After settlement, the average weekly wage in a factory had increased from Rs. 8 to 12
and standard deviation had increased from Rs. 1 to 1.5. The wages have become
higher and more uniform, after settlement. Comment.
3(b) Calculate the Karl Pearson’s coefficient of correlation from the following pairs of
values and interpret the result:
Values of X 12 9 8 10 11 13 7
Values of Y 14 8 6 9 11 12 3
Q.3 (c) Distinguish between correlation and regression.
(d) The two regression coefficients are -2.7 and -0.3 and the coefficient of correlation is
0.90. Comment
Answers
Explanation:
Comment.
3(b) Calculate the Karl Pearson’s coefficient of correlation from the following pairs of
values and interpret the result:
Values of X 12 9 8 10 11 13 7
Values of Y 14 8 6 9 11 12 3
and standard deviation had increased from Rs. 1 to 1.5. The wages have become
higher and more uniform, after settlement. Comment.
3(b) Calculate the Karl Pearson’s coefficient of correlation from the following pairs of
values and interpret the result:
Values of X 12 9 8 10 11 13 7
Values of Y 14 8 6 9 11 12 3......
The Karl Pearson Correlation Coefficient is a widely used method for the measurement of the degree of the relationship between "linear related variables" by "numeric representation".
Explanation:
Given: After the settlement, the "avg weekly" wage in a factory increased from Rs. 8 to Rs 12 and "Standard deviation" (SD) had increased from Rs.1 to Rs 1.5.
We must Find: "Authenticity of statement": That wages have become "higher & more uniform", after the settlement.
Solution:
Coefficient of Variation (Coef Var) = (Standard deviation (SD)/Mean)*100 %
Earlier "Avg weekly wages" = 8, Mean is = 8
& Standard Deviation (SD) = 1
Coefficient of Variation (Coef.Var) = (1/8)*100=12.5 %
After the settlement, "Avg" weekly wages is = 12, Mean is = 12
& Standard Deviation (SD) = 1.5
Coefficient of Variation (Coeff. Var)= (1.5/12)*100=12.5 %
12 > 8
Therefore, wages have become higher is "Correct", but since the Coeff. Var. is the same therefore there is no impact on "uniformity of wages" and that wage have become "more uniform" is "not correct" wages.
3(c). "Correlation" is used to represent the "linear relationship" between 2 variables. Whereas, "regression" is used to fit the "best line" & estimate one variable based on another variable
3(d) The 2 regression coefficients are -2.7 & -0.3 & the coefficient of correlation is 0.90.
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