Question

the plot shown below describes the relationship between students scores on the first exam in a class and their corresponding scores on the second exam in the class. a line was fit to the data to model the relationship. which of these linear equations best describes the given model? choose 1 answer: (a) $hat{y}=2x + 10$ (b) $hat{y}=x + 10$ (c) $hat{y}=2x$ (d) $hat{y}=x$ based on this equation, estimate the score on the second exam for a student whose first exam score was 88.

Explanation:

Step1: Analyze the line's slope and y - intercept

The line passes through the origin (0,0) which means the y - intercept is 0. Also, the line has a slope of 1 as for every increase of 1 in the x - value (Exam 1 score), the y - value (Exam 2 score) increases by 1. The equation of a line is $\hat{y}=mx + b$ where $m$ is the slope and $b$ is the y - intercept. So the best - fitting equation is $\hat{y}=x$.

Step2: Use the equation for prediction

We are given $x = 88$ and the equation $\hat{y}=x$. Substitute $x = 88$ into the equation. So $\hat{y}=88$.

Answer:

1. D. $\hat{y}=x$
2. 88