Question

Let sugar be the explanatory variable and calories be the response variable; which scenario best describes ŷ = 57 + 2.5x?

Answer 1

Answer:

e.

Step-by-step explanation:

calories is y or response variable and sugar is the explanatory variable, x.

if x(sugar) is 1

y = 57 + 2.5(1) = 59.5, a 2.5 increase.

if it is 2

y = 57 + 2.5(2) = 62, another 2.5 increase.

if zero grams of sugar x = 0

y = 57 + 2.5(0) = 57 calories.

Answer 2

Answer: Choice E)

The amount of calories in fruit juice increases by 2.5 for every one gram of sugar. The calorie amount estimated by this model is 57 if there are zero grams of sugar.

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Explanation:

x = amount of sugar (in grams)

y = number of calories in the juice

ŷ = estimate of y, so its the estimate of calories in the juice

The regression equation rearranges to ŷ = 2.5x + 57

This is in the form y = mx+b where m = 2.5 is the slope and b = 57 is the y intercept.

The slope tells us what the rate of change is. Specifically, it tells us how much the amount of calories (y) is going up each time the amount of sugar (x) goes up. Each time x goes up by 1, y goes up by 2.5

The y intercept 57 is the starting or initial amount of calories. If you have 0 grams of sugar, the lowest amount of sugar possible, then you start off with 57 calories. We can see this by plugging x = 0 into ŷ = 2.5x + 57 (you should get ŷ = 57). Visually, the y intercept is where the line crosses the y axis.

All of these facts point to choice E as the final answer.