Chapter 14 - Chapter 14 Correlation and Regression...

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Chapter 14 Correlation and Regression PowerPoint Lecture Slides Essentials of Statistics for the Behavioral Sciences Eighth Edition by Frederick J. Gravetter and Larry B. Wallnau
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Chapter 14 Learning Outcomes
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Chapter 14 Learning Outcomes (continued)
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Tools You Will Need Sum of squares ( SS ) (Chapter 4) Computational formula Definitional formula z -Scores (Chapter 5) Hypothesis testing (Chapter 8) Analysis of Variance (Chapter 12) MS values and F -ratios
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14.1 Introduction to Correlation Measures and describes the relationship between two variables Characteristics of relationships Direction (negative or positive; indicated by the sign, + or – of the correlation coefficient) Form (linear is most common) Strength or consistency (varies from 0 to 1) Characteristics are all independent
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Figure 14.1 Scatterplot for Correlational Data
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Figure 14.2 Positive and Negative Relationships
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Figure 14.3 Different Linear Relationship Values
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14.2 The Pearson Correlation Measures the degree and the direction of the linear relationship between two variables Perfect linear relationship Every change in X has a corresponding change in Y Correlation will be –1.00 or +1.00 y separatel Y and X of variablity Y and X of ity covariabil r
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Sum of Products (SP) Similar to SS (sum of squared deviations) Measures the amount of covariability between two variables SP definitional formula: ) )( ( Y X M Y M X SP
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SP – Computational formula Definitional formula emphasizes SP as the sum of two difference scores Computational formula results in easier calculations SP computational formula: n Y X XY SP
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Pearson Correlation Calculation Ratio comparing the covariability of X and Y (numerator) with the variability of X and Y separately (denominator) Y X SS SS SP r
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Figure 14.4 Example 14.3 Scatterplot
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Pearson Correlation and z -Scores Pearson correlation formula can be expressed as a relationship of z -scores. N z z n z z r Y X Y X : Population 1 : Sample
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Learning Check A scatterplot shows a set of data points that fit very loosely around a line that slopes down to the right. Which of the following values would be closest to the correlation for these data?
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Learning Check - Answer A scatterplot shows a set of data points that fit very loosely around a line that slopes down to the right. Which of the following values would be closest to the correlation for these data?
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Learning Check Decide if each of the following statements is True or False
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Learning Check - Answers 20 40 20 10 ) 20 )( 20 ( 20 SP
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14.3 Using and Interpreting the Pearson Correlation Correlations used for: Prediction Validity Reliability Theory verification
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Interpreting Correlations Correlation describes a relationship but does not demonstrate causation Establishing causation requires an experiment in which one variable is
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