chapter 16 predicting who’ll win the super bowl: using linear regression part iv significantly...
TRANSCRIPT
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Chapter 16 Predicting Who’ll Win the Super Bowl:
Using Linear Regression
Part IVSignificantly Different:
Using Inferential Statistics
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What you will learn in Chapter 16
How prediction works and how it can be used in the social and behavioral sciences
How and why linear regression workspredicting one variable from another
How to judge the accuracy of predictions
The usefulness of multiple regression
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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 anotherCorrelation 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
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Remember…
The greater the strength of the relationship between two variables (the 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.
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The Logic of PredictionPrediction is an activity that computes
future outcomes from present onesWhat if you wanted to predict college GPA
based on high school GPA?
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Scatter Plot
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Regression LineRegression 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.”
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Prediction of Y given X = 3.0
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Error in PredictionPrediction is rarely perfect…
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Drawing the World’s Best Line
Linear Regression FormulaY=bX + a
Y = dependent variablethe predicted score or criterion
X = independent variablethe score being used as the predictor
b = the slope direction and “steepness” of the line
a = the interceptpoint at which the line crosses the y-axis
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Slope & Intercept
Slope – calculating b
Intercept – calculating a
2 2
( / )
[( ) / ]
XY X Y nb
X X n
Y b Xa
n
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How Good Is Our Prediction?
Standard error of estimate the measure of how much each data point
(on average) differs from the predicted data point or a standard deviation of all the error scores
The higher the correlation between two variables (and the better the prediction), the lower the error will be
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Using the ComputerSPSS and Linear Regression
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SPSS Output
What does it all mean?
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SPSS Scatterplot
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The More Predictors the Better? Multiple Regression
Multiple Regression FormulaY = bX1 + bX2 + a
Y = the value of the predicted scoreX1 = the value of the first independent
variableX2 = the value of the second independent
variableb = the regression weight for each variable
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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.
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Glossary Terms to Know
Regression lineLine of best fit
Error in predictionStandard error of the estimate
CriterionIndependent variable
PredictorDependent variable
Y primeMultiple Regression