Question

((econometrics))

For each of the following pairs of concepts BRIEFLY explain the MAJOR differences, if any, between the concepts involved.

1-correlation analysis vs regression analysis.

2- application of the CLR model vs those of the CNLR model.

3- interpretation of regression results which include an intercept term vs. that do not include an intercept term

Answer 1

(1) Correlation and regression are the two analysis based on multivariate distribution.  

Correlation is described as the analysis which let is know the Assocation or the absence of the relationship between two variables 'x' and 'y' . The objective of correlation analysis is to find a numerical value expressing the relationship between variables. It is used to represent linear relationship between two variables.

Regression analysis predicts the value of the dependent variable based on the known value of the independent variable , assuming that average mathematical relationship between two or more variables. The objective of regression analysis is to estimate values on the basis of the values of fixed variables. It is used to fit a best line and estimate one variable on the basis of another variable.

(2) Classical linear regression (CLR):

Model statistical-tool used in predicting future values of a target (dependent) variable on the basis of the behavior of a set of explanatory factors (independent variables). A type of regression analysis model, it assumes the target variable is predictable, not chaotic or random.

Classical Normal Linear Regression Model (CNLRM):

The method of ordinary least squares is attributed to Carl Friedrich Gauss, a German mathematician. Under certain Assumption, this method of estimation has some very attractive statistical properties that made it one of most powerful and popular method of regression analysis.

The two variable Population Regression Function:

However, the Population functions can’t be obtained directly, hence we estimated them from the help of sample regression functions:

(3) Linear Regression Model with Intercept:

The linear regression be intercept if the line regression intersection with Y axis in

not origin. It means that mathematically B ≠ 0 that is intersection point of

regression line with Y axis

Y = B + B X + e , i = 1,2,3, ⋯ , n (1)

Y = depended variyable

X = independent variable

B, B = regression parameter

e = value of random error

Linear Regression Model without Intercept :

The linear regression be without intercept when the line regression to pass through the origin. It means that mathematically B = 0

We can write the simple linear regression model

Yi = B1Xi1 + ei (2)

The parameters B0 and B1 usually anknown and estimate by least squars method.

From(3,4)

Where

Sxy : Standard deviation between X and Y

Sx: Standard deviation of X

But linear regression without intercept :