Question

USE EXCEL TO ANSWER THE FOLLOWING:

A container of one dozen large eggs was purchased at a local grocery store. Each egg was measured to determine its diameter (in millimeters) and weight (in grams). The results for the 12 eggs are given in the following table. Weight is the dependent variable. Calculate the r-sqr, correlation coefficient, and explain each value.

Index	1	2	3	4	5	6	7	8	9	10	11	12
Diameter (mm)	42.2	45.45	47.8	47.4	47.7	43.5	44.4	43.9	46.2	45.9	44.3	44.5
Weight (grams)	52.8	58.5	60.2	59	57.4	54.1	53.9	54.5	56.2	55.8	54.3	56.1

Answer 1

X Values
∑ = 543.25
Mean = 45.271
∑(X - M_x)² = SS_x = 34.862

Y Values
∑ = 672.8
Mean = 56.067
∑(Y - M_y)² = SS_y = 58.287

X and Y Combined
N = 12
∑(X - M_x)(Y - M_y) = 39.568

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 39.568 / √((34.862)(58.287)) = 0.8778

Which correlation between Diameter and weight is positive

Now r^2=0.8778^2=0.7705

Which means 77.05% of variation in y is explained by x.