Using the following data set, report the correlations between weight and the fiv
ID: 3276597 • Letter: U
Question
Using the following data set, report the correlations between weight and the five heights provided. Comment on the direction and strength of the relationship for those five correlations.
Gender Weight (kg) Stature (cm) Eye Height, Standing (cm) Acromial Height, Standing (cm) Sitting Height (cm) Knee Height, Sitting (cm) Subject m 81.3 167.5 155.5 139 86.3 50 1 m 66.6 175 166 142.5 93 49 2 m 90.7 180 168.8 151.9 95 51 3 m 73.5 168.9 156.9 139.5 87.6 54.4 4 m 84 189 179 155 90 60 5 f 48 147.5 135.5 119 77 43 6Explanation / Answer
Weigth(kg) - 81.3, 66.6, 90.7, 73.5, 84, 48
Stature(cm) - 167.5, 175, 180, 168.9, 189, 147.5
X Values
= 444.1
Mean = 74.017
(X - Mx)2 = SSx = 1163.188
Y Values
= 1027.9
Mean = 171.317
(Y - My)2 = SSy = 989.308
X and Y Combined
N = 6
(X - Mx)(Y - My) = 887.168
R Calculation
r = ((X - My)(Y - Mx)) / ((SSx)(SSy))
r = 887.168 / ((1163.188)(989.308)) = 0.827
The value of R is 0.827. This is a strong positive correlation, which means that high X variable scores go with high Y variable scores (and vice versa).
The value of R2, the coefficient of determination, is 0.6839.
Weigth(kg) - 81.3, 66.6, 90.7, 73.5, 84, 48
Eye Height, Standing (cm) - 155.5, 166, 168.8, 156.9, 179, 135.5
Result Details & Calculation
X Values
= 444.1
Mean = 74.017
(X - Mx)2 = SSx = 1163.188
Y Values
= 961.7
Mean = 160.283
(Y - My)2 = SSy = 1104.068
X and Y Combined
N = 6
(X - Mx)(Y - My) = 898.232
R Calculation
r = ((X - My)(Y - Mx)) / ((SSx)(SSy))
r = 898.232 / ((1163.188)(1104.068)) = 0.7926
The value of R is 0.7926. This is a strong positive correlation, which means that high X variable scores go with high Y variable scores (and vice versa).
The value of R2, the coefficient of determination, is 0.6282.
Weigth(kg) - 81.3, 66.6, 90.7, 73.5, 84, 48
Acromial Height, Standing (cm) - 139, 142.5, 151.9, 139.5, 155, 119
Result Details & Calculation
X Values
= 444.1
Mean = 74.017
(X - Mx)2 = SSx = 1163.188
Y Values
= 846.9
Mean = 141.15
(Y - My)2 = SSy = 807.175
X and Y Combined
N = 6
(X - Mx)(Y - My) = 869.065
R Calculation
r = ((X - My)(Y - Mx)) / ((SSx)(SSy))
r = 869.065 / ((1163.188)(807.175)) = 0.8969
The value of R is 0.8969. This is a strong positive correlation, which means that high X variable scores go with high Y variable scores (and vice versa).
The value of R2, the coefficient of determination, is 0.8044.
Weigth(kg) - 81.3, 66.6, 90.7, 73.5, 84, 48
Sitting Height (cm) - 86.3, 93, 95, 87.6, 90, 77
Result Details & Calculation
X Values
= 444.1
Mean = 74.017
(X - Mx)2 = SSx = 1163.188
Y Values
= 528.9
Mean = 88.15
(Y - My)2 = SSy = 201.915
X and Y Combined
N = 6
(X - Mx)(Y - My) = 373.675
R Calculation
r = ((X - My)(Y - Mx)) / ((SSx)(SSy))
r = 373.675 / ((1163.188)(201.915)) = 0.7711
The value of R is 0.7711. This is a strong positive correlation, which means that high X variable scores go with high Y variable scores (and vice versa).
The value of R2, the coefficient of determination, is 0.5946.
Weigth(kg) - 81.3, 66.6, 90.7, 73.5, 84, 48
Knee Height, Sitting (cm) - 50, 49, 51, 54.4, 60, 43
Result Details & Calculation
X Values
= 444.1
Mean = 74.017
(X - Mx)2 = SSx = 1163.188
Y Values
= 307.4
Mean = 51.233
(Y - My)2 = SSy = 161.233
X and Y Combined
N = 6
(X - Mx)(Y - My) = 303.777
R Calculation
r = ((X - My)(Y - Mx)) / ((SSx)(SSy))
r = 303.777 / ((1163.188)(161.233)) = 0.7015
The value of R is 0.7015. This is a moderate positive correlation, which means there is a tendency for high X variable scores go with high Y variable scores (and vice versa).
The value of R2, the coefficient of determination, is 0.4921.
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