With the help of following data, determine both the regression equations Psychology (X): Mean= 30, Standard deviation=1.6 Sociology (Y): Mean= 25, Standard deviation= 1.7 Coefficient of correlation = 0.95
To determine the regression equations using the provided data, you need to find the slope (β) and intercept (α) values. The regression equation for Psychology (X) can be represented as Y = α + βX, and the regression equation for Sociology (Y) can be represented as X = α' + β'Y.
First, let's find the slope (β) using the formula:
β = (rSy) / Sx
where r is the coefficient of correlation, Sy is the standard deviation of Y, and Sx is the standard deviation of X.
β = (0.95 * 1.7) / 1.6
β ≈ 1.005
Now, let's find the intercept (α) using the formula:
α = Ȳ - βX̄
where Ȳ is the mean of Y and X̄ is the mean of X.
α = 25 - (1.005 * 30)
α ≈ -5.15
Therefore, the regression equation for Psychology (X) is:
Y = -5.15 + 1.005X
To find the regression equation for Sociology (Y), we need to find the slope (β') and intercept (α').
β' = (rSx) / Sy
β' = (0.95 * 1.6) / 1.7
β' ≈ 0.895
Now, let's find the intercept (α'):
α' = X̄ - β'Ȳ
α' = 30 - (0.895 * 25)
α' ≈ 7.63
Therefore, the regression equation for Sociology (Y) is:
X = 7.63 + 0.895Y
So, the regression equation for Psychology (X) is Y = -5.15 + 1.005X, and the regression equation for Sociology (Y) is X = 7.63 + 0.895Y.