# 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 = b_{0} + b_{1} * x_{1} + b_{2} * x_{2} + ... + b_{n} * x_{n}

Where b_{0}, b_{1}, ...b_{n} are regression coefficients

**Coefficient of Determination**

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

r = (nΣxy - (Σx)(Σy) )/ (√nΣx^{2 - (}Σx)^{2 *} √nΣy^{2 - (}Σy)^{2 )}

Coefficient of Determination r^{2} = 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.