1. What is the Regression Coefficient?

A regression coefficient is a number that measures the relationship between a dependent variable and an independent variable in a regression model.

Formula for Simple Linear Regression:

Y = a + bX

Where:

• Y = Dependent variable

• X = Independent variable

• a = Intercept (value of Y when X = 0)

• b = Regression coefficient (slope of the line)

📝 Note:

• The regression coefficient of y on x is denoted by b_yx.
• The regression coefficient of x on y is denoted by b_xy.
• The regression coefficient of y on x is not equal to that of x on y.

4. Properties of Regression Coefficients

1.  If one regression coefficient is greater than 1, then the other will be less than 
2. They are not independent of the change of scale. There will be change in the regression coefficient if x and y are multiplied by any constant.
3. AM of both regression coefficients is greater than or equal to the coefficient of correlation.
4. GM between the two regression coefficients is equal to the correlation coefficient.
5. If b_xy is positive, then b_yx is also positive and vice versa.