Week12_Nov3_Correlation_Answers

Week12_Nov3_Correlation_Answers - HP 1100 Tutorial for Week...

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HP 1100 Tutorial for Week 12 Correlation [Dataset] “Week12_Nov3_Correlation.sav” 1. Scatter Plot a) Generate a scatter plot of X and Y: Graphs -> Legacy Dialogs -> Scatter/Dot b) Evaluate the relationship between X and Y from the graph: **Questions: Does it look linear or non-linear? Linear What is the direction of the relationship? Positive What is the degree of the relationship? Need to calculate “ r ”. 2. The Pearson Correlation a) Compute the Pearson correlation r between X and Y: By formula: Measure the variability of X: SS X = Σ ( X ´ X ) 2 = ( 6 5 ) 2 + ( 3 5 ) 2 + ( 5 5 ) 2 + ( 6 5 ) 2 + ( 4 5 ) 2 + ( 6 5 ) 2 = 8 Measure the variability of Y: SS Y = Σ ( Y ´ Y ) 2 =( 4 3 ) 2 +( 1 3 ) 2 +( 0 3 ) 2 +( 7 3 ) 2 +( 2 3 ) 2 +( 4 3 ) 2 = 32 Measure the covariability of X and Y: SP = Σ ( X ´ X )( Y ´ Y ) = ( 6 5 ) ( 4 3 ) + ( 3 5 ) ( 1 3 ) + ( 5 5 ) ( 0 3 ) + ( 6 5 ) ( 7 3 ) + ( 4 5 ) ( 2 3 ) + ( 6 5 ) Pearson correlation r is: r = SP SS X SS Y = 11 8 × 32 = 0.688 Obtain from SPSS: Analyze -> Correlate -> Bivariate -> Select “Pearson” b) Evaluate the relationship between X and Y from Pearson correlation r **Questions: What is the direction of the correlation? Positive.
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