Question

Respond to the following in a minimum of 175 words, please type response:

How can regression modeling be used to understand the association between two variables.

Respond to the following in a minimum of 175 words, please type response:

How can simple regression modeling be extended to understand the relationship among several variables.

Answer 1

Solution:

The regression modelling is the analytical tool to understand the relationship between two variable or more than two variable. There is a two-variable regression model where one is the independent variable and another variable is the dependent variable. It is used to predict the dependent variable based on the value of the independent variable. The sample regression model consists of two variables, parameters and an error term. The two-parameter is intercept and slope coefficient. The value of the slope coefficient determines the effect of the independent variable on the value of a dependent variable. Suppose the value of the slope coefficient is positive, this mean that the value of increases in an independent variable leads to an increase in the dependent variable. The error term is also known as residual which is the difference between the actual value of the dependent variable and the predicted value of the dependent variable. Suppose the estimated two linear regression model is given below:
Yi = 2478 + 2.05 Xi

Here, Yi is the dependent variable and Xi is the independent variable.

The interpretation of the slope coefficient is given below which shows the association between two variable.

Slope coefficient states that if the independent variable increased by one unit lead to an increase in the dependent variable by 2.05 unit.

Multilinear regression modelling
The Simple linear regression model can be extended to the multilinear regression model which show the relationship between a dependent(1 variable) and independent(more than 1 variable) variable. Here, the dependent variable depends on more than two variable.

For example, the dependent variable is the selection of the candidate and the independent variable consist of skills level of candidate and t another independent variable is the education level of the candidate.
The multiple linear regression model is given as,
Yi = 2305 + 2.05 X1 - 8.05X2
Here, the dependent variable Yi is dependent on two independent( X1 and X2) variable.
The interpretation for the slope coefficient is that,
2.05 mean is that if the X1 is increased by one unit then the dependent variable increased by 2.05 unit assuming another variable is constant.
(-8.05) mean is that if the X2 is increased by one unit then the dependent variable decreased by 8.05 unit assuming another variable is constant.
There is some important assumption under the classical linear regression model which is given below.
1) The parameters should in linear form.
2) There is no relationship between two or more error term.
3) The population variance should be equal(It is known as Homoscedasticity).

There is also another assumption of CLRM.
So, the model could be extended to understand the relationship between a dependent variable and independent variables.