Part IV
Significantly Different
Using Inferential Statistics
Chapter 15 
Using Linear Regression
Predicting Who’ll Win the Super Bowl
What you will learn in Chapter 15
 How prediction works and how it can be used
in the social and behavioral sciences
 How and why linear regression works
 predicting one variable from another
 How to judge the accuracy of predictions
 The usefulness of multiple regression
What is Prediction All About?
 Correlations can be used as a basis for the
prediction of the value of one variable from
the value of another



Correlation can be determined by using a set
of previously collected data (such as data on
variables X and Y)
calculate how correlated these variables are
with one another
use that correlation and the knowledge of X to
predict Y with a new set of data
Remember…
 The greater the strength of the relationship
between two variables (higher the absolute
value of the correlation coefficient) the more
accurate the predictive relationship
 Why???

The more two variables share in common
(shared variance) the more you know about
one variable from the other. 
The Logic of Prediction
 Prediction is an activity that computes future
outcomes from present ones

What if you wanted to predict college GPA
based on high school GPA?
Scatter Plot
Regression Line
 Regression line – reflects our best guess as
to what score on the Y variable would be
predicted by the X variable.

Also known as the “line of best fit.”
Prediction of Y given X = 3.0
Error in Prediction
 Prediction is rarely perfect…
Drawing the World’s Best Line
 Linear Regression Formula
Y=bX + a
 Y = dependent variable


the predicted score or criterion
 X = independent variable
 the score being used as the predictor
 b = the slope
 direction of the line
 a = the intercept
 point at which the line crosses the y-axis
Hasbro
Slope & Intercept
 Slope – calculating b
 Intercept – calculating a
Number of Complaints (y) by
Reindeer Age (x)
Complaints by Reindeer Age:
Intermediate Calculations
SS Reg, SS Error, R2, and
Correlation
Now You Try!!
Participant
Hours/Week Video Games
College GPA
1
3
3.8
2
15
2.1
3
22
2.5
4
30
0.6
5
11
3.1
6
25
1.9
7
6
3.9
8
12
3.8
9
17
1.7
Chapter 6
16
Printout: Slope Int, SS Reg, SS Error
and R2
College GPA by SAT scores
Slope
0.003478
-1.07148Intercept
0.000832 0.957866
Rsquare
0.686069 0.445998
F
SS
Regression
17.48335
8dfs
SS
3.477686 1.591314 Residual
Severity of Injuries by # hrs per week strength
training;
Slope
-0.12507
6.847277Intercept
Stand Error
0.045864
1.004246
R2
0.209854
2.181672
7.436476
28
SS
Regression
35.39532
SS
133.2713 Residual
Using the Computer
 SPSS and Linear Regression
SPSS Output
 What does it all mean?
SPSS Scatterplot
The More Predictors the Better?
Multiple Regression
 Multiple Regression Formula

Y = bX1 + bX2 + a
 Y = the value of the predicted score
 X1 = the value of the first independent variable
 X2 = the value of the second independent
variable
 b = the regression weight for each variable
The BIG Rule…
 When using multiple predictors keep in mind...


Your independent variables (X1,, X2 ,, X3 , etc.)
should be related to the dependent variable
(Y)…they should have something in common
However…the independent variables should
not be related to each other…they should be
“uncorrelated” so that they provide a “unique”
contribution to the variance in the outcome of
interest.
Glossary Terms to Know
 Regression line
 Line of best fit
 Error in prediction
 Standard error of the estimate
 Criterion
 Independent variable
 Predictor
 Dependent variable
 Y prime
 Multiple Regression