Question

we expect that students who do well on the midterm exam in a course will usually do well on the final exam. gary smith of pomona college looked at the exam scores of all 346 students who took his statistics class over a 10 - year period. assume that both the midterm and final exam were scored out of 100 points. the actual least - squares line for predicting final - exam scores y from midterm - exam scores x was $hat{y}=46.6 + 0.41x$. predict the score of a student who scored 50 on the midterm. 49.44 188.46 48.65 67.1 60.79

Explanation:

Step1: Identify the regression - line formula

The least - squares line is $\hat{y}=46.6 + 0.41x$.

Step2: Substitute the midterm score

Given $x = 50$, substitute it into the formula: $\hat{y}=46.6+0.41\times50$.

Step3: Calculate the value of $\hat{y}$

First, calculate $0.41\times50 = 20.5$. Then, $46.6+20.5=67.1$.

Answer:

$67.1$