Explain how simple regression modeling can be extended to understand the relationship among several variables?

Step 1 Independent and dependent variables in regression: In a simple regression, the variable of interest, regarding which, the prediction is being made, is the dependent or response variable, the variable which explains the variation in the response variable is the independent or predictor variable. Regression: Regression analysis estimates the relationship among variables. That is, it estimates the relationship between one dependent variable and one or more independent variables. The general form of first-order regression model is $y-cap={\beta }_0+{\beta }_{1}x+ϵ$, Where, the variable y is the dependent variable that is to be modelled or predicted, the variable x is the independent variable that is used to predict the dependent variable, and ε is the error term. Step 2 Multiple regression: A multiple regression analysis is used when two or more independent variables are used to predict a value of a single dependent variable. The general multiple regression equation is as follows: $haty=b_o+b_1{x}_1+...+b_k{x}_k+varepsilon$ where, haty the predicted value of response or dependent variable $x_1,x_2$,..., are the k predictor variables $b_1,b_2,...,b_k$ are the estimated slopes corresponding
to $x_1,x_2,...x_k$, respectively $b_0$ is the estimated intercept of the line, from the sample data varepsil is the error term in the model. Step 3 Regression is a tool that helps to pool data together to help people and companies to make informed decisions. It can be used to predict future economic conditions, trends or values. Multiple regression is a broader class of regressions that encompasses liner and nonlinear regressions with multiple explanatory variables. Regression is a data mining technique used to predict a range of numeric values (also called continuous values), given a particular data set. For example, regression might be used to predict the cost of a product or service, given other variables. Thus, for large data sets, regression provides an easy way of analysis.