Question

18. The correlation coefficients for two sets of data are shown below. Label each statement as true or false. SET A SET B r = 0.9 r = 0.25 a. Set A must have fewer values than set B. b. The trend line for set B must be steeper than the trend line for set A. c. The points on set A must be more spread out than the points on set B.

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Answer 1

Set A with r=0.9 and Set B with r=0.25 have provided statements to be labeled true or false. The correlation coefficient only measures the strength of a linear relationship, not the number of data points, the slope of the trend line, or the distribution's spread. Thus, all provided statements are false.

Step-by-step explanation:

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. Two sets of data, Set A with r = 0.9 and Set B with r = 0.25, have different strengths of correlation. Statements are made about these sets, and we must assess them as true or false based on the given r values.

The correlation is significant if it is strong enough to provide a reliable linear model for prediction. In Set A, r = 0.9 indicates a very strong positive linear relationship, likely significant. In Set B, r = 0.25 indicates a weak linear relationship, and its significance would depend on the sample size and the context of the data.