pearson’s correlation and bivariate regression lab exercise: chapter 9 1
DESCRIPTION
Interval/Ratio Measures of Association Pearson’s r – ranges from −1.00 to 1.00 – symmetric Analyze | Correlate | Bivariate – pairwise and listwise deletion of missing data 3TRANSCRIPT
Pearson’s Correlation and Bivariate Regression
Lab Exercise:Chapter 9
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Example Questions:
• Do opposites really attract? Is there a negative correlation between the educational levels of spouses?
• One more year in school typically results in how much more annual income?
• Schooling accounts for how much of the differences in persons’ incomes?
• What annual income would we predict for someone with 16 years of schooling?
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Interval/Ratio Measures of Association
• Pearson’s r– ranges from −1.00 to 1.00– symmetric
• Analyze | Correlate | Bivariate– pairwise and listwise deletion of missing data
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Bivariate Correlation
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Scatterplot: Do opposites attract?*Check linearity, strength, direction, and homoscedasticity
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Bivariate Linear Regression: Income on Schooling
• Equation for a straight line
• “Best-fitting” straight line
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Y = a + b(X)
Bivariate Linear Regression (cont.)• Analyze | Regression | Linear
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Answering Questions with Statistics Chapter 9 8
Regression Output of INCOME86 on
EDUC for 1980 GSS Young Adults
Bivariate Linear Regression (cont.)• Unstandardized coefficients
• Regression equation
• Predicted value Ŷ: substitute value for X (16 yrs?)= $21,604.089
• Regression residual: Y - Ŷ9
Y = -3089.255 + 1543.334(X) INCOME86 = -3089.255 + 1543.334(EDUC)
Bivariate Linear Regression (cont.)
• Multiple correlation coefficient (R)– indicates strength but not direction
• Coefficient of determination (R2)
• Coefficient of alienation (residual or unexplained)
coefficient of determination = R2
coefficient of alienation = 1 - R2
Bivariate Linear Regression (cont.)
• Some limitations to remember– regression does not prove causality– for interval-ratio level variables• Can be used with caution (requires special
interpretation) for grouped interval ratio or ordinal variables with >5 categories
– linear means only linear
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