Answer to Question #228429 in Statistics and Probability for Yogesh

Question

1(a) 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.
1(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
1(c) Distinguish between correlation and regression.
1(d) The two regression coefficients are -2.7 and -0.3 and the coefficient of correlation is 0.90.
Comment.

Answer 1

Solution:

(a) Since the mean wage has increased, therefore, it is correct to say that mean wage has become higher, after settlement.

In order to compare the uniformity of the wages before and after settlement, we have to compare their coefficient of variation.

$\begin{aligned} C V \text { before settlement }= \frac{1}{8} \times 100=12.5 \\ C V \text { before settlement } =\frac{1.5}{12} \times 100=12.5 \end{aligned}$

Since these coefficients are same, therefore, it is not correct to say that wages have become more uniform.

(b)

X Values:

∑ = 70

Mean = 10

∑(X - M_x)² = SS_x = 28

Y Values:

∑ = 63

Mean = 9

∑(Y - M_y)² = SS_y = 84

X and Y Combined:

N = 7

∑(X - M_x)(Y - M_y) = 46

R Calculation:

r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 46 / √((28)(84)) = 0.9485

Interpretation: This is a strong positive correlation, which means that high X variable scores go with high Y variable scores (and vice versa).

(c):

The main difference in correlation vs regression is that the measures of the degree of a relationship between two variables; let them be x and y. Here, correlation is for the measurement of degree, whereas regression is a parameter to determine how one variable affects another.

(d):

Correlation coefficient is 0.90.

Correlation between Xand Y variablesis high and positive.

Y Dependent variable can predict the impact of independent variable X and other variable.

High correlation value indicates less regression.

R² =( 0.90)²=0.81

R² is a statistical measure of how close the data are to be fitted to regression line and whether the model is a good fit or not.

R² value is 0.81 is high. It indicates smaller differences between the oserved data fitted values.

R² of 0.81 means 81% of Variance in Y variable is predictable from the X variable.

Regression coefficients are negative: -2.7 and -0.3.

The proportion of variations between data VARIABLES is high.