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Correlation and Regression Analysis – An Application

Systems Engineering Program. Department of Engineering Management, Information and Systems. EMIS 7370/5370 STAT 5340 : PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS. Correlation and Regression Analysis – An Application. Dr. Jerrell T. Stracener, SAE Fellow.

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Correlation and Regression Analysis – An Application

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  1. Systems Engineering Program Department of Engineering Management, Information and Systems EMIS 7370/5370 STAT 5340 : PROBABILITY AND STATISTICS FOR SCIENTISTS AND ENGINEERS Correlation and Regression Analysis – An Application Dr. Jerrell T. Stracener, SAE Fellow Leadership in Engineering

  2. Montgomery, Peck, and Vining (2001) present data concerning the performance of the 28 National Football league teams in 1976. It is suspected that the number of games won(y) is related to the number of yards gained rushing by an opponent(x). The data are shown in the following table:

  3. Correlation Analysis • Statistical analysis used to obtain a quantitative • measure of the strength of the relationship between • a dependent variable and one or more independent • variables

  4. Scatter Plot

  5. Sample correlation coefficient Notes: -1  r  1 R=r2  100% = coefficient of determination

  6. R=r2  100% =0.5447

  7. Correlation To test for no linear association between x & y, calculate Where r is the sample correlation coefficient and n is the sample size.

  8. Correlation Conclude no linear association if then treat y1, y2, …, yn as a random sample

  9. Correlation Take α=0.05 and check from the T-table, we get Since t=-5.5766 < -2.0555, we conclude that there is linear association between x and y and proceed with regression analysis

  10. Linear Regression Model Simple linear regression model where Y is the response (or dependent) variable 0 and 1are the unknown parameters  ~ N(0,) and data: (x1, y1), (x2, y2), ..., (xn, yn)

  11. Least squares estimates of 0 and 1

  12. estimates of 1

  13. estimates of 0

  14. Point estimate of the linear model is Least squares regression equation

  15. Regression Fitted Line Plot

  16. Point estimate of2

  17. (1 -)100% confidence interval for 0is where and where Interval Estimates for y intercept (0)

  18. Interval Estimates for y intercept (0) Take =0.05, then 95% confidence interval for 0is

  19. Interval Estimates for y intercept (0) Apply to the equation and we get the lower and upper bound for :

  20. Interval Estimates for slope(1) (1 -)100% confidence interval for 1is where and where

  21. Interval Estimates for slope(1)

  22. Confidence interval for conditional mean of Y, given x=2205 Given x equal to 2205, we can calculate the confidence interval of conditional mean of Y

  23. Confidence interval for conditional mean of Y, given x=2205 and

  24. Prediction interval for a single future value of Y, given x and

  25. Prediction interval for a single future value of Y, given x=2000 Given x= 2000,

  26. Prediction interval for a single future value of Y, given x=2000 and

  27. Excel Calculation

  28. Excel Regression Analysis Output

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