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, we need to calculate the regression coefficients: the slope (b) and the intercept (a). The regression equation for predicting Y (Sociology) from X (Psychology) is:
Y = a + bX
To calculate the regression coefficients, we first need to find the standard error of estimate (SEE). The SEE is given by the formula:
SEE = StdDev(Y) * √(1 - r^2)
where StdDev(Y) is the standard deviation of Y and r is the coefficient of correlation.
First, let's calculate the SEE:
StdDev(Y) = 1.7
r = 0.95
SEE = 1.7 * √(1 - 0.95^2)
Now, let's calculate the values:
SEE = 1.7 * √(1 - 0.9025)
SEE = 1.7 * √(0.0975)
SEE = 1.7 * 0.312
SEE ≈ 0.5304
Now, we can calculate the slope (b):
b = r * (StdDev(Y) / StdDev(X))
where StdDev(X) is the standard deviation of X.
StdDev(X) = 1.6
b = 0.95 * (1.7 / 1.6)
b = 0.95 * 1.0625
b ≈ 1.0094
Finally, we can calculate the intercept (a):
a = Mean(Y) - b * Mean(X)
Mean(X) = 30
Mean(Y) = 25
a = 25 - 1.0094 * 30
a ≈ -3.282
Therefore, the regression equation for predicting Sociology (Y) from Psychology (X) is:
Y = -3.282 + 1.0094X
This equation allows you to estimate the value of Y (Sociology) given the value of X (Psychology).