Glue Strength. In the text Quality Control and Industrial Statistics, Fifth Edition (Homewood, IL: Irwin. 1986), A. J. Duncan presents data relating breaking strength (lbs) and thickness of application (0.001 inch) for two different kinds of glue, denoted A and C. The following table provides the data for observations on sixteen specimens.
We want to regress breaking strength on the two predictor variables of thickness and glue type. The indicator variable for type of glue is
Use the technology of your choice to do the following.
- a. Obtain the
scatterplot of breaking strength versus thickness, using a different plot symbol for the two kinds of glue. Based on this plot, does it appear that glue type is a useful predictor variable? Explain your answer. - b. Obtain the
regression analysis of breaking strength on thickness and glue. Conduct t-tests for the individual utility of the two predictor variables at the 5% level of significance. Interpret your results. - c. Based on the output in part (b), obtain the individual regression equations relating breaking strength to thickness for the two kinds of glue.
- d. Obtain plots of residuals versus fitted values, residuals versus thickness, and residuals versus glue, and a normal probability plot of the residuals. Perform a residual analysis to assess the appropriateness of the regression equation, constancy of the conditional standard deviations, and normality of the conditional distributions. Check for outliers and influential observations.
- e. Provide a scatterplot of breaking strength versus thickness with the regression lines for each kind of glue, Based on this plot and your residual analysis in part (d), do you feel that this model fits the data well? Explain your answer.
- f. To check for possible interaction between the two predictor variables, perform the regression analysis of breaking strength on thickness, glue, and the cross-product term involving glue and thickness. Is there an interaction between thickness and. glue type? Use α = 0.05.
Want to see the full answer?
Check out a sample textbook solutionChapter B Solutions
Introductory Statistics (10th Edition)
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill