, the residual by predicted plot and the normal quantile plot in assessing whether the assumptions of the multiple linear regression model are satisfied.

4. Dielman, Problem 6.19, page 267. The data is in traffic6.JMP . Hint: Find an appropriate regression model and then use standardized residuals.