Mathematics 216 Computer-oriented Approach to Statistics

Study Guide :: Unit 6

Bivariate Analysis

Introduction

In Unit 6, we focus on statistical techniques that examine relationships between two variables. They may be two quantitative variables, two qualitative variables, or one qualitative and one quantitative variable.

Correlation is one method that explores the relationship between two quantitative variables. For example, correlation analysis could be used to find out whether there is a significant linear relationship between the annual dollar amount that firms spend on advertising and the annual dollar amount of sales. You will be able to apply the knowledge of hypothesis tests that you gained in previous units to determine the significance of the correlation.

If a significant correlation between two variables is found, the bivariate analysis can be expanded by conducting regression analysis to determine the best linear equation relating the two variables. This equation then permits the researcher to predict one of the variables, given the value of the other variable. For example, if there is a significant correlation between advertising expenditures and sales, regression analysis will help you identify a linear equation that best relates advertising to sales. Doing so will allow a firm to predict next year's sales based on a budgeted advertising amount. In forming the prediction, you are applying the knowledge of confidence interval tests you acquired in previous units.

In this last unit of the course, you will examine the relationship between two qualitative (categorical) variables using a chi-square hypothesis test of independence. You could use this type of test, for example,  to see if an individual's gender is related to the political party that individual prefers to vote for in the next election.

We end the course with the study of Analysis of Variance (ANOVA). One can view ANOVA as a way of examining the relationship between a qualitative and a quantitative variable. For example, ANOVA can be used to examine the relationship between two variables such as the city one resides in (City A, City B, City C, and so on) and the annual earnings the individual achieves (a quantitative variable). One can alternatively view the ANOVA example as a test of hypothesis used to compare mean annual earnings between three or more samples (City A, City B, City C, and so on).

Correlation

Learning Objectives

After completing the readings and exercises assigned for this topic, you should be able to:

  1. Draw a scatter plot for a set of ordered pairs.
  2. Distinguish between the independent (explanatory) variable, x, and the dependent (response) variable, y.
  3. Distinguish between the different types of correlation.
  4. Compute the linear correlation coefficient.
  5. Perform a hypothesis test for a population correlation coefficient.
  6. Distinguish between correlation and causation.

Important Note: For help accessing the eText resources referred to below, see Navigating Your eText on the course home page.

Required Reading

Elementary Statistics, Chapter 9, Section 9.1 Correlation

Try It Yourself Examples

Work through each Try It Yourself example in this section of the eText. Check your work against the solutions provided.

Exercises in Your eText

Do the following exercises in your eText:

Chapter 9, Section 9.1 Exercises 1, 3, 7, 21, 25, 27, 31. Write out the step-by-step solutions or explanations. For test of hypothesis questions, use your calculator to compute the t-statistic and use the Critical Value approach. Check your work against the solutions provided.

Optional Multimedia Resources

Additional optional multimedia resources related to Chapter 9 Section 9.1 are available on the textbook publisher’s MyLab website.

Linear Regression

Learning Objectives

After completing the readings and exercises assigned for this topic, you should be able to:

  1. Define the terms:
    • line of best fit
    • regression line; y intercept of regression line
    • residual
    • slope
  2. Compute the equation of the regression line.
  3. Interpret the slope and y intercept of a regression line.
  4. Predict y-values using a regression equation.

Important Note: For help accessing the eText resources referred to below, see Navigating Your eText on the course home page.

Required Reading

Elementary Statistics, Chapter 9, Section 9.2 Linear Regression

Try It Yourself Examples

Work through each Try It Yourself example in this section of the eText. Check your work against the solutions provided.

Exercises in Your eText

Do the following exercises in your eText:

Chapter 9, Section 9.2 Exercises 1-12 (inclusive), 17, 19. Write out the step-by-step solutions or explanations. Check your work against the solutions provided.

Optional Multimedia Resources

Additional optional multimedia resources related to Chapter 9 Section 9.2 are available on the textbook publisher’s MyLab website.

Measures of Regression and Prediction Intervals

Learning Objectives

After completing the readings and exercises assigned for this topic, you should be able to:

  1. Define the terms:
    • total variation, explained variation, unexplained variation.
  2. Compute and interpret coefficient of determination.
  3. Using the computer and StatCrunch, compute and interpret the standard error (se) of estimate for a regression line. (You will not have to use your calculator to compute se.)
  4. Using the computer and StatCrunch, construct and interpret a prediction interval for y. (You will not have to use your calculator to compute the prediction interval.)

Important Note: For help accessing the eText resources referred to below, see Navigating Your eText on the course home page.

Required Reading

Elementary Statistics, Chapter 9, Section 9.3 Measures of Regression and Prediction Intervals

Try It Yourself Examples

Work through each Try It Yourself example in this section of the eText. Check your work against the solutions provided.

Exercises in Your eText

Do the following exercises in your eText:

Chapter 9, Section 9.3 Exercises 1-10 (inclusive), 11, 13. Write out the step-by-step solutions or explanations. Do not use your calculator to compute these (leave this for the computer component of this course). Check your work against the solutions provided.

