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6. Why can't you obtain a correlation coefficient greater than ±1?

8. As the value of r approaches ±1, what does it indicate about the following:
a) The consistency in the X-Y pairs
b) The variability of the Y scores at each X
c) The closeness of the Y scores to the regression line
d) the accuracy with which we can predict Y if X is known

12. For each of the following indicate whether it is a positive linear, negative linear, or nonlinear relationship:
a) Quality of performance (Y) increases with increased arousal (X) up to an optimal level; then quality of performance decreases with increased arousal
b) Overweight people are (X) less healthy (Y)
c) As number of minutes of exercise increases each week (X), dieting individuals lose more pounds (Y)
d) The number of bears in an area (Y) decreases as the area becomes increasingly populated by humans (X)

18. A researcher measures the following scores for a group of people. The X variable is the number of errors on a math test, and the Y variable is the person's level of satisfaction with his/her performance.
a) With such ratio scores, what should the researcher conclude about this relationship? (Hint: compute something)

b) How well will we be able to predict satisfaction scores using this relationship?

Participant Errors X Satisfaction Y
1 9 3
2 8 2
3 4 8
4 6 5
5 7 4
6 10 2
7 5 7

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#### Solution Preview

6. Correlation coefficient value represents how closely the relationship between two variables is linear. In this case, it cannot be more than 100%. Therefore, the correlation coefficient needs to be between -1 and 1.

8. d is the right answer.

12. For each of the following indicate whether it is a positive linear, negative linear, or nonlinear relationship:
a) ...

#### Solution Summary

The solution assists with answering several statistics example questions.

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