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, y
46/27
12/28
13/45
10/34
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 r for Mathematics and English scores is approximately 0.91, indicating a strong positive linear relationship.

b. This suggests that schools excelling in Mathematics also excel in English.

a. Correlation Coefficient Calculation:

The correlation coefficient (\(r\)) is determined by the formula:

`\[ r = (n(\sum xy) - (\sum x)(\sum y))/(√([n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2])) \]`

Using the provided data, where x represents the Mathematics scores and y represents the English scores, we calculate
`\(r \approx 0.91\)` (rounded to the nearest hundredth).

b. Interpretation:

The correlation coefficient of 0.91 indicates a strong positive linear relationship between the percentages of students scoring 85 or better in Mathematics and English. As r approaches 1, it signifies a more robust positive correlation. In this context, schools with higher percentages in Mathematics tend to also have higher percentages in English, suggesting a positive association between performance in these subjects. However, correlation does not imply causation, and other factors may contribute to this observed relationship.