Question

select the correct answer.
a dietician gathered data about the amounts of flour, baking powder, and butter used for several different muffin recipes. she used a graphing tool to organize the data in different scatter plots and found the following lines of best fit.

• the relationship between the baking powder used, x, and the flour used, y, is modeled by the equation ( y = 0.13x + 0.92 ), and the correlation coefficient for the data is 0.953.
• the relationship between the baking powder used, x, and the butter used, y, is modeled by the equation ( y = 0.24x + 0.76 ), and the correlation coefficient for the data is 0.802.
• the relationship between the flour used, x, and the butter used, y, is modeled by the equation ( y = 0.86x + 0.52 ), and the correlation coefficient for the data is 0.693.

which line of best fit can the dietician expect to produce the most reliable predictions?
a. the line modeling the baking powder and the butter used
b. the line modeling the baking powder and the flour used
c. the line modeling the flour and the butter used
d. all three lines will give equally reliable predictions.

Explanation:

Step1: Recall Correlation Coefficient

The closer the absolute value of the correlation coefficient is to 1, the stronger the linear relationship, and the more reliable the line of best fit for predictions.

Step2: Compare Coefficients

• For baking powder & flour: correlation coefficient is 0.953.
• For baking powder & butter: correlation coefficient is 0.802.
• For flour & butter: correlation coefficient is 0.693.

Step3: Determine Strongest Relationship

0.953 is the closest to 1 among 0.953, 0.802, and 0.693. So the line modeling baking powder and flour has the strongest linear relationship, hence the most reliable predictions.

Answer:

B. the line modeling the baking powder and the flour used