For each menu item at a fast food restaurant, fat content (in grams) and number of calories were recorded. A scatterplot of these data is given: sparta the restaurant decides to add six new high-calorie, low-fat pasta dishes to its menu.
What is a plausible value for the new correlation coefficient describing the relationship between fat and calories?
A plausible value for the correlation between fat content and calories is:.
A. +0.2.
B. –0.9.
C. +0.9.
D. –1.0

Step-by-step explanation:

Hello!

Given the variables

Y-axis: X₁: Calories of a fast food menu.

X-axis: X₂: Fat of a fast food menu (grams)

The coefficient of correlation (r)

This coefficient shows the degree of correlation between the variables and its range of values is between -1 and 1

If r = 0 then there is no linear correlation between X₁ and X₂ Graphically, the slope is zero

If r < 0 then there is a negative association between X₁ and X₂ (i.e. when one variable increases the other one decreases) In a graphic, the slope of the line is negative.

If r > 0 then there is a positive association between X₁ and X₂ (i.e. Both variables increase and decrease together)  

The closer to 1 or -1 the coefficient is, the stronger the association between variables. Using the absolute value of the correlation coefficients you can compare them, the greater the value, the stronger is the association between variables.

Looking at the scatter plot you can see that the number of calories grows with the fat content of the menu forming an approximately straight line, which means that there must be a strong positive correlation between these two variables. (using for example one of the options +0.90)

Meaning: To ↑x₁ corresponds ↑x₂ and to ↓x₁ corresponds ↓x₂

Now if the restaurant adds n=6 new menus with high calories (↑x₁) and low fat content (↓x₂) these new me nus won't follow a direct relationship, but an indirect one (negative correlation), so you'd expect the value of the correlation coefficient to drop (get closer to zero)

The coefficient won't get close to -1 since that would be a complete negative correlation (all foods having low fat and high calories), which could happen if the restaurant changed all menus.

Since they are only adding new ones, the new possible values for the coefficient of correlation could be A. +0.2 or D -0.1

I hope this helps!