Question

What is the fundamental approach for finding the optimal values of the coefficients of the betas mening the regression equaiton?

Answer 1

The beta coefficient is the degree of change in the outcome variable for every 1-unit of change in the predictor variable(independent variable).

Beta coefficient (or Betas or Beta Weights or Standardized Coefficients) compares the strength of the effect of each individual predictor variable to the dependent variable. The higher the absolute value of the beta coefficient, the stronger will be the effect.

If the beta coefficient is positive, then increase in the predictor variable will increase the beta coefficient value. If the beta coefficient is negative then the increase in the predictor variable will decrease the beta coefficient value.

Eg:  if the β is .50 then for each 1 unit increase in the predictor variable, the outcome variable will increase by .50 units.

The fundamental approach for finding optimal values of beta is given below:

Let the regression equation is :

To get the optimal estimate of β we calculate

Using the principal of maxima and minima,

Solving we get,