Question

shiras math test included a survey question asking how many hours students spent studying for the test. the scatter plot below shows the relationship between how many hours students spent studying and their score on the test. 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 $hat{y}=x + 45$ b $hat{y}=10x + 45$ c $hat{y}=-10x + 45$

Explanation:

Step1: Determine the slope - intercept form

The general form of a linear regression equation is $\hat{y}=mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Estimate the y - intercept

The line intersects the y - axis around $y = 45$, so $b\approx45$.

Step3: Estimate the slope

Pick two points on the line, say $(0.5,50)$ and $(1.5,60)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{60 - 50}{1.5 - 0.5}=\frac{10}{1}=10$.

Answer:

B. $\hat{y}=10x + 45$