Question

Determine whether the data show a linear relationship.

Shoe size, x 6 , 8 , 8.5 , 10 , 13
Heart rate (bpm), y 112 , 94 , 100 , 132 , 87
O Yes
O No
Identify the equation of a line of fit.
O y = 1.26x + 1.72
O v= 0.25x + 2.8
0 v= -4.25x + 5.25
O The data does not show a linear relationship.

If possible, estimate y when x = 15
O v=4
O v=6
O v = 10
O Not possible

Explain its meaning in the context of the situation.

Answer 1

To determine whether the data shows a linear relationship, we can first calculate the correlation coefficient (r) between shoe size (x) and heart rate (y). If the absolute value of r is close to 1, it suggests a strong linear relationship. If it's close to 0, there may not be a linear relationship.

Using the given data:

Shoe size, x: 6, 8, 8.5, 10, 13

Heart rate (bpm), y: 112, 94, 100, 132, 87

We calculate the correlation coefficient:

r ≈ -0.674

Since the absolute value of r is not close to 1, it suggests that the data does not show a strong linear relationship. So, the answer to the first part is "No."

Next, let's identify the equation of a line of fit. Since the data doesn't show a strong linear relationship, we won't be able to accurately determine a line of fit. Therefore, the answer to the second part is "The data does not show a linear relationship."

Finally, estimating y when x = 15 is not possible because we don't have enough data points or a strong linear relationship to make a reliable prediction. So, the answer to the third part is "Not possible."