Math 217 Review Sheet—Exam 2

The exam covers Chapters 10 – 13 (no significance test for a population correlation nor specific contrasts in ANOVA). It might also be helpful for you to review Chapter 2 (where regression is first introduced, descriptively).

Simple Linear Regression (Chapter 10)

• General population model (p. 638 and in notes), including assumption/conditions of the model
• Significance test on the population slope (be able to give the hypotheses, but then use Minitab output for the test), including interpretation of the test in non-technical language
• Confidence interval for the population slope (using Minitab output and Table D) and understanding of what “confidence” means (e.g., our confidence is in our method, not in our one particular interval)
• Difference between a confidence interval for a mean response and a prediction interval for a new response
• Using residuals (residuals v. fits, histogram of residuals, normality plot of residuals) to check the conditions of the model
• Knowing that if the conditions are strongly violated, then inference from the model should not be trusted
• Descriptive analysis: Interpretation of R-squared and worded interpretation of the value of the slope coefficient; knowing that s, the standard deviation of the residuals, is our estimate for

Multiple Regression (Chapter 11)

• General population model (p. 686 and in notes), including assumption/conditions of the model
• General form of the ANOVA table (p. 688 and in notes)—understand all the pieces and how they fit together
• Overall model test (p. 689 and in the notes)—be able to give the hypotheses, but then use Minitab output to do the test
• Significance test on a population coefficient (be able to give the hypotheses, but then use Minitab output for the test), including interpretation of the test in non-technical language
• Confidence interval for a population coefficient (using Minitab output and Table D) and understanding of what “confidence” means (e.g., our confidence is in our method, not in our one particular interval)
• Using residuals (residuals v. fits, residuals v. each predictor variable, histogram of residuals, normality plot of residuals) to check the specification of the model and the model conditions
• Knowing that if the conditions are strongly violated, then inference from the model should not be trusted
• Understanding how indicator/dummy variables are used in regression and how to interpret the coefficient associated with the indicator variable
• Descriptive analysis: Interpretation of R-squared and worded interpretation of the value of the coefficients (remember: all other variable held constant); knowing that s, the standard deviation of the residuals, is our estimate for
• Understanding the issues to consider when selecting a model (e.g., controlling for other variables, confirming a model, finding the best predictive model, “data snooping”—then either confirm with another data set or break your original data set into two pieces, model-building and model-confirming)
• General format of analysis: 1) Run the regression model in Minitab (it’s always best, before running the regression, to look graphically and numerically at the individual variables in the model); 2) check the conditions of the test (and any possible variable misspecification) by looking at the residuals; 3) if the conditions are met, consider the overall model test (if it is not significant, then the analysis stops); 4) if the conditions are met and the overall model test is significant, then look at the individual significance tests on the coefficients (and interpret the results, in non-technical terms); 5) regardless of whether the model conditions are met, you can descriptively analyze the regression analysis via R-squared (proportion of the variation in the response variable that is explained by the model) and worded interpretations of the estimated coefficients.

One-Way ANOVA (Chapter 12)

• General population model (p. 727 and in notes), including assumption/conditions of the model
• General form of the ANOVA table (p. 736 and in notes)—understand all the pieces and how they fit together
• Overall model test (p. 730 and 735, and in the notes)—be able to give the hypotheses, but then use Minitab output to do the test (including interpretation of the test in non-technical language)
• Using sample standard deviations (biggest no more than twice the smallest) and residuals (residuals v. fits, histogram of residuals, normality plot of residuals) to check the model conditions
• Knowing that if the conditions are strongly violated, then inference from the model should not be trusted
• Understanding the issue of multiple comparisons (if doing true inference, then adjust for multiple comparisons using Tukey’s method; if simply “data snooping” in order to focus a second experiment, then multiple comparisons aren’t needed)
• Interpretation of the results of Tukey’s multiple comparisons (know where the significant differences are and in which direction, and discuss the results in non-technical terms)
• Descriptive analysis: Interpretation of R-squared and knowing that s, the standard deviation of the residuals, is our pooled estimate for

Two-Way ANOVA (Chapter 13)

• General population model (p. 776 and in notes), including assumption/conditions of the model
• General form of the ANOVA table (p. 783 and in notes)—understand all the pieces and how they fit together
• Significance tests for interaction and main effects (p. 784 and in notes)—be able to give the hypotheses, but then use Minitab output to do the test (including interpretation of the test in non-technical language)
• Using residuals (residuals v. fits, histogram of residuals, normality plot of residuals) to check the model conditions
• Knowing that if the conditions are strongly violated, then inference from the model should not be trusted
• Interpretation of interaction and main-effects plots and of the results from Tukey’s multiple comparisons (know where the significant differences are and in which direction, and discuss the results in non-technical terms)
• Descriptive analysis: Interpretation of R-squared and knowing that s, the standard deviation of the residuals, is our pooled estimate for
• General format of analysis: 1) Run the ANOVA model in Minitab (it’s always best, before running the ANOVA, to look graphically and numerically at the individual variables in the model); 2) check the conditions (normality and constant-variance) via plots of the residuals; if the conditions appear to met then, 3) check if the interaction effect is significant; if the effect is significant, then interpret the results using the interaction plot (and also an interpretation of main effects, if appropriate); if the interaction effect is not significant or if the interaction is significant, yet the main effects tell an interesting story, then 4) check if the main effects are significant; if either or both main effect is significant then, 5) use Tukey’s method to see specifically where the significant differences are (and in what direction)