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Correlation Coefficient : Just how strong is this relationship?

Correlation Coefficient : Just how strong is this relationship?. AP Statistics Newell. Carbs vs. Fat. Here are data on 9 different types of hamburgers at McDonalds. Carbs vs. Fat. Are we looking for an explanatory-response relationship or just a relationship here?

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Correlation Coefficient : Just how strong is this relationship?

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  1. Correlation Coefficient: Just how strong is this relationship? AP Statistics Newell

  2. Carbs vs. Fat Here are data on 9 different types of hamburgers at McDonalds.

  3. Carbs vs. Fat • Are we looking for an explanatory-response relationship or just a relationship here? • What relationship do you expect? • Enter carbs into L1 and fat into L2. Create the scatterplot. • Describe the strength, form, and direction of the scatterplot. Are there any outliers?

  4. Carbs vs. Fat

  5. Correlation • A correlation is a LINEAR relationship. • The correlation coefficient is a number that summarizes how strong the LINEARrelationship is as well as the direction of that LINEAR relationship. • Correlation = LINEAR relationship

  6. Fun facts about the correlation coefficient • A measure of the strength and direction of a LINEAR relationship • r or R (as a statistic, as a parameter use r or rho) • -1 ≤ r ≤ 1 • Negative r = negatively sloping line • Positive r = positively sloping line • r = 1 or -1 perfect linear relationship • r = 0  no linear relationship • r has no units… we’ll see why in a minute

  7. Examples of r

  8. Carbs vs. Fat • Is the correlation coefficient positive or negative here? • Is the correlation coefficient closer to 1 or to 0? • Let’s find this on our calculators…

  9. Calculator Instructions • Before we begin, turn diagnostics on 2nd CATALOG  DiagnosticOn  ENTER • Enter data into two lists • Go to: STAT  CALC  8: LinReg(a+bx)  ENTER • Enter your two lists, separated by a comma. The explanatory variable should be first.

  10. Examples… Match R to each picture • r = -.9668 • r = .8621 • r = -.8984 • r = .1990

  11. What happens to r when the data changes? • Add 20 to each explanatory value Put cursor on name L3. 2nd 1  + 20  Enter • Find the correlation between L3 and L2 (L3 is the explanatory variable)

  12. What happens to r when the data changes? • Multiply each explanatory value by 5 Put cursor on name L3. 2nd 1  *5  Enter • Find the correlation between L3 and L2 (L3 is the explanatory variable)

  13. What happens to r when the data changes? • Find the correlation between L1 and L2 where L2 is now the explanatory variable.

  14. What happens to r when the data changes? R does NOT change if • You change one variable’s values by adding or multiplying the same number to each value • You switch the explanatory and response variables

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