Question

a panel of judges was asked to judge the quality of different kinds of potato chips. the relationship between their ratings and the price of the chips is shown in the scatter plot below. 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 $hat{y}=2.5x - 0.5$ b $hat{y}=2.5x + 0.5$ c $hat{y}=0.5x + 0.5$ d $hat{y}=0.5x - 0.5$

Explanation:

Step1: Identify the y - intercept

The line intersects the y - axis above the origin. When \(x = 0\), the value of \(y\) (ratings) is positive. In the slope - intercept form \(y=mx + b\), \(b\) is the y - intercept. This rules out options A and D since they have \(b=- 0.5\).

Step2: Estimate the slope

Pick two points on the line, say \((1,1)\) and \((2,2.5)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{2.5 - 1}{2 - 1}=\frac{1.5}{1}=1.5\approx2.5\) (approximate estimate as we are looking at a scatter - plot line). The slope of option C is \(m = 0.5\) and of option B is \(m = 2.5\).

Answer:

B. \(\hat{y}=2.5x + 0.5\)