Question

Each pair of data below is in the form (x, y). They may have a weak correlation (0 <r<0.5), a moderate correlation (0.5 <r<0.8), or a strong correlation (0.8 <r<1.0) (a) (weight, neck) (c) (age, body fat) (e) (age, wrist) (8) (forearm, height) (i) (weight, body fat) (k) (hip, abdomen) (b) (weight, height) (d) (chest, hip) (f) (ankle, wrist) (h) (bicep, forearm) () (knee, thigh) (1) (abdomen, hip) 1. Find the correlation coefficient for each pair of data a-l. Then identify each one as strong, moderate, or weak.

Answer 1

The correlation coefficient value between each pair is obtained in excel in by following these steps,

Step 1: Write the data values in excel. The screenshot is shown below,

A B C D E F G 1 Age Weight Height Neck Chest Abdom. Hip 2 22 173.25 72.25 38.5 93.6 83 98.7 3 22 154 66.25 34 95.8 87.9 99.2 4 23 154.25 67.75 36.2 93.1 85.2 94.5 H I J K L M N Thigh knee Ankle Bicep Forearm Wrist Body 58.7 37.3 23.4 30.5 28.9 18.2 6.1 59.6 38.9 24 28.8 25.2 16.6 25.3 59 37.3 21.9 32 27.4 17.1 12.3

Step 2: DATA > Data Analysis > Correlation. The screenshot is shown below,

DATA REVIEW Data Analysis INSERT PAGE LAYOUT FORMULAS AL ZA X Data Analysis Analysis Tools Anova: Single Factor Anova: Two-Factor With Replication Anova: Two-Factor Without Replication Correlation Covariance Descriptive Statistics Exponential Smoothing F-Test Two-Sample for Variances Fourier Analysis Histogram LOK Cancel Help

Step 3: Select all the data values, Grouped By: Column. The screenshot is shown below,

A B C D E F G 1 Age Weight Height Neck Chest Abdom. Hip 202020 98.7 Correlation 99.2 Input ок | 94.5 Input Range: SAS1:SN$10 104.1 Cancel Grouped By: O Columns 93.9 O Rows Help 102.5 Labels in first row 101.9 Output options 107.8 O Output Range: SA$15 O New Worksheet Ply: - 95.3

The result is obtained. The screenshot is shown below,

EF Neck Chest Abdom. H Hip к Ankle M Forearm N Wrist O Body Age Weight Height Thigh Knee Bicep 1 0.51 0.01 16 Age 17 Weight 18 Height 19 Neck 20 Chest 21 Abdom. 22 Hip 23 Thigh 24 Knee 25 Ankle 26 Bicep 27 Forearm 28 Wrist 29 Body 0.37 0.30 -0.03 0.36 0.43 0.25 0.35 0.37 0.08 0.68 0.40 0.20 0.35 1 0.75 0.70 0.89 0.58 0.93 0.83 0.76 0.82 0.71 0.83 0.83 0.12 0.61 0.44 0.05 0.55 0.26 0.17 0.34 0.48 0.84 0.82 -0.35 0.95 0.71 0.95 0.94 0.85 0.91 0.67 0.59 0.56 0.42 0.55 0.43 0.33 0.50 0.68 0.83 0.85 -0.49 1 0.71 0.86 0.90 0.64 0.37 0.18 0.10 0.79 0.89 0.83 0.91 0.58 0.64 0.60 0.35 0.61 0.86 0.56 0.35 0.41 0.63 0.46 0.44 0.58 0.41 1 0.80 0.66 0.00 0.47 0.85 -0.34 -0.37

Answer:

	Pair	Correlation	Strength
a)	(weight, neck)	0.70	Moderate
b)	(weight, height)	0.75	Moderate
c)	(age, body fat)	0.35	Weak
d)	(chest, hip)	0.95	Strong
e)	(age, wrist)	0.20	Weak
f)	(ankle, wrist)	0.58	Moderate
g)	(forearm, weight)	0.84	Strong
h)	(bicep, forearm)	0.80	Strong
i)	(weight, body fat)	0.12	Weak
j)	(knee, thigh)	0.95	Strong
k)	(hip, abdomen)	0.71	Moderate
l)	(abdomen, hip)	0.71	Moderate