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Introduction to Linear Regression

Introduction to Linear Regression. Math 153 – Introduction to Statistical Methods. This Week’s Objectives. Understand the significance of a correlation coefficient. Understand how to use the TI-83 to find a regression equation. Determine the best predictor for a data set.

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Introduction to Linear Regression

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  1. Introduction to Linear Regression Math 153 – Introduction to Statistical Methods

  2. This Week’s Objectives • Understand the significance of a correlation coefficient. • Understand how to use the TI-83 to find a regression equation. • Determine the best predictor for a data set. • Understand the effect of outliers on a regression equation.

  3. r The Correlation Coefficient • Measures the strength or weakness of a linear relationship. • Value of r is between –1 and 1 inclusive. • Closer r is to –1, the more negative the linear relationship. • Closer r is to +1, the more positive the linear relationship. • r close to 0 implies no linear relationship.

  4. Website Exercise Part 1 • Connect to the URL below and match the correlation coefficient to the appropriate graph. When you get 10 correct, use the PrintScreen key on your keyboard to paste an image to the clipboard. Then open Word and paste the screen image into a Word document. Email me the file when you have completed it. • Correlation Coefficient Web Exercise

  5. How To Tell If Relationship is Linear • Compare the value of r to the critical value found in table A-6. If the |r | is GREATER than the critical value found in table A-6, then the data supports linear relationship. • If the data supports a linear relationship, use the regression equation as your predictor.

  6. How Tell If Relationship is Linear • Compare the value of r to the critical value found in table A-6. If the |r | is LESS than the critical value found in table A-6, then the data does not support a linear relationship. • If the data does not support a linear relationship, use the value of y-bar, the mean of the y values as your prediction.

  7. Determining r • Enter the x values of your data into L1. • Enter the y values of your data into L2. • Select STAT >> TEST >> LinRegTTest. • If you need further assistance, please go to the TI Tutorial.

  8. Height and Weight of Randomly Selected Baseball Players Determine the correlation coefficient of the data set above.

  9. TI – 83 Printout of LinRegTTest • Enter the data into L1 and L2. • Use STAT>>TEST>> LinRegTTest • Arrow down to find the value of r.

  10. Is there a linear relationship? • Use table A-6 to determine the critical value for 7 pairs of data. • The critical value for a .05 level of significance is 0.754. • The correlation coefficient r is 0.763. • Since |0.763| > 0.754, the data supports a linear relationship.

  11. Determining a Regression Equation • The regression equation is of the form y = a + bx, where a is the y-intercept and b is the slope. • For this example, a = -386.5 and b = 7.9 • Regression equation is y = -386.5 + 7.9x

  12. Can I Make A Prediction? • A regression equation is only valid to make predictions for data elements near the general range of x values used to create the regression equation. • Since our data elements in this example are between 71” and 76”, we can make predictions using x values in this general range. • Also, our regression equation is only valid for predictions of similar data.

  13. Can I Make A Prediction?Website Exercise Part 2 • Would our regression equation be valid to predict the weight of a baseball player who is 67”? • Would our regression equation be valid to predict the weight of a football player who is 73”? • Would our regression equation be valid topredict the weight of a baseball player who is 73”? • Why or why not? Email me your response.

  14. Making a Prediction • Predict the weight of a baseball player who is 73”. • Since our predictor is in the range of of the data used to create our regression equation AND since we are making a prediction about a baseball player AND since our correlation coefficient is greater than our significance level, we can use our regression equation to make a prediction.

  15. Making the Prediction • Our regression equation is y = -386.5 + 7.9x. • Our value of x is 73”. • Therefore, our predicted weight of a baseball player who is 73” tall is • y = -386.5 + 7.9 * 73 • y = 190.2

  16. Effects of Outliers • Outliers are data points that are far away from the general data values. • Like their effect on the mean and standard deviation, they effect regression equations as well, including whether or not the data is linear.

  17. Website Exercise Part 3 • Connect to the URL below and click the cursor to create a point at (0.0, 200.5). Email me a detailed explanation on the effect the outlier has on the slope, y-intercept and correlation coefficient of the regression equation? • Effects of Outliers Web Exercise

  18. Review • Connect to the URL below and take the practice multiple-choice exercise. If you have less than 80% correct, you should go back and review the Linear Regression chapter and either ask me or the tutoring center for help. • http://student.ccbcmd.edu/elmo/math141s/practice/linreg.htm

  19. Homework • Your next web assignment can be found at the Webquest link. Complete all questions using Microsoft Word and Statdisk. Email me your completed project.

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