BSC. STATISTICS (IDL)

YEAR IV

STAT 473: FURTHER TOPICS IN REGRESSION

MARCH, 2021 DUE DATE: 27TH MARCH, 11:59PM

Answer ALL. Copied work will not be accepted. You may use any of these softwares SAS, R or MINITAB.

1. In a small-scale experimental study of the relation between degree of brand liking (Y ) and moisture content (X1) and sweetness (X2) of the product, the following results were obtained from the experiment based on a completely randomized design (data are coded):

Yi 64 73 61 76 72 80 71 83 83 89 86 93 88 95 94 100 X1i 4 4 4 4 6 6 6 6 8 8 8 8 10 10 10 10 X2i 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4

(a) Obtain the scatter plot matrix and correlation matrix. What information do these diagnostic aids provide here?

(b) Fit regression model Yi = 0 + 1Xi1 + 2Xi2 + i to the data. State the estimated regression function. How is 1 interpreted here?

(c) Obtain the residuals and make a box plot of the residuals. What information does the plot provide?

(d) Plot the residuals against Y , X1, X2, and X1X2 on seperate graphs. Also make a normal probability plot. Interpret the plots and summarize your ndings. (e) Conduct the Breusch-Pagan test for constancy of the error variance, assuming log2 i = 0 + 1X1 + 2X2; use = 0.01. State the alternatives, decision rule, and conclusion. (f) Conduct a formal test for lack of t of the rst-order tregression function; use = 0.01. State the alternatives, decision rule, and conclusion.

2. Assume that regression model Yi = 0 + 1Xi1 + 2Xi2 + i with independent normal error terms to Question 1 is appropriate.

(a) Test whether there is a regression relation, using = 0.01. State the alternatives, decision rule, and conclusion. What does your test imply about 1 and 2?

(b) What is the p-value of the test in part (a)? (c) Estimate 1 and 2 jointly by the bonferroni procedure, using a 99% family condence coecient. Interpret your results.

3. Refer to Question 1.

(a) Calculate the coecient of multiple determination R2. How is it interpreted here?

(b) Calculate the coecient of simple determination R2 between Yi and Yi. Does it equal the coecient of multiple determination in part (a)?

4. Assume that regression model Yi = 0 + 1Xi1 + 2Xi2 + i with independent normal error terms to Question 1 is appropriate. (a) Obtain an interval estimate of E{Yh} when Xh1 = 5 and Xh2 = 4. Use a 99% condence coecient. Interpret your interval. (b) Obtain a prediction interval for a new observation Y{h(new)} when Xh1 = 5 and Xh2 = 4. Use a 99% condence coecient. Interpret your interval.

Note: Use Brand preference dataset CH06PR05.txt