## Math 113: Study Guide Chapters 9-10

1. Know the assumptions / properties of Pearson's Linear Correlation Coefficient.
1. What values is it between?
2. What does a value of zero mean / not mean?
3. What happens if you change the scale of either variable?
4. What happens if you switch the variables?
5. What type of relationship does it measure?
6. What type of distribution does it have?
7. How many degrees of freedom does it have?
8. What type of distribution do the ordered pairs (x,y) have?
2. Know the assumptions / properties of the contingency tables.
1. What is the null hypothesis?
2. How are the sample data selected?
3. What requirement must be met?
4. What type of data is used?
5. What type of distribution does it have?
6. How many degrees of freedom does it have?
7. What type of test is it?
3. Know the assumptions / properties of multinomial experiments.
1. What is the null hypothesis?
2. What requirement must be met?
3. What is the sample data?
4. What distribution does it have?
5. How many degrees of freedom does it have?
6. What type of test is it?
4. Know the guidelines for using the regression equation.
1. Know the guidelines for using a regression equation from page 501.
2. What is the equation that should be used if there is no significant linear correlation (pg 500)?
5. Know the properties of multiple regression.
1. When does the largest value of R-square occur?
2. When does the largest value of the adjusted R-square occur?
3. How is the Analysis of Variance used to test the regression equation?
4. How does correlation between independent variables affect the choice of variables?
5. What tools can be used to perform multiple regression.
6. What are the degrees of freedom?
6. Contingency Table. Use Statdisk. Write the null hypotheses. Find one (not all of them) expected frequency. Identify the degrees of freedom. Find the p-value. Write the decision and conclusion.
7. A statistical test that you have never seen and a p-value are given. Give the conclusion.
8. The value of the correlation coefficient, r, and the total variation are given. Find the coefficient of determination, explained variation, and unexplained variation.
9. 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. Also give a conclusion based on the test statistic and degrees of freedom (use table A-4 to get critical value).
10. 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. Also give a conclusion based on the test statistic and the critical value.
11. 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. Also give a conclusion based on the test statistic and the sample size (use table A-6 to get critical value).
12. Use Statdisk to perform linear regression. Write the null hypothesis. Find the value of the correlation coefficient and the p-value. What is the decision? What is the conclusion? Should the regression equation be used? Write the equation that should be used (either the regression equation if significant or the mean of the dependent variable if not). Predict the value of y for a specified value of x.
13. Work a chi-square goodness of fit (multinomial experiment) problem using Statdisk. The observed frequencies are given to you. Give the degrees of freedom, critical value, test statistic, p-value, decision, and conclusion.
14. Linear regression problem. The summary statistics are given to you. Identify the null hypothesis, the correlation coefficient, critical value (table A-6), decision, conclusion. Tell whether or not the regression equation should be used and estimate dependent variable. Look at Q-Q Plots and Kolmogorov Smirnov statistics to determine if the data is normally distributed.
15. Use SPSS to perform multiple regression.
1. Open a data file and a select cases to reduce the sample size. This means that everyone has the potential to have different answers, so I will have you print out your output so that I can check your answers.
2. Create a correlation matrix (Analyze / Correlation / Bivariate) for five variables. Compare four variables to a fifth and write the correlation coefficient and whether or not each pair is significantly correlated.
3. Perform a Kolmogorov Smirnov test (Analyze / Nonparametric / 1 Sample KS) and determine if a variable is normally distributed. (You can do a Q-Q plot if you like and have extra time, but it's not required).
4. Perform multiple regression and record the coefficients and p-values for each independent variable. Also record the r-square and adjusted r-square value. Determine which three variables are least significant by looking at the p-values and re-perform the multiple regression without those variables. Did the adjusted r-square increase or decrease by eliminating the variable?
5. Add your name to the SPSS output, print it out, and turn it in with your test.

### Notes

• You will need to use your calculator, Statdisk, and SPSS to complete this test.
• 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.
• Problem 15 may be worked with a partner (maximum of two people in a group). Each person should answer all questions on their test, but only turn in one printout per group.
 # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total Pts 5 5 5 5 5 9 2 3 5 4 5 8 13 11 15 100