Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl.
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Transcript Part IV Significantly Different Using Inferential Statistics Chapter 15 Using Linear Regression Predicting Who’ll Win the Super Bowl.
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