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:

Step1: Understand correlation coefficient

The correlation coefficient $r$ measures the strength and direction of a linear relationship. Values of $r$ range 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.

Step2: Analyze given correlation coefficient

The given correlation coefficient is $r = 0.219$. Since $0.219$ is close to 0, it implies a weak linear relationship between the number of clues $x$ and the time $y$ to complete the puzzle.

Step3: Determine reliability of predictions

When there is a weak linear relationship, the line - of - best - fit is not reliable for making predictions.

Answer:

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