Presentation1.pptx
- 1. A researcher carefully computes the correlation coefficient between two variables and gets r = 1.23. What does this value mean?
- 2. A error was made! All correlation coefficients: −1 ≤ r ≤ 1.
- 3. It has been noted that there is a positive correlation between the U.S. economy and the height of women's hemlines (distance from the floor of the bottom of a skirt or dress) with shorter skirts corresponding to economic growth and lower hemlines to periods of economic recession. Comment on the conclusion that economic factors cause hemlines to rise and fall.
- 4. A positive correlation does exist; however, correlation does not imply causation.
- 5. Given a set of paired data (X,Y) a. if Y is independent of X, then what value of a correlation coefficient would you expect? b. if Y is linearly dependent on X, then what value of a correlation coefficient would you expect?
- 6. a. r = 0. b. r ≈ 1 or r ≈ −1 (these two are same as |r| ≈ 1).
- 7. A researcher has a large number of data pairs (age, height) of humans from birth to 70 years. He computes a correlation coefficient. a. Would you expect it to be positive or negative? Why? b. What would you suggest to be a major problem with this approach?
- 8. a. Positive since in general people grow in height increasing with age. b. The underlying data is not linear. During the first few years of life, height increases rapidly and irregularly. After teenage years height is essentially constant. A correlation coefficient is a measure of the scatter about a straight line. A better plan would be to restrict the data set to children only.
- 9. A researcher wishes to test the idea that show size and mathematical ability are correlated; that is, people with larger feet have higher mathematical skills. To test this he conducts a study of an entire town of 2000 persons measuring their shoe size and administering a math test. He finds that there is a significant correlation between shoe size and math skills with people with larger feet having higher math skills. What might an important problem with this approach?
- 10. The problem is the "entire town." This includes infants, children, as well as adults. Clearly small children have smaller feet and have not yet learned as many math skills. A more appropriate study would be to include only adults or persons in a specified age group; as an example, 25 to 65.
- 11. How does the correlation coefficient relate to the slope of the regression line?
- 12. The sign of the correlation coefficient is the same as the sign of the slope, but the magnitude of the correlation coefficient is a measure of scatter about the slope.