Question

What is a residual plot and how should it look?

What kind of statistical test would you use?

What is Cook's distance?

What are “LINE” approximations in regression analysis?

Answer 1

What is a residual plot and how should it look?

Answer --> In a regression analysis residual is the difference between observed value of an dependent variable (Y) and the predicted value () . each data point has one residual

and a residual plot is the plot of residual on the vertical axis and the independent variables on the horizontal axis.

Below, the residual plots show three typical patterns. The first plot shows a random pattern, indicating a good fit for a linear model.

The other plot patterns are non-random (U-shaped and inverted U), suggesting a better fit for a nonlinear model.

What kind of statistical test would you use?

Answer --> for testing the residuals generally Durbin Watson tests are used to check if there is autocorrelation among the residuals of a linear regression

What is Cook's distance?

Answer--> Data points who have large residual values may sometime distort the outcome or overall accuracy of a regression. Such data points if removed from the regression analysis cause a significant change in the parameters of regression equation. These data points are called influential points and are associated with high value of Cook's distance. as a Thumb rule if cook's distance is greater than 1 then we consider that data point as highly influential.

What are “LINE” approximations in regression analysis?

Answer--> In mathematics, a Line approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations such as a regression of the form

where c= intercept and m=slope or tangent

so if there is a linear relationship between x an y then the slope m suggest the rate of change of y for evry unit change in x