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. state the equation of the least - squares regression line if each student scored the same on the midterm and the final. $hat{y}=346 + x$ where $hat{y}=$ predicted grade on final and $x =$ grade on midterm. $hat{y}=x$, where $hat{y}=$ predicted grade on midterm and $x =$ grade on final. $hat{y}=x$, where $hat{y}=$ predicted grade on final and $x =$ grade on midterm. $hat{y}=hat{x}$, where $hat{y}=$ predicted grade on final and $x =$ grade on midterm. $hat{y}=hat{x}$, where $hat{y}=$ predicted grade on final and $x =$ grade on midterm.

Explanation:

Step1: Recall regression - line concept

In a situation where the mid - term and final scores are the same for each student, the predicted value $\hat{y}$ (final score) should be equal to the actual value $x$ (mid - term score). The general form of a simple linear regression line is $\hat{y}=a + bx$, where $a$ is the intercept and $b$ is the slope. When the two scores are equal, the intercept $a = 0$ and the slope $b = 1$.

Answer:

$\hat{y}=x$, where $\hat{y}=$ predicted grade on final and $x =$ grade on midterm.