Question

1. Basic concepts of linear regression Aa Aa Match the following key linear regression terms with their respective descriptions Residual Least Squares Criterion Response Variable Explanatory Variable Regression Equation A procedure used to develop an estimate of the regression equation that minimizes the sum of the squared errors The variable that you are predicting or explaining The variable that is doing the predicting or explaining The equation that describes the relationship between the response variable and the explanatory variable The difference between the observed value of the response variable and its predicted value

Answer 1

Answer

Lets us consider one regression equation y = ax + b

where y is dependent variable or response variable and x is independent variable or explanatory variable, a is slope and b is intercept of equation

So, regression equation is the equation that describes the relationship between explanatory and response variable.

y is response variable because when we change x value, the value of y changes or it responses to x value. So, y or response variable is the variable that we are predicting or explaining

x value is independent or we can say that x value is used to explain the y value. So, x is the explanatory variable that is doing the predicting or explaining

By the definition of residual, i.e. we define residual as the difference between predicted y values and actual y values. So, we can say that residual is the difference between observed value of the response variable and its predicted value.

least square criterian is the method used to check how well the trendline fits the data, i.e. it is used to minimise the sum of squared errors.