Optional Multimedia Resources

Additional optional multimedia resources related to Chapter 9 Section 9.3 are available on the textbook publisher’s MyLab website.

Chapter 9 Review (Extra Online Practice)

For more practice working with the topics in this chapter of the eText, work through this review. Or, if you feel you have mastered this material, you may skip to the computer lab section of this unit.

Review Learning Objectives

Before proceeding to the online exercises, briefly review the Learning Objectives for each of the topics (listed below) presented in previous sections of this Study Guide:

  • Correlation
  • Regression
  • Measures of regression and prediction intervals
Optional Practice in the MyLab Study Plan

For more practice on the topics/sections of this chapter of your eText, visit Pearson MyLab, and work interactively through the exercises in the Study Plan. For help accessing this resource, see Accessing Pearson MyLab on the course home page.

Computer Lab 6A

In this Computer Lab you will learn to use StatCrunch to develop solutions to exercises related correlation and regression, most of which is from Chapter 9 of your eText.

Computer Lab 6A Detailed Instructions

To view all of the Computer Lab 6A exercises and the detailed step by step instructions that will guide you to use StatCrunch to complete these exercises, see Computer Lab 6A.

Test of Independence

Learning Objectives

After completing the readings and exercises assigned for this topic, you should be able to:

  1. Define the terms:
    • contingency table
    • marginal frequencies, joint frequencies
    • row
  2. Compute the expected frequencies using a contingency table.
  3. Use chi-square independence test to test the independence of two variables.

Important Note: For help accessing the eText resources referred to below, see Navigating Your eText on the course home page.

Required Reading

Elementary Statistics, Chapter 10, Section 10.2 Independence

Try It Yourself Examples

Work through each Try It Yourself example in this section of the eText. Check your work against the solutions provided.

Exercises in Your eText

Do the following exercises in your eText:

Chapter 10, Section 10.2 Exercises 1, 5, 7, 13, 17. Write out the step-by-step solutions or explanations. Check your work against the solutions provided. Omit Exercise 3 in Section 10.2.

Optional Multimedia Resources

Additional optional multimedia resources related to Chapter 10 Section 10.2 are available on the textbook publisher’s MyLab website.

Analysis of Variance (ANOVA)

Learning Objectives

After completing the readings and exercises assigned for this topic, you should be able to:

  1. Verify the requirements to perform a one-way ANOVA.
  2. Define the terms:
    • mean square between; mean square within.
  3. Complete missing entries in the ANOVA Summary Table for a given problem and use this table to compute the test statistic for the ANOVA hypothesis test.

Important Note: For help accessing the eText resources referred to below, see Navigating Your eText on the course home page.

Required Reading

Elementary Statistics, Chapter 10, Section 10.4 Analysis of Variance

Try It Yourself Examples

Work through each Try It Yourself example in this section of the eText. Check your work against the solutions provided.

Exercises in Your eText

Do the following exercises in your eText:

Chapter 10, Section 10.4 Exercises 1 to 3 (inclusive), 9, and 11. Write out the step-by-step solutions or explanations. Use StatCrunch to conduct the ANOVA hypothesis in 9 and 11 above. Check your work against the solutions provided.

Optional Multimedia Resources

Additional optional multimedia resources related to Chapter 10 Section 10.4 are available on the textbook publisher’s MyLab website.

Chapter 10 Review (Extra Online Practice)

For more practice working with the topics in this chapter of the eText, work through this review. Or, if you feel you have mastered this material, you may skip to the computer lab section of this unit.

Review Learning Objectives

Before proceeding to the online exercises, briefly review the Learning Objectives for each of the topics (listed below) presented in previous sections of this Study Guide:

  • Test of Independence
  • Analysis of Variance
Optional Practice in the MyLab Study Plan

If you would like more practice on the various topics/sections of Chapter 10, you may wish to visit the website that accompanies your textbook, and work interactively through online exercises located in the Study Plan. For help accessing this resource, see Accessing Pearson MyLab on the course home page.

Computer Lab 6B

In Computer Lab 6B, you will use StatCrunch to develop solutions to exercises related to Chi-Square Independence Test and One Way Analysis of Variance, most of which is based on Chapter 10 of your text.

Computer Lab 6B Detailed Instructions

To view all of the Computer Lab 6B exercises and the detailed step by step instructions that will guide you to use StatCrunch to complete these exercises, see Computer Lab 6B.

Self-Test 6

To access Self-Test 6, click MATH 216 Self-Test 6.

It is important that you work through all the exercises in the unit self-tests and the eText chapter quizzes. No grades are assigned to the self-tests. They are designed to, along with the unit assignments, help you master the content presented in each unit.

Each unit self-test has two parts: one on theory (A) and one on computer work (B). Working through these will help you review key exercises in the unit, which will help you prepare for assignments and exams.

Assignment 6

After completing Self-Test 6, complete Assignment 6, which you will find on the course home page. Submit your solutions to this assignment for marking using the drop box on the course home page.