# Compare the population regression function and the sample regression function?

Home, - Critically appraise the coefficient of determination?

Question

a) What is the difference between the population regression function and the sample regression function?

b) Critically appraise the coefficient of determination.

Regression Model

The sample regression function normally represents the relationship between the dependent variable Y and two or more independent variables, and the model was framed based on the information taken from a sample of the population of interest. On the other hand, the population regression function represents the conditional mean of variable Y (dependent variable) for the fixed variable X

The regression equation is of the form

Y = b0 + b1 * x1 + b2 * x2 + ... + bn * xn

Where b0, b1, ...bn are regression coefficients

Coefficient of Determination

The coefficient of correlation is calculated by using the formula given below

r = (nΣxy - (Σx)(Σy) )/ (√nΣx2 - (Σx)2  * √nΣy2 - (Σy)2 )

Coefficient of Determination r2 = r * r

Coefficient of determination is calculated by squaring the correlation coefficient and it falls between 0 and 1. The coefficient of determination (also known as R square) close to 1 indicates that the model is good fit in predicting the dependent variable and the model is highly reliable. For example, when the coefficient of determination is 0.75, then, 75% of the dependent variable variation is explained by the regression model while the remaining 25% left unexplained. In general, the coefficient of determination of 0.70 and above is considered good. 