Question

1. Describe the two components of a one variable regression equation.

2. Explain what a residual is when developing a regression model.

Answer 1

Answer --->

1) The two components of a one variable regression equation.

--> One Variable regression equation is also know as simple linear regression in which one variable is considered as explanatory variable, and the other is considered as dependent variable.

Simple linear equation is as below

Yi = α + β Xi + εi i = 1,2,3,.....,n

Y = Dependenat variable

X = Independant variable

β = Regression Coefficient

α = Intercept

ε = Recidual

In one variable regression equation 'α' & 'β' are consider are two component.

β = Regression Coefficient also know as Slope of line of best fit. It explain that average change in Dependant variable when one unilt change in independant variable.

Sign of regression coefficient tell you direction of correlation between independent variable the dependent variable. A positive coefficient indicates that as the value of the independent variable increases, the average of the dependent variable also increases. A negative coefficient indicate that independent variable increases, the dependent variable decrease.

α = Intercept is can be explain as average value of Dependant variable in absense of independant variable.

If range of independant variable does not contail value 'Zero' then it as no practical meaning. It is a bias/constant value we add in get estimated value of dependant variable closer to actual value of dependnat variable.

2) What a residual is when developing a regression model.

ε = Residual is the difference between estimated/explained value of dependant variable and actual value of dependant vraible at the same value of independant variable =x.