Answer:
b.
About 44% of the variation in the final exam score can be explained by the students' scores on the 3rd exam. The remaining 56% is due to other factors or unexplained randomness.
Step-by-step explanation:
Hello!
X: Third exam score of a statistics student.
Y: Final exam score of a statistics student.
The estimated regression line is: y = -173.51 + 4.83x
Where
-173.51 is the estimation of the intercept and you can interpret it as the value of the estimated average final exam score when the students scored 0 points on their third exam.
4.83 is the estimation of the slope and you can interpret is as the modification on the estimated average score of the final exam every time the score on the third exam increases 1 point.
R²= represents the coefficient of determination.
Its interpretation is: 44% of the variability of the final exam scores of the statistics students are explained by the scores in the third exam, under the estimated model y = -173.51 + 4.83x.
I hope it helps!
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A random sample of 11 statistics students produced data where x is the third exam score out of 80, and y is the final exam score out of 200. The corresponding regression line has the equation: y = -173.51 + 4.83x, and the value of r2 (the "coefficient of determination") is found to be 0.44. What is the proper interpretation of r2?
a.
Due to the number of points on the two exams, the third exam score will likely be 44% of the final exam score.
b.
About 44% of the variation in the final exam score can be explained by the students' scores on the 3rd exam. The remaining 56% is due to other factors or unexplained randomness.
c.
For each 1 point increase in the 3rd exam score, we expect the final exam score to increase by 0.44 points.
d.
For each 1 point increase in the 3rd exam score, we expect the final exam score to increase by 0.44 percent.
e.
44% of the students scored within 1 standard deviation of the mean on each of the two tests.
