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Correlation: Problems

Correlation: Problems. SD Line. True or false: the SD line always goes through the point of averages. True or false: the SD line always goes through the point (0, 0). SD Line. SD Line. Male college students have an average height of 69 inches, with an SD of 3 inches.

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Correlation: Problems

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  1. Correlation: Problems

  2. SD Line • True or false: the SD line always goes through the point of averages. • True or false: the SD line always goes through the point (0, 0).

  3. SD Line

  4. SD Line • Male college students have an average height of 69 inches, with an SD of 3 inches. • Their average weight is 140 pounds with an SD of 20 pounds. • The correlation between height and weight is 0.6. • If one of these students is 72 inches tall, how heavy would he have to be to fall on the SD line?

  5. Husbands and Wives • A study of the IQs of husbands and wives obtained the following results: for husbands, average IQ = 100, SD = 15, for wives, average IQ = 100, SD = 15. correlation coefficient r = 0.6.

  6. Pick the Scatter Diagram

  7. Heights • Suppose men always married women who were exactly 8% shorter. What would the correlation between their heights be? • Is the correlation between the heights of husbands and wives in the U.S. around –0.9, -0.3, 0.3, or 0.9?

  8. Gasoline Economy • For a representative sample of cars, would the correlation between the age of the car and its gasoline economy (miles per gallon) be positive or negative? • The correlation between gasoline economy and income of the owner turns out to be positive. How do you account for this positive association?

  9. Grade Point Averages • Three data sets are collected, and the correlation coefficient is computed in each case. The variables are: • GPA in freshman and sophomore year. • GPA in freshman and senior year. • Pick a likely value for the correlation coefficient: -0.50, 0.0, 0.30, 0.60, 0.95.

  10. Homework, Midterm, Final • In one class, the correlation between scores on the final and on the midterm was 0.50, while the correlation between the scores on the final on the homework was 0.25. • True or false, and explain: the relationship between the final scores and the midterm scores is twice as linear as the relationship between the final scores and the homework scores.

  11. Human Growth • A longitudinal study of human growth has been under way since 1929. The scatter diagram shows the height of 64 boys, measured at age 4 and 18. • The average height at age 4 is around: 38, 42, 44 inches. • The SD of height at 18 is around: 0.5, 1.0, 2.5 inches. • The correlation coefficient is around: 0.50, 0.80, 0.95. • Which is the SD line: solid or dashed?

  12. Comparing IQ Test • In a large psychology study, each subject took two IQ test. • You are trying to predict the score on form M from the score on form L. • On the whole, will the prediction error be smaller when the score on form L is 75, or 125? Or is it about the same for both?

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