Analysis of variance (ANOVA) table

The p-value of 0.000 indicates that the factor of color is significant.

Lack-of-fit tests

Residual Plot Choices

main topic 

    Histogram of residuals . An exploratory tool to show general characteristics of the data, including:

    Typical values, spread or variation, and shape

    Unusual values in the data

Long tails in the plot may indicate skewness in the data. If one or two bars are far from the others, those points may be outliers. Because the appearance of the histogram changes depending on the number of intervals used to group the data, use the normal probability plot and goodness-of-fit tests to assess the normality of the residuals.

    Normal probability plot of residuals. The points in this plot should generally form a straight line if the residuals are normally distributed. If the points on the plot depart from a straight line, the normality assumption may be invalid. If your data have fewer than 50 observations, the plot may display curvature in the tails even if the residuals are normally distributed. As the number of observations decreases, the probability plot may show substantial variation and nonlinearity even if the residuals are normally distributed. Use the probability plot and goodness-of-fit tests, such as the Anderson-Darling statistic , to assess whether the residuals are normally distributed.

You can display the Anderson-Darling statistic (AD) on the plot, which can indicate whether the data are normal. If the p-value is lower than the chosen a-level , the data do not follow a normal distribution. To display the Anderson-Darling statistic, choose Tools > Options >  Individual Graphs > Residual Plots. For additional tests of normality, see Stat > Basic Statistics > Normality Test.

    Residuals versus fits . This plot should show a random pattern of residuals on both sides of 0. If a point lies far from the majority of points, it may be an outlier . Also, there should not be any recognizable patterns in the residual plot. The following may indicate error that is not random:

    a series of increasing or decreasing points

    a predominance of positive residuals, or a predominance of negative residuals