## Math 113: Study Guide Chapters 9-10

1. Know the assumptions / properties of Pearson's Linear Correlation Coefficient.
• What values is it between?
• What does a value of zero mean / not mean?
• What happens if you change the scale of either variable?
• What happens if you switch the variables?
• What type of relationship does it measure?
• What type of distribution does it have?
• How many degrees of freedom does it have?
• What type of distribution do the ordered pairs (x,y) have?
2. Know the assumptions / properties of the contingency tables.
• What is the null hypothesis?
• How are the sample data selected?
• What requirement must be met?
• What type of data is used?
• What type of distribution does it have?
• How many degrees of freedom does it have?
• What type of test is it?
3. Know the assumptions / properties of multinomial experiments.
• What is the null hypothesis?
• What requirement must be met?
• What is the sample data?
• What distribution does it have?
• How many degrees of freedom does it have?
• What type of test is it?
4. Know the guidelines for using the regression equation.
• Know the guidelines for using a regression equation from page 530.
• What is the equation that should be used if there is no significant linear correlation (pg 528-529)?
5. Know the properties of multiple regression.
• When does the largest value of R-square occur?
• When does the largest value of the adjusted R-square occur?
• How is the Analysis of Variance used to test the regression equation?
• How does correlation between independent variables affect the choice of variables?
• What tools can be used to perform multiple regression.
• What are the degrees of freedom?
6. Three scatter plots are given. Draw the line of best fit through each graph.
7. Three situations are given. Provide the test (correlation, goodness of fit, contingency table) that should be used in each situation.
8. Write a concise definition of a multinomial experiment.
9. Multiple regression problem. Four different models are presented to you and the model summary from SPSS shown (# of independent variables, R, R2, and adjusted R2). Rank the models in order from best (1) model to worst (4) model. Then the ANOVA table is given for another model. Look at the ANOVA table and be able to tell if the model is a good model, how large the sample was, and how many independent variables there were.
10. Contingency Table. Write the null hypotheses. Find one (not all of them) expected frequency. Identify the degrees of freedom. Use the chi-square table to look up the critical value. The test statistic and p-value are given, state the decision and conclusion.
11. Know what happens to the test statistic of a contingency table when the data is manipulated. Three parts. Do NOT write "the same" but give a numerical answer. Look up the critical value in the chi-square table and give a conclusion.
12. A statistical test that you have never seen and a p-value are given. Give the conclusion.
13. Know what happens to the linear correlation coefficient when the data is manipulated. Three parts. Do NOT write "the same" but give a numerical answer. Look up the critical value in the correlation coefficient table and give a conclusion. Find the coefficient of determination and explained and unexplained variation. Look at a q-q plot and determine if the data appears normally distributed.
14. Know what happens to the test statistic of a multinomial experiment when the data is manipulated. Two parts. Do NOT write "the same" but give a numerical answer. Know the null hypothesis, how many degrees of freedom there are, look up the critical value from the chi-square table and give a conclusion.
15. Linear regression problem. The summary statistics are given to you. Look at a scatter plot and determine whether or not there appears to be any linear correlation. Identify the null hypothesis, the correlation coefficient, critical value (look up in table), decision, conclusion. Tell whether or not the regression equation should be used and estimate dependent variable. Use the appropriate equation to estimate a value of the dependent variable. Find the coefficient of determination.
16. Multiple regression problem. Use common sense to determine whether a certain variable should increase or decrease as another variable changes. Rank the correlation of four variables based on their correlation coefficients. The coefficients table from linear regression in SPSS is given; determine which three variables should be eliminated from the model.

### Notes

• Portions of the chi-square and Pearson correlation coefficient tables are given to you on the test. You do not need your book to answer this test.
• Questions 1-5 are true/false with several parts, but all dealing with the same area.
• You will need to use your calculator. There is no Statdisk or SPSS on this exam. Do NOT waste your time on the problems putting them into Statdisk as enough information is already given to you in the problem to answer the questions.
• Watch your time, it can easily get away from you if you spend too much time on any one problem. Move quickly, answer the ones you know how to do first.
 # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Total Pts 5 5 5 5 5 3 3 2 5 8 9 3 13 11 10 8 100