What do you mean by regression analysis; explain in your own words

Regression analysis:

In “Statistical Methods” has defined Regression as, “The measure of the average relationship between two or more variables in terms of the original units of the data”.

Morris Hamburg has defined Regression Analysis as, “The method by which estimates are made of the values of a variable from knowledge of the values of one or more other variables and to the measurement of the errors involved in this estimation process”.

Correlation analysis attempts to study the relationship between the two variables x and y. Regression analysis attempts to predict the average x for a given y. in Regression it is attempted to quantify the dependence of one variable on the other. Example; There are two variables x and y. y depends on x. the dependence is expressed in the form of the following equation:

Y=a+bx

Regression analysis used to estimate the values of the dependent variables from the values of the independent variables.

Regression analysis uses to get a measure of the error involved while using the regression line as a basis for estimation.

Regression coefficient is used to calculate correlation coefficient. The square of correlation coefficient measures the degree of association of correlation that prevails between the given two variables.

Correlation coefficient measures the degree of co variability between the given variables x and y. the regression analysis uses to study the ‘nature of relationship’ between the given variables; the value of one variable is predicted based on another.

Correlation analysis does not study cause and effect relationship of the given variables. It is not stated that one variable is the cause and other the effect. In regression analysis one variable is taken as dependent and another independent. Here there is possibility to study the cause and effect relationship.

In statistics, regression analysis examines the relation of a dependent variable (response variable) to specified independent variables (explanatory variables). The mathematical model of their relationship is the regression equation. The dependent variable is modeled as a random variable because of uncertainty as to its value, given only the value of each independent variable. A regression equation contains estimates of one or more hypothesized regression parameters ("constants"). These estimates are constructed using data for the variables, such as from a sample. The estimates measure the relationship between the dependent variable and each of the independent variables. They also allow estimating the value of the dependent variable for a given value of each respective independent variable.

Uses of regression include curve fitting, prediction (including forecasting of time-series data), modeling of causal relationships, and testing scientific hypotheses about relationships between variables.