Question

Suppose John is a high school statistics teacher who believes that scoring higher on homework assignments leads to higher test scores. Immediately after giving the most recent test, he surveyed each of the 21 students in his class and asked them what their homework average was for material related to this test. He then matched each student's test grade with his or her survey response. After compiling the data, he used homework averages to predict each student's test score. He found the least-squares regression line to be ^ y = 0.2 x + 82 . He also calculated that the value of r , the correlation coefficient, was 0.82. Which of the choices identifies the correct value of the coefficient of determination. R 2, and gives a correct interpretation of its meaning? A. R2 = 0.6724, meaning 67.24% of the total variation in test scores can be explained by the least‑squares regression line. B. R2 = 0.6724, meaning 67.24% of the total variation in homework averages can be explained by the least‑squares regression line. C. R2 = 0.8, meaning 82% of the total variation in test scores can be explained by the least‑squares regression line. D. R2 = 0.82, meaning 82% of the total variation in homework averages can be explained by the least‑squares regression line. E. R2 = 0.9055, meaning 90.55% of the total variation in test scores can be explained by the least‑squares regression line.

Answer 1

Answer:

A. R2 = 0.6724, meaning 67.24% of the total variation in test scores can be explained by the least‑squares regression line.

Step-by-step explanation:

John is predicting test scores of students on the basis of their home work averages and he get the following regression equation

y=0.2 x +82.

Here, dependent variable y is the test scores and independent variable x is home averages because test scores are predicted on the basis of home work averages.

The coefficient of determination R² indicates the explained variability of dependent variable due to its linear relationship with independent variable.

We are given that correlation coefficient r= 0.82.

coefficient of determination R²=0.82²=0.6724 or 67.24%.

Thus, we can say that 67.24% of total variability in test scores is explained by its linear relationship with homework averages.

Also, we can say that, R2 = 0.6724, meaning 67.24% of the total variation in test scores can be explained by the least‑squares regression line.