The most accurate interpretation of the slope is "For every 1% increase in a student's final exam score, we expect to see a 0.62% increase in the course grade."
How is it so?
The slope of the regression line represents the change in the predicted course grade (Y) for a one-unit change in the final exam score (X). In this case, the slope is given as 0.62.
So, for every 1% increase in a student's final exam score (X), the predicted course grade (Y) is expected to increase by 0.62%. This implies a positive relationship between the final exam score and the course grade.
In mathematical terms, you can express this relationship using the equation of a line:
![\[ Y = mX + b \]](https://img.qammunity.org/2024/formulas/engineering/college/gs5mdh4b9u33mdxhk122331rt0fnb6fw97.png)
where:
-
is the predicted course grade,
-
is the final exam score,
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is the slope (0.62 in this case),
-
is the y-intercept (the point where the line crosses the y-axis).
So, interpreting the slope (0.62), for every 1% increase in
(final exam score),
(predicted course grade) is expected to increase by 0.62%.
Complete question:
Final and course grade: For this data set, X represents the final exam score as a percentage, and Y represents the predicted course grade as a percentage. The regression line for this data set has slope 0.62. Which of the following statements is the most complete and accurate interpretation of the slope?
Students with higher final exam scores tend to have higher course grades.
For every 1% increase in a student's final exam score, we expect to see a 0.62% decrease in the course grade.
For every 1% increase in a student's final exam score, we expect to see a 0.62% increase in the course grade.
For every 1% increase in a student's final exam score, we expect to see a 62% increase in the course grade.