Estimating Regression Coefficient b
The relationship between the variables Y and X in a simple regression equation is given by $Y = a + bX$. The coefficient $b$, also known as the slope, represents the change in Y for a unit change in X. Its estimate can be calculated using the correlation coefficient ($r$) and the standard deviations of X ($SX$) and Y ($SY$).
Regression Coefficient Formula
The formula to estimate the regression coefficient $b$ is:
$ b = r \times \frac{S_Y}{S_X} $
Given Values
- Correlation coefficient, $r = 0.75$
- Standard deviation of X, $SX = 3$
- Standard deviation of Y, $SY = 2$
Calculation Steps
- Substitute the given values into the formula for $b$:
$ b = 0.75 \times \frac{2}{3} $
- Perform the multiplication:
$ b = \frac{3}{4} \times \frac{2}{3} $
$ b = \frac{3 \times 2}{4 \times 3} $
$ b = \frac{6}{12} $
- Simplify the fraction to find the final estimate for $b$:
$ b = 0.5 $
Result
The estimate of the regression coefficient $b$ is 0.5.
Important Questions from Correlation Analysis
The value of simple correlation coefficient lies in the interval:
Which option is correct for the correlation ratio E 2?
Let θ be the angle made by the line of regression of Y on X. If σ Y= 2σ X and the correlation coefficient between X and Y is 0.3, the value θ equals
The multiple correlation coefficient R 1,23 as compared to any simple correlation coefficients between the distinct variable X 1 ,X 2, and X 3is
The coefficients of the regression β X|y and β Y|x , are known, The coefficient of correlation equals:
