Question

select the correct answer.
charlie gathered data about the time it takes him to complete a crossword puzzle and the number of clues in the puzzle. he used a graphing tool to organize the data in a scatter plot and find the line of best fit.
he found the relationship between the number of clues, x, and the time required to complete the puzzle, y, is modeled by the equation y = 0.376x + 15.48, and the correlation coefficient for the data is 0.219.
could the line of best fit be used to make reliable predictions about the time it takes charlie to complete a crossword puzzle?
a. yes, because the slope of the line of best fit is closer to 0 than to 1, which indicates a strong association between the variables.
b. yes, because the correlation coefficient is closer to 0 than to 1, which indicates a strong association between the variables.
c. no, because the slope of the line of best fit is closer to 0 than to 1, which indicates a weak association between the variables.
d. no, because the correlation coefficient is closer to 0 than to 1, which indicates a weak association between the variables.

Explanation:

The correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables. The value of \(r\) ranges from \(- 1\) to \(1\). A value close to \(1\) or \(-1\) indicates a strong linear relationship, while a value close to \(0\) indicates a weak linear relationship. Here, \(r = 0.219\) which is close to \(0\), so there is a weak association between the number of clues (\(x\)) and the time required to complete the puzzle (\(y\)). The slope of the regression line does not determine the strength of the association. The line of best fit is used for reliable predictions when there is a strong association. Since the association is weak (because \(r\approx0.219\)), the line of best fit cannot be used for reliable predictions.

Answer:

D. No, because the correlation coefficient is closer to 0 than to 1, which indicates a weak association between the variables.