Chapter 11 Simple Linear Regression and Correlation 503

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Chapter 11 Simple Linear Regression and Correlation 503 STAT - Probability and Statistics for

Chapter 11 Simple Linear Regression and Correlation 503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

Introduction: 503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour

Introduction: 503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

Regression Analysis: The concept of regression analysis deals with finding the best relationship between

Regression Analysis: The concept of regression analysis deals with finding the best relationship between Y and X. Regression analysis measures the strength of the relationship, and allows for prediction of the response values Y for given values of the regressor X (x. ) 503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

The Simple Linear Regression Model 503 STAT - Probability and Statistics for Engineers and

The Simple Linear Regression Model 503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

The Fitted Regression Line The Method of Least Squares 503 STAT - Probability and

The Fitted Regression Line The Method of Least Squares 503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

Example: Estimate the regression line for the pollution data of the following table And

Example: Estimate the regression line for the pollution data of the following table And then, predict the value of y when x=30 503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

The scatter diagram for these data It can be seen from this scatter diagram

The scatter diagram for these data It can be seen from this scatter diagram that the points closely follow a straight line, indicating that the assumption of linearity between the two variables appears to be reasonable. 503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

Solution: Prove that 503 STAT - Probability and Statistics for Engineers and Scientists –

Solution: Prove that 503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

• ANOVA Table: Source of Variation (SV) Sum of Squares (SS) Degrees of

• ANOVA Table: Source of Variation (SV) Sum of Squares (SS) Degrees of Freedom (df) Regression SSR 1 Error SSE Total SST Mean Square (MS) 503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili F

Computational Formulas: 503 STAT - Probability and Statistics for Engineers and Scientists – Dr.

Computational Formulas: 503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

or or 503 STAT - Probability and Statistics for Engineers and Scientists – Dr.

or or 503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

Source of Variation SV Regression Error Total Sum of Squares Degrees of Freedom Mean

Source of Variation SV Regression Error Total Sum of Squares Degrees of Freedom Mean Squares SS 3390. 6 323. 3 3713. 9 df 1 31 32 MS = SS/df 3390. 6 10. 4 F (F- ratio = MSR/MSE) 325. 08 For testing: 503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

CORRELATION: 503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour

CORRELATION: 503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

Example: loblolly pine 503 STAT - Probability and Statistics for Engineers and Scientists –

Example: loblolly pine 503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili

503 STAT - Probability and Statistics for Engineers and Scientists – Dr. Mansour Shrahili