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STA291

STA291. Statistical Methods Lecture 10. Measuring something over time…. Like a company’s stock value:. It kind of just sits there, making your eyes glaze over. And even though we’re measuring one variable (of interest), we need to look at two variables at a time …. Time Plot.

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STA291

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  1. STA291 Statistical Methods Lecture 10

  2. Measuring something over time… • Like a company’s stock value: • It kind of just sits there, making your eyes glaze over. • And even though we’re measuring one variable (of interest), we need to look at two variables at a time …

  3. Time Plot

  4. Terrible, Misleading Time Plot

  5. Analyzing RelationshipsBetween Two Quantitative Variables • Is there an association between the two variables? • Positive or negative? • What is it’s shape? • How strong is the association? • Notation • Response variable: Y • Explanatory variable: X

  6. Sample Measure of Linear Relationship • Sample Correlation Coefficient: • Alternatively: • Population measures: Divide by N instead of n-1

  7. Properties of the Correlation I • The value of r does not depend on the units(e.g., changing from inches to centimeters) that X and Y are measured in • r is standardized (has no units itself) • r is always between –1 and 1 • r measures the strength and direction of the linear association between X and Y • r>0 positive linear association • r<0 negative linear association

  8. Properties of the Correlation II • r = 1 when all sample points fall exactly ona line with positive slope (perfect positive linear association) • r = – 1 when all sample points fall exactlyon a line with negative slope (perfect negative linear association) • The larger the absolute value of r, the stronger is the degree of linear association

  9. Properties of the Correlation III • If r is close to 0, this does not necessarily meanthat the variables are not associated • It only means that they are not linearly associated • The correlation treats X and Y symmetrically; that is, it does not matter which variable is explanatory (X) and which one is response (Y), the correlation remains the same

  10. All Correlation r = 0.82

  11. Scatter Diagram of Murder Rate (Y) andPoverty Rate (X) for the 50 States r = 0.63

  12. Looking back • Time plots • General two-variable analysis • Sample correlation, r

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