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**Kin 304 Regression Linear Regression Least Sum of Squares**

Assumptions about the relationship between Y and X Standard Error of Estimate Multiple Regression Standardized Regression

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**Prediction Can we predict one variable from another?**

Linear Regression Analysis Y = mX + c m = slope; c = intercept Regression

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**Linear Regression Correlation Coefficient (r) how well the line fits**

Standard Error of Estimate (S.E.E.) how well the line predicts Regression

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**Least Sum of Squares Curve Fitting**

(Residual) Regression

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**Assumptions about the relationship between Y and X**

For each value of X there is a normal distribution of Y from which the sample value of Y is drawn The population of values of Y corresponding to a selected X has a mean that lies on the straight line In each population the standard deviation of Y about its mean has the same value

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**Standard Error of Estimate**

measure of how well the equation predicts Y has units of Y true score 68.26% of time is within plus or minus 1 SEE of predicted score Standard deviation of the normal distribution of residuals Regression

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**Right Hand L. = 0.99Left Hand L. + 0.254 r = 0.94 S.E.E. = 0.38cm**

Regression Kin 304 Spring 2009

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**How good is my equation? Regression equations are sample specific**

Cross-validation Studies Test your equation on a different sample Split sample studies Take a 50% random sample and develop your equation then test it on the other 50% of the sample Regression

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**Multiple Regression More than one independent variable**

Y = m1X1 + m2X2 + m3X3 …… + c Same meaning for r, and S.E.E., just more measures used to predict Y Stepwise regression variables are entered into the equation based upon their relative importance Regression

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**Building a multiple regression equation**

X1 has the highest correlation with Y, therefore it would be the first variable included in the equation. X3 has a higher correlation with Y than X2. However, X2 would be a better choice than X3. to include in an equation with X1, to predict Y. X2 has a low correlation with X1 and explains some of the variance that X1 does not. X3 Y X1 X2

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**Standardized Regression**

The numerical value is of mn is dependent upon the size of the independent variable Y = m1X1 + m2X2 + m3X3 …… + c Variables are transformed into standard scores before regression analysis, therefore mean and standard deviation of all independent variables are 0 and 1 respectively. The numerical value of zmn now represents the relative importance of that independent variable to the prediction Y = zm1X1 + zm2X2 + zm3X3 …… + c Regression

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