Homework 6, Statistics 112, Fall 2006
This homework is due Friday, December 1st by 5 pm. You can put in my mailbox in the statistics department on the fourth floor of Huntsman Hall if you do not hand it in during class on Thursday.
1. (a) Dielman, Problem 7.2, page 285-286. The data is in COLLEGE7.JMP.
(b) Dielman, Problem 7.4, pages 290-291.
2. Dielman, Problem 7.15, page 303-304.
3. In television’s early years, most commercials were 60 seconds long. Now, however, commercials can be any length. The objective of commercials remains the same – to have as many viewers as possible remember the product in a favorable way and eventually buy it. In an experiment to determine how the length of a commercial is related to people’s memory of it, 60 randomly selected people were asked to watch a 1-hour television program. In the middle of the show, a commercial advertising a brand of toothpaste appeared. Some viewers watched a commercial that lasted for 20 seconds, others watched one that lasted for 24 seconds, 28 seconds, ..., 60 seconds. In addition to varying the length of the commercial, the experiment varied the type of commercial. There were three types: humorous, musical and serious. After the show, each person was given a test to measure how much he or she remembered about the product. The memory test scores (on a 30-point test), lengths and type of commercial are stored in tvcommercials.JMP.
(a) Fit a multiple regression model that predicts memory test score based on the commercial’s length and type. Include in your model an interaction between length and type. Examine the residual plot vs. predicted, the normal quantile plot of the residuals and the Cook’s distances and leverages. Note any problems with the multiple linear regression model we have fit, but proceed ahead with the rest of this question using the multiple regression model we have fit.
(b) Make an interaction plot for the multiple regression in (a). When the length of the commercial is 28 seconds, which type of commercial does the model estimate as being best for maximizing memory test score?
(c) What information in the output indicates that there is no evidence of an interaction between length and type?
4. Problem 3 continued.
(a) Because there is no evidence of an interaction between length and type, we prefer to use the simpler multiple regression model that has the commercial’s length and indicator variables for the commercial’s type, but no interactions between length and type, as explanatory variables. Fit this multiple regression model.
(b) Is there evidence that not all types of commercials have the same mean memory scores when the length of the commercial is held fixed? Is there evidence that the length of the commercial is associated with mean memory scores for fixed types of commercials? State hypotheses in terms of the parameters of the model you fit in 3(a), give p-values and state your conclusions.
(c) Based on the model you fit in 4(a), what is a point estimate and a 95% confidence interval for the difference between the mean memory test score of people watching humorous commercials compared to musical commercials if both of the commercials are of the same length? Hint: For the confidence interval, you need to use Custom Test.
(d) Based on the model you fit in 4(a), which type of commercial would you advise an advertiser to use to maximize the mean memory test score?