## 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 is given. Give the conclusion.
8. Know what happens to the test statistic of a multinomial experiment when the data is manipulated. Two parts.
9. Know what happens to the test statistic of a contingency table when the data is manipulated. Three parts.
10. Know what happens to the linear correlation coefficient when the data is manipulated. Three parts.
11. Work a chi-square goodness of fit problem using Statdisk. The observed frequencies are given to you. Give the degrees of freedom, critical value, test statistic, p-value, decision, and conclusion.
12. Work a linear regression problem using Statdisk. You will need to load data files and copy / paste data. Give the linear correlation coefficient, critical values, decision, regression equation from Statdisk, mean of y, and predict y for a given value of x.
13. The value of the correlation coefficient, r, and the total variation are given. Find the coefficient of determination, explained variation, and unexplained variation.
14. Use SPSS to create a correlation matrix (Analyze, Correlation, Bivariate). Rank the variables from highest correlation to lowest correlation to the specified variable. 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 two 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?
15. 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). Look at the normal probability plots and determine if the data appears normally distributed. Predict the value of y for a specified value of x.

### Notes

 # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total Pts 5 5 5 5 5 11 2 4 6 6 7 9 6 10 14 100