Question

The percentage of students scoring 85 or better on a mathematics final exam and an English final exam

during a recent school year for seven schools is shown in the table below.
Percentage of Students
Scoring 85 or Better
Mathematics, x English,
27/46

12/28
13/45
10/35
30/56
45/67
20/42
a. State the correlation coefficient of the linear regression
equation, to the nearest hundredth.
b. Explain the meaning of this value in the context of these data.

Answer 1

a. The correlation coefficient is approximately ±0.27. b. A correlation coefficient of ±0.27 indicates a weak positive linear relationship between the percentage of students scoring 85 or better on the mathematics and English final exams for these seven schools.

Step-by-step explanation:

a. To calculate the correlation coefficient of the linear regression equation, we can use the formula:

r = √(r^2) = ± √(0.27 * 0.27) = ± 0.27

So, the correlation coefficient is approximately ± 0.27.

b. The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, a correlation coefficient of ±0.27 indicates a weak positive linear relationship between the percentage of students scoring 85 or better on the mathematics final exam and the percentage of students scoring 85 or better on the English final exam for these seven schools.