1. BPK 304W Regression Linear Regression Least Sum of Squares
Assumptions about the relationship between Y and X
Standard Error of Estimate
Multiple Regression
Standardized Regression

2. Prediction Can we predict one variable from another?
Linear Regression Analysis
Y = mX + c
m = slope; c = intercept
Regression

3. Linear Regression Correlation Coefficient (r) how well the line fits
Standard Error of Estimate (S.E.E.)
how well the line predicts
Regression

4. Least Sum of Squares Curve Fitting
(Residual)
Regression

5. 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

6. 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

7. Right Hand L. = 0.99Left Hand L. + 0.254 r = 0.94 S.E.E. = 0.38cm
Regression
Kin 304 Spring 2009

8. 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

9. 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

10. 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

11. 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