Question

1. In a study published in Medicine and Science in Sports and Exercise (volume 17, no.2, page 189) the measurements of 252 men (ages 22 – 81) are given. Of the 14 measurements taken of each man, some have significant correlations and others don’t. The partial table shown below lists only the first 9 rows of data and 9 of the measurements.

Age (yr.)	Weight (lb.)	Height (in.)	Neck (cm)	Chest (cm)	Wrist (cm)	Hip (cm)	Thigh (cm)	Knee (cm)	Body Fat %
22	173.25	72.25	38.5	93.6	18.2	98.7	58.7	37.3	6.1
22	154.00	66.25	34.0	95.8	16.6	99.2	59.6	38.9	25.3
23	154.25	67.75	36.2	93.1	17.1	94.5	59.0	37.3	12.3
23	198.25	73.50	42.1	99.6	19.2	104.1	63.1	41.7	11.7
23	159.75	72.25	35.5	92.1	18.2	93.9	56.1	36.1	9.4
23	188.15	77.50	38.0	96.6	18.3	102.5	59.1	37.6	10.3
24	184.25	71.25	34.4	97.3	17.7	101.9	63.2	42.2	28.7
24	210.25	74.75	39.0	104.5	18.8	107.8	66.0	42.0	20.9
24	156.00	70.75	35.7	92.71	17.3	95.3	56.4	36.5	14.2

1. Using your intuition, classify the following (x, y) pairs as having a weak correlation (0 < r < 0.5), a moderate correlation (0.5 < r < 0.8), or a strong correlation (0.8 < r < 1.0).

1. (weight, neck)                       i         (weight, height)

iii. (age, wrist)                            iv.        (weight, body fat)

v.   (chest, hip)                             vi.        (age, weight)

vii. (chest, neck)                          viii.      (height, knee)

2. Pick 3 pairs from (a) and calculate the correlation coefficient.   Compare the results with those obtain by intuition in part a. You only need to calculate the actual correlation coefficient for these 3. In part a, you are ‘guessing’ if the correlation coefficient is weak, moderate or strong.

3. Find the regression line (‘best fit line’) for the pairs (weight, neck) and (weight, body fat). You will have 2 equations for lines.

4. Use the results of part c to predict the following.

1. The neck circumference of a man whose weight is 180 pounds.
2. The body fat of a man whose weight is 180 pounds.

Answer 1

Answer:

solved in excel using the data analysis tool

Select data analysis tool then click on correaltion for calculation correlation and click on regression for to find best fit line.

Answer(a & b)

(1) (weight,neck)- =0.698 moderate correaltion

(2) (weight,height) =0.745 moderate correlation

(3)(age,wrist) =0.204 weak correaltion

(4)(weight,body fat)=0.116 weak correlation

(5) chest,hip=0.952 strong correlation

(6) Age,weight=0.365 weak correaltion

(7) chest,neck=0.508 ~.51 moderate correlation

(8)height, knee=0.173-weak correlation

Answer(c) Regression line for weight and neck is

neck=21.92+0.086*weight

The regression line for body fat and weight is

body fat=7.90+0.042*weight

Answer(d) neck circumference =21.92+0.086*180=37.4

body fat=7.90+0.042*180=15.46

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