Part IV Significantly Different Using Inferential Statistics

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Part IVSignificantly DifferentUsing Inferential
Statistics

• Chapter 15 ?
• Using Linear Regression
• Predicting Wholl Win the Super Bowl

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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

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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 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

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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. ?

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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?

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Scatter Plot
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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.

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Prediction of Y given X 3.0
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Error in Prediction

• Prediction is rarely perfect

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Drawing the Worlds Best Line

• Linear Regression Formula
• YbX 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

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Hasbro
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Slope Intercept

• Slope calculating b
• Intercept calculating a

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Number of Complaints (y) by Reindeer Age (x)
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Complaints by Reindeer Age Intermediate
Calculations
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SS Reg, SS Error, R2, and Correlation
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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
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Printout Slope Int, SS Reg, SS Errorand R2
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College GPA by SAT scores
Slope 0.003478 -1.07148 Intercept
0.000832 0.957866
Rsquare 0.686069 0.445998
F 17.48335 8 dfs
SS Regression 3.477686 1.591314 SS Residual
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Severity of Injuries by hrs per week strength
training
Slope -0.12507 6.847277 Intercept
Stand Error 0.045864 1.004246
R2 0.209854 2.181672
7.436476 28
SS Regression 35.39532 133.2713 SS Residual
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Using the Computer

• SPSS 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 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

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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
• Howeverthe independent variables should not be
  related to each otherthey 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 line
• Line of best fit
• Error in prediction
• Standard error of the estimate
• Criterion
• Independent variable
• Predictor
• Dependent variable
• Y prime
• Multiple Regression