# Exam 2 Study Guide: Chapters 7-10

1. Suppose you were to collect data for a pair of variables and want to make a scatter plot. Which variable would you use as the explanatory variable and which as the response variable. Explain your choices. What would you expect to see in the scatter plot. Discuss the likely direction, form, and scatter. Look at problems 7.1-4
2. Look at a plot of the residual vs the predicted value and tell what it indicates about the appropriateness of the linear model that was fit to the data. Explain more than "good fit" or "bad fit". Two parts. Look at problems 8.3-4
3. Look at some scatter plots. Identify which plots show little or no association, negative association, linear association, moderately strong association, and very strong association. Then take the given values for the correlation coefficient and match them to the scatter plots. Look at problems 7.5-6 and 7.11-12.
4. An introduction to the data and then the regression equation, table of coefficients, r-squared, and a residual plot from a regression problem are given. Describe the context of the data. Write a model to predict one of the variables. Explain whether or not a linear model is appropriate. Explain the reliability of the estimates. Find the residual for a given data point. Look at problems 8.8, 22, 26, 31.
5. A table of coefficients and the analysis of variance table from a regression problem are given. Write a model to predict a variable's value. Interpret the slope for your model. Find the value of r2, compare all the information you have for this problem with the information for the last problem and determine which is a better model and explain why. Find the standard deviation of the response variable. Look at the problems mentioned for the last problem and especially classroom activity 2.
6. A scatter plot with the regression line drawn on it is given. Each axis is centered about its mean and the tick marks are one standard deviation apart. A rise and run for the regression line are indicated on the graph. Find the standard deviation for the response and predictor variables. Use the graph to determine the slope of the line. Use algebra to find the equation of the best fit line. Use the equation to estimate the response variable for a given value of the predictor variable. Use algebra to find the correlation coefficient (formula is given to you). Look at the notes from class.
7. Two scatter plots are given, one with an outlier and one without an outlier. The normal probability plots for the two models are also given as well as the regression equations and the value of r-squared. Compare the information given and decide which model would be better to use. Justify your answer. Look at problems 9.11-12
8. Look at a scatter plot. Determine if the correlation would be strengthened or weakened if the outlier was removed. Is there a reasonable justification for removing the outlier? Explain. Look at problems 9.15-16
9. A scatter plot is shown. Circle the outliers and put an X through the points that have high leverage. The plot also indicates two subsets of data. Draw and label three regression lines, one for all of the data and one for each subset. Decide whether or not the data should be subsetted. Explain your reasoning. Read the section on subsets in chapter 9.
10. Six scatter plots and regression equations are generated for a set of data, one for each power in the ladder of powers. Determine which model is the best model. The regression equation is given as a power, you should write it mathematically on your test (for example, the 1/2 power is the square root and the 0 power means log [for the ladder]). Use the best model to predict a value, this will require that you know how to solve for the response variable and undo the transformation. Look at problems 10.4-8, 13-19

## Notes

• Most of the problems are similar to problems in the textbook. Very few of the problems are identical to the problems from the text.
• You will not need Minitab or Active Stats. Your computer screens should be off during the exam.
• Whenever there are problems that ask for an explanation, be sure you explain. Those parts are worth more points based on the explanation.
• You will need a calculator. You will need a straight edge, although I have some in the classroom if you don't have one.
• Here is some sample output to look at for questions 4, 5, and 6.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 Total 8 8 13 14 12 14 7 8 8 8 100