## Math 113: Study Guide Chapters 9-10

1. Know the assumptions / properties of Pearson's Linear Correlation Coefficient. (7 points)
2. Know the assumptions / properties of the contingency tables. (6 points)
3. Know the assumptions / properties of multinomial experiements. (6 points)
4. Know the guidelines for using the regression equation. (5 points)
5. Look at a scatterplot and identify the linear correlation as strong negative, moderate negative, none, moderate positive, or strong positive. (2 points)
6. Know what happens to the linear correlation coefficient when the data is manipulated. Two parts. (4 points)
7. Know what happens to the test statistic of a multinomial experiment when the data is manipulated. Two parts (4 points)
8. Find the expected frequencies for a contingency table. (4 points).
9. Look at a multiple regression output. (6 points)
1. Pick the three most significant independent variables (The ones with the smallest p-values or largest t-values [called t statistics on the output]).
2. Pick the three least significant independent variables (The ones with the largest p-values or smallest t-values [called t statistics on the output]).
10. Work a contingency table problem using the conting program on the calculator. (9 points)
1. Find the test statistic (using the calculator).
2. The critical value (use the Chi-square table).
3. Fill in the blanks to finish the conclusion.
11. Work a chi-square goodness of fit problem using your TI calculator. (12 points)
1. Find the test statistic (using the calculator)
2. Look up the critical value (in the Chi-square table)
3. Write the decision.
4. Fill in the blanks to complete the conclusion.
12. Work a linear regression problem using your TI calculator. (9 points)
1. Find the linear correlation coefficient
2. Test to see if there is significant linear correlation (use Table A6 to find the critical value)
3. Write the regression equation (Remember, if you fail to reject in step 2, then the regression equation is y-hat equals y-bar).
13. A linear regression problem was performed on a computer and the output is given. The output contains the constant (from the regression equation), the standard error of the y estimate (ignore), the value of r-squared, the number of observations, the degrees of freedom, the x-coefficient (from the regression equation) and the standard error of the coefficient (ignore). Given this information, find ... (25 points)
1. The coefficient of determination (2 points)
2. The value of the linear correlation coefficient (2 points)
3. The sample size (2 points)
4. Test to see if there is significant linear correlation using Table A6. (9 points)
1. Write the critical value
2. Write the test statistic
3. Identify the type of linear correlation as significant negative, none, or significant negative.
5. Write the equation of the regression line. (3 points)
6. Estimate the dependent variable for a given value of the independent variable. (3 points)
7. Given the total variation, find ... (4 points)
1. The variation explained by the regression equation
2. The variation unexplained by the regression equation.

### Notes

• Problems 1 - 10 must be worked individually.
• Problems 11 - 13 may be worked in groups of up to size 3.