Linear Regression.

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Presentation transcript:

Linear Regression

Index of Fit

Coefficient of Determination Correlation between X and Y is given by Estimate

Coefficient of Determination Correlation between X and Y is given by Estimate Estimate

Coefficient of Determination Then, a natural estimate for the correlation r is given by R is called the coefficient of determination and is an estimate of the correlation between the input x and the response y.

Sum of Squares

Sum of Squares

Residual Analysis

Analysis of Residuals

Note that if we sum the square of the residuals, we get SSR.

Standardized Residuals But, we do not know s,

Standardized Residuals Our best estimate of s is given by These are called the standardized residuals

Standardized Residuals

Residuals

Standardized Residuals