Question

the scatter plot shows the relationship between daily high temperatures in two cities. scatter plot image omitted the linear correlation coefficient for this data is ( r = 0.993 ). which statement is the best interpretation of the linear correlation coefficient for the data? (\bigcirc) a. the correlation coefficient indicates no relationship between temperatures in the two cities. (\bigcirc) b. the correlation coefficient indicates very little correlation between the temperatures in the two cities. (\bigcirc) c. the correlation coefficient indicates weak support of the claim that as the temperature rises in one city it will rise in the other city. (\bigcirc) d. the correlation coefficient indicates strong support of the claim that as the temperature rises in one city it will rise in the other city.

Explanation:

The linear correlation coefficient \( r \) ranges from -1 to 1. A value close to 1 (like \( r = 0.993 \)) indicates a strong positive linear relationship. This means as one variable (temperature in Seattle) increases, the other (temperature in Sacramento) is likely to increase. Option A is wrong because \( r = 0.993 \) shows a relationship. Option B is wrong as 0.993 is a strong correlation, not very little. Option C is wrong because "weak support" is incorrect; 0.993 is strong. Option D correctly states that the high positive \( r \) (0.993) shows strong support for the claim that as temperature rises in one city, it rises in the other.

Answer:

D. The correlation coefficient indicates strong support of the claim that as the temperature rises in one city it will rise in the other city.