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# 0673chapter10 - Chapter 10 Correlation and Regression 10-2...

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Chapter 10 Correlation and Regression 10-2 Correlation 1. a. r = the correlation in the sample. In this context, r is the linear correlation coefficient computed using the chosen paired (points in Super Bowl, number of new cars sold) values for the randomly selected years in the sample. b. ρ = the correlation in the population. In this context, ρ is the linear correlation coefficient computed using all the paired (points in Super Bowl, number of new cars sold) values for every year there has been a Super Bowl. c. Since there is no relationship between the number of points scored in a Super Bowl and the number of new cars sold that year, the estimated value of r is 0. 2. Correlation is the existence of a relationship between two variables – so that knowing the value of one of the variables allows a researcher to make a reasonable inference about the value of the other. Correlation does not imply causality, as there are other factors besides causality that can be behind a relationship between two variables – e.g., they both could be heavily influenced by some third variable without having any cause-and-effect influence on each other. 3. Correlation is the existence of a relationship between two variables – so that knowing the value of one of the variables allows a researcher to make a reasonable inference about the value of the other. Correlation measures only association and not causality. If there is an association between two variables, it may or may not be cause-and-effect – and if it is cause-and-effect, there is nothing in the mathematics of correlation analysis to identify which variable is the cause and which is the effect. 4. Yes; since Table A-6 gives the critical values ±0.312, there is sufficient evidence to support a claim of a linear correlation between the before and after weights. No; the value of r. while it indicates a significant linear correlation, does not indicate the diet is effective in reducing weight. A correlation simply indicates that the after weight can be predicted from the before weight (and vice-versa), but not whether the after weight was generally larger or smaller (or even the same) compared to the before weight. 5. a. From Table A-6 for n = 62 [closest entry is n=60], C.V. = ±0.254. Therefore r = 0.758 indicates a significant (positive) linear correlation. Yes; there is sufficient evidence to support the claim that there is a linear correlation between the weight of discarded garbage and the household size. b. The proportion of the variation in household size that can be explained by the linear relationship between household size and weight of discarded garbage is r 2 = (0.758) 2 = 0.575, or 57.5%. 6. a. From Table A-6 for n = 8, C.V. = ±0.707. Therefore r = 0.693 indicates a significant (positive) linear correlation. Yes; there is sufficient evidence to support the claim that there is a linear correlation between the heights of mothers and the heights of their daughters.

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