Question

the correlation between education and income as measured on 80 people is r = 0.65. explain whether or not each of the following possible conclusions is justified. a) when education increases, income increases as well. b) the form of the relationship between education and income is straight. c) there are no outliers in the scatterplot of income vs. education. d) whether we measure education in years or months, the correlation will still be 0.65. a) is this conclusion justified? explain. a. yes, because the correlation coefficient between education and income is positive. b. no, because this cannot be concluded from the correlation alone. there may be a nonlinear relationship or outliers. c. no, because the correlation coefficient between education and income is negative. d. no, because the correlation coefficient between education and income is positive. e. yes, because the correlation coefficient between education and income is negative.

Explanation:

Step1: Analyze correlation concept

Correlation coefficient only measures linear relationship. Just because $r = 0.65$ doesn't mean there are no other types of relationships like non - linear ones.

Step2: Evaluate conclusion

We cannot solely conclude based on the correlation coefficient about the nature of the relationship as there could be non - linear relationships or outliers affecting the result.

Answer:

B. No, because this cannot be concluded from the correlation alone. There may be a nonlinear relationship or outliers.