Question

One of the engineers has been reviewing the data and thinks humidity may be a factor that is affecting the packaging process. The engineer tracked the humidity levels for a random sample of cereal packages over 30 days along with the humidity level on that day during production.  

1. Calculate the correlation coefficient, r.

2. Interpret the correlation coefficient, r. Be sure to address both the direction and strength of the association between package weights and humidity level.

3. What next steps would you recommend the company to take based on these results? Be specific, creative, and logical.

Weight	Humidity
19.987	19
19.997	19
20.02	20
20.117	22
20.21	21
20.222	22
20.226	22
20.258	23
20.321	23
20.334	24
20.396	24
20.412	24
20.434	25
20.468	25
20.527	26
20.541	25
20.541	26
20.554	27
20.555	29
20.556	28
20.611	31
20.616	30
20.622	31
20.634	32
20.64	31
20.691	32
20.721	33
20.773	34
20.816	36
21.002	38

Answer 1

1. X Values
? = 613.802
Mean = 20.46
?(X - M_x)² = SS_x = 1.827

Y Values
? = 802
Mean = 26.733
?(Y - M_y)² = SS_y = 757.867

X and Y Combined
N = 30
?(X - M_x)(Y - M_y) = 35.622

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

r = 35.622 / ?((1.827)(757.867)) = 0.9573

2.

Y2 0.95732 0.9164

Which means 91.64% of variation in humidity is explained by thickness

3. Based on this observation we should suggest that in order to have an effective packaging process kindly take care that humidity is been maintained accordingly