The correlation coefficient between sodium content and calories per serving is 0.976
How to determine the correlation coefficient
From the question, we have the following parameters that can be used in our computation:
The table of values
Using a graphing tool, we have the following summary
X Values
Sum of x, ∑ = 284
Mean of x = 35.5
Deviation, ∑(X - Mx)² = SSx = 2066
Y Values
Sum of y, ∑ = 5480
Mean of y = 685
Deviation, ∑(X - My)² = SSy = 419400
X and Y Combined
N = 8
∑(X - Mx)(Y - My) = 28730
The correlation coefficient is calculated using
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
So, we have
r = 28730 / √((2066)(419400))
Evaluate
r = 0.976
Hence, the correlation coefficient is 0.976
Question
The table and scatter plot show the sodium content (in mg) and number of calories per serving for 16 fast food items. Calculate the correlation coefficient between sodium content and calories per serving.
Sodium content (g) 25 44 63 32 37 20 11 52
Calories 590 830 1080 680 750 420 310 820