Chapter 14

# 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
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
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
Figure 14.2 Positive and Negative Relationships

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Figure 14.3 Different Linear Relationship Values
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
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
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
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?
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
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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