Math 113: Study Guide - Chapters 9-10

  1. Three scatter plots are given. Draw the line of best fit through each graph.
  2. Six situations are given. Provide the test (correlation, goodness of fit, contingency table) that should be used in each situation. Example: "A random sample of blond students taken to see if their IQ is related to their height" would be a correlation problem because both variables are scale (numerical), not categorical.
  3. True or False: Know the properties / assumptions 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?
  4. True or False: 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?
  5. True or False: 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?
  6. True or False: 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?
  7. Know the guidelines for using the regression equation.
    1. What is the requirement on the residuals?
    2. Know the guidelines for using a regression equation from page 530.
    3. What is the equation that should be used if there is no significant linear correlation (pg 528-529)?
  8. A statistical test that you have never seen before is given to you with type of test, test statistic, and p-value. Work the hypothesis test to come up with a decision and conclusion.
  9. Write a concise sentence definition of a multinomial experiment.
  10. Multiple Regression:
    1. You are given eight independent variables and their correlation coefficients; rank them from most correlated to least correlated.
    2. You are the number of independent variables, R2 and adjusted-R2 for five different models; rank the models from best to worst.
  11. The ANOVA table from multiple regression is given to you.
    1. Work a hypothesis test.
    2. Find the sample size and number of independent variables.
    3. Look at the p-value from an Anderson-Darling test for normality and determine if the residuals are normally distributed.
  12. You are given the coefficients table from multiple regression.
    1. Decide which predictors have coefficients that are significantly different from zero. That's another way of saying which predictors contribute significantly to the model.
    2. Decide which predictor contributes the least to the model.
    3. Determine if the overall model should or should not be used for prediction.
  13. Multinomial Experiment: The test statistic and p-value are given to you. Find the critical value and finish the hypothesis test.
  14. The test statistic for a multinomial experiment is given.
    1. Complete a hypothesis test.
    2. Give the value of the test statistic when the order of the categories is rearranged or the observed frequencies are multiplied by a constant.
  15. Contingency Table: The test statistic is given.
    1. Know the null hypothesis.
    2. Find the expected frequency for one of the cells.
    3. Know the degrees of freedom and look up the critical value.
    4. Complete a hypothesis test and give a conclusion.
  16. The test statistic for a contingency table is given.
    1. Look up the critical value and complete the hypothesis test.
    2. Know how the test statistic is affected if the order of the rows or columns is changed, the rows and columns are interchanged, and the observed frequencies are multiplied by a constant.
  17. Linear Regression: The sample size, correlation coefficient, p-value, mean for each variable, and regression equation are given to you.
    1. Look at a scatter plot and say if there appears to be any linear correlation.
    2. Work a hypothesis test involving regression.
    3. Estimate the value of the dependent variable for a specific value of the independent variable.
    4. Give the value of the test statistic when the data is manipulated or the variables are switched.
    5. Find the coefficient of determination and the amount of explained and unexplained variation.
    6. Look at three scatter plots with different models on it. Rank the models from best to worst as far as explained variation and model simplicity.

Notes:

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