The assumption of a random sample and independent observations cannot be tested with diagnostic plots. In this particular plot we are checking to see if there is a pattern in the residuals. This is useful for checking the assumption of homoscedasticity. The third plot is a scale-location plot (square rooted standardized residual vs. Observations lie well along the 45-degree line in the QQ-plot, so we may assume that normality holds here. The normality assumption is evaluated based on the residuals and can be evaluated using a QQ-plot (plot 2) by comparing the residuals to 'ideal' normal observations. The tests and intervals estimated in summary(lm3) are based on the assumption of normality. To assess if the homoscedasticity assumption is met we look to make sure that there is no pattern in the residuals and that they are equally spread around the y = 0 line. To assess the assumption of linearity we want to ensure that the residuals are not too far away from 0 ( standardized values less than -2 or greater than 2 are deemed problematic). If the model does not meet the linear model assumption, we would expect to see residuals that are very large (big positive value or big negative value). The plot of residuals versus predicted values is useful for checking the assumption of linearity and homoscedasticity. Residual = observed y – model-predicted y The first plot depicts residuals versus fitted values. The plot() function provide 6 diagnostic plots and here we will introduce the first four. The basic tool for examining the fit is the residuals.

One method to find influential points is to compare the fit of the model with and without each observation. Thus, influential points have a large influence on the fit of the model.

Influential observations : An influential observation is defined as an observation that changes the slope of the line.

Leverage points: A leverage point is defined as an observation that has a value of x that is far away from the mean of x.

In other words, the observed value for the point is very different from that predicted by the regression model.

Outliers: an outlier is defined as an observation that has a large residual.

Normality: For any fixed value of X, Y is normally distributed.īefore we go further, let's review some definitions for problematic points.

Independence: Observations are independent of each other.

Homoscedasticity: The variance of residual is the same for any value of X.

Linearity: The relationship between X and the mean of Y is linear.

Again, the assumptions for linear regression are: Regression diagnostics are used to evaluate the model assumptions and investigate whether or not there are observations with a large, undue influence on the analysis. The model fitting is just the first part of the story for regression analysis since this is all based on certain assumptions.

Another word for diagnostic errors