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: Choose 1 answer: (Choice A) A \hat y=2.5x-0.5 y ^ ​ =2.5x−0.5 (Choice B) B \hat y=2.5x+0.5 y ^ ​ =2.5x+0.5 (Choice C) C \hat y=0.5x+0.5 y ^ ​ =0.5x+0.5 (Choice D) D \hat y=0.5x-0.5 y ^ ​ =0.5x−0.5 Based on this equation, estimate the rating of chips whose cost is \$1.10.$1.10.dollar sign, 1, point, 10, point Round your answer to the nearest hundredth.

Answer 1

A: y = 2.5x - 0.5

B: 2.25

Explanation:

Answer 2

A.
`\hat y = 2.5x -0.5`

B.
`\hat y = 2.5(1.10) -0.5=2.25`

Explanation:

Part a

In order to calculate th slope we just need to select any two points and then we need to calculate the rise and run.

For this case as we can see on the figure attached we select two points (1,2) and (2.6,6). The rise on this case is 6-2=4 and the run 2.6-1=1.6 so then the approximately slope is given by:

`m =(rise)/(run)=(4)/(1.6)=2.5`

Then in order to find the intercept we just need to find the value for the function when X=0.

At X=0.25 the value of Y=0. So then for X=0 we assume that the function would be a nehative value. And the only equation with a negative value for the intercept and the slope =2.5 is the option a, so the best answer would be:

A.
`\hat y = 2.5x -0.5`

Part b

Since we have the model now we just need to replace X=1.10 and see what we got:

`\hat y = 2.5(1.10) -0.5=2.25`