Question

A study was conducted using a random sample of Taco Bell products to determine whether grams of protein content (x) was related to calorie content (y). The following information was obtained:

ŷ = 402.3 – 0.508x, Coefficient of determination = 53.14%

What is the value of the correlation between protein content and calorie content?

	a.	0.2824
	b.	0.5314
	c.	-0.7290
	d.	-0.2824

Answer 1

Given that, the regression equation is

ŷ = 402.3 – 0.508x

where, y-intercept = 402.3 and slope = -0.508 (negative)

Coefficient of determination = R^{​​​​​​2} = 53.14%

=> Coefficient of determination = R^{​​​​​​2} = 0.5314

We want to find, the correlation coefficient (r) between protein content and calorie content.

r = √(R^{​​​​​​2}) = √(0.5314) = 0.7290

Since, the slope is negative we can says that there is a negative correlation between protein content and calorie content.

Therefore, required correlation coefficient is r = -0.7290

Answer : c) -0.7290