1. © McGraw-Hill Higher Education. All Rights Reserved. Chapter 2F Statistical Tools in Evaluation

2. © McGraw-Hill Higher Education. All Rights Reserved. Linear Regression l Predict one variable from others l If measurement on one variable is difficult l Prediction is not perfect but contains error l Error (SEE) is low if r is high l Equation is Y=(bX)+C l Y is the predicted value l b is the slope of the line and X is the value of the other l C is the Y intercept (constant)

3. © McGraw-Hill Higher Education. All Rights Reserved. Prediction-Regression Analysis Regression – statistical model used to predict performance on one variable from another. Simple regression – predicting a score on one variable (Y) from one other variable (X). Multiple regression – predicting a score on one variable (Y) from two or more other variables (X 1, X 1, etc.)

4. © McGraw-Hill Higher Education. All Rights Reserved. General Prediction Equation Y = (bX) + C b = slope of regression line (rate of change in Y per unit change in X) c = Y-intercept or constant (Y when X=zero)

5. © McGraw-Hill Higher Education. All Rights Reserved. Standard Error of Estimate (SEE) R=regression while r=correlation Predicted Score = Y Y will not be perfect unless r = 1 When r  1 there is prediction error The standard deviation of this error = SEE SEE = S y  1 - r 2

6. © McGraw-Hill Higher Education. All Rights Reserved. Standard Error of Estimate (SEE) Expect to find the subjects’ real score in the boundaries: Y ± 2 (SEE)95% of the time The equation with the lowest SEE is the most accurate.

7. © McGraw-Hill Higher Education. All Rights Reserved. Other important measures R = correlation between predicted and real score  Ranges between 0 and 1.00  An index of prediction accuracy R 2 = coefficient of determination  Proportion of variance in criterion (Y scores) explained by the predictor (X scores)  An index of prediction accuracy

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9. Regression Equation l Y=(bX)+C l Y is the predicted value l b is the slope of the line and X is the value l C is the Y intercept (constant)

10. © McGraw-Hill Higher Education. All Rights Reserved. Confidence Intervals (CI) l SEE x 2 l Determines error around the predicted score l Multiply the SEE x 2 to get 95% confidence

11. © McGraw-Hill Higher Education. All Rights Reserved. Simple Regression l Trying to predict height from weight. l Run SPSS regression and choose linear.

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13. Simple Regression Solved l Subject #1, Y=(bx)+C l Y=(.06x115)+56.81 l Y=6.9+56.81 l Y=63.71 l Predicted score = 63.71+(SEEx2) l Answer = 63.71+6.98 l 95% of the time the real score will fall between 56.73 - 70.69

14. © McGraw-Hill Higher Education. All Rights Reserved. Multiple Regression Predict criterion (Y) using several predictors (X 1, X 2, X 3, etc) Basic multiple regression equation has one intercept (c) and several bs (one for each predictor variable). Y = (bX 1 + bX 2 + bX 3 ) + c Important measures: R, R 2, SEE

15. © McGraw-Hill Higher Education. All Rights Reserved. Multiple Regression l Trying to predict height from weight and Rgrip. l Run SPSS regression and choose linear.

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17. Multiple Regression Solved l Subject #1, Y= (bX 1 ) + (bX 2 ) + C l Y=(.02x115) + (.08x18) + 56.14 l Y=2.3+1.44+56.14 l Y=59.88 l Predicted score = 59.88+(SEEx2) l Answer = 59.88+4.24 l 95% of the time the real score will fall between 55.64 – 64.12

18. © McGraw-Hill Higher Education. All Rights Reserved. Outcomes l Simple vs. Multiple Regression –R increased –SEE decreased THEREFORE –95% confidence intervals decreased –Prediction accuracy increased

19. © McGraw-Hill Higher Education. All Rights Reserved. SPSS l Analyze –Regression –Linear l Dependent variable (what to predict) l Independent variable (used to predict) l Constant, B value(s) and SEE