1. Regression is a technique closely related to correlation that is used to make about scores on one variable from knowledge of scores on another variable. 2. The regression line is the straight line through a set of points in the scatter diagram. fitting line, including the beginning and end points. (This will be only your best guess at the best-fitting line, of course!) 4. Based on the regression line you drew, what approximate GPA would you predict for an individual who obtained a score of 14 on the University Aptitude Test? 5. How does your prediction compare to the GPA obtained by Randall, the examinee who actually scored a 14 on the UAT? What Does the Regression Equation Mean? this point a bit more later, but for the moment, keep in mind that the difference between Y and Y is called the residual .) from knowledge of X. (Of course, just as one rarely sees a "perfect" correlation coefficient of 1.00, one hardly ever comes across a "perfect" standardized b of 1.00 !) .8 , a = 1 . Finally, X is simply the observed or known value of X (such as UAT score) on the basis of which you will predict GPA (or Y ). The Best-Fitting Line The formulas for calculating b (the slope of the regression line) and a (the y -intercept) are: b = N X 2 ( X ) 2 N ( X Y ) ( X ) ( Y ) a = Y b X WORKSHEET 1 Values Needed for Calculating the Correlation Coefficient and Regression Line Values Needed for Calculating the Correlation Coefficient and Regression Line N = X = Y = ( X ) 2 = ( Y ) 2 = ( X ) ( Y ) = 7. The equation for the regression line is Y = (Round answers to four significant digits. For example, 1.234 or .1234.) after the decimal point. For example, 2.12. a. UAT = 4 Y = b. UAT = 10 Y = c. UAT = 17 Y = ( Y Y ) is called the residual. a. UAT = 4 Y (actual GPA = b. UAT = 10 Y (actual GPA) = and c. UAT = 17 Y (actual GPA) = 10. Correlation is a special case of regression in which scores on both variables are in or units. This is useful because it means that in correlation, the intercept is always 0. 11. Testing the Statistical Significance of a Correlation Coefficient the t value: t = r 1 r 2 N 2 Round answers to two significant digits after the decimal point. For example, .12 or 2.12 . 12. How to Interpret a Regression Plot When the slope of the regression line is 0 , variable X (the predictor) and variable Y (the criterion) are essentially 13. In the case in the previous question described above, your best guess at the criterion score is going to be the .

1. 1. Regression is a technique closely related to correlation that is used to make about scores on
one variable from knowledge of scores on another variable. 2. The regression line is the straight
line through a set of points in the scatter diagram. fitting line, including the beginning and end
points. (This will be only your best guess at the best-fitting line, of course!) 4. Based on the
regression line you drew, what approximate GPA would you predict for an individual who
obtained a score of 14 on the University Aptitude Test? 5. How does your prediction compare to
the GPA obtained by Randall, the examinee who actually scored a 14 on the UAT? What Does
the Regression Equation Mean? this point a bit more later, but for the moment, keep in mind that
the difference between Y and Y is called the residual .) from knowledge of X. (Of course, just as
one rarely sees a "perfect" correlation coefficient of 1.00, one hardly ever comes across a
"perfect" standardized b of 1.00 !) .8 , a = 1 . Finally, X is simply the observed or known value of
X (such as UAT score) on the basis of which you will predict GPA (or Y ). The Best-Fitting Line
The formulas for calculating b (the slope of the regression line) and a (the y -intercept) are: b = N
X 2 ( X ) 2 N ( X Y ) ( X ) ( Y ) a = Y b X WORKSHEET 1 Values Needed for Calculating the
Correlation Coefficient and Regression Line Values Needed for Calculating the Correlation
Coefficient and Regression Line N = X = Y = ( X ) 2 = ( Y ) 2 = ( X ) ( Y ) = 7. The equation for
the regression line is Y = (Round answers to four significant digits. For example, 1.234 or
.1234.) after the decimal point. For example, 2.12. a. UAT = 4 Y = b. UAT = 10 Y = c. UAT =
17 Y = ( Y Y ) is called the residual. a. UAT = 4 Y (actual GPA = b. UAT = 10 Y (actual GPA)
= and c. UAT = 17 Y (actual GPA) = 10. Correlation is a special case of regression in which
scores on both variables are in or units. This is useful because it means that in correlation, the
intercept is always 0. 11. Testing the Statistical Significance of a Correlation Coefficient the t
value: t = r 1 r 2 N 2 Round answers to two significant digits after the decimal point. For
example, .12 or 2.12 . 12. How to Interpret a Regression Plot When the slope of the regression
line is 0 , variable X (the predictor) and variable Y (the criterion) are essentially 13. In the case
in the previous question described above, your best guess at the criterion score is going to be the