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# chapter15 - Chapter 15 Correlation and Regression...

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Chapter 15 Correlation and Regression PowerPoint Lecture Slides Essentials of Statistics for the Behavioral Sciences Seventh Edition by Frederick J. Gravetter and Larry B. Wallnau

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Chapter 15 Learning Outcomes
Concepts to review Sum of squares (SS) (Chapter 4) Computational formula Definitional formula z-Scores (Chapter 5) Hypothesis testing (Chapter 8)

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15.1 Introduction to Correlation and Regression Measures and describes a relationship between two variables. Characteristics of relationships Direction (negative or positive) Form (linear is most common) Strength
Figure 15.1 Scatterplot for correlational data

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Figure 15.2 Examples of positive and negative relationships
Figure 15.3 Examples of different values for linear relationships

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15.2 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 =
Sum of Products (SP) Similar to SS (sum of squared deviations) Measures the amount of covariability between two variables - - = ) )( ( 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 n Y X XY SP ∑ ∑ - =
Calculation of the Pearson correlation 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 15.4 Example 15.3 Scatterplot
Pearson Correlation and z-scores Pearson correlation formula can be expressed as a relationship of z-scores. 1 1 - = - = ν ζ ρ Ποπυλατιον Σαμπλε Ψ Ξ

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Learning Check A scatterplot shows a set of data points that are clustered 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 A scatterplot shows a set of data points that are clustered 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 TF Decide if each of the following statements is True or False .
Answer TF 20 40 20 10 ) 20 )( 20 ( 20 - = - = - = ΣΠ

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chapter15 - Chapter 15 Correlation and Regression...

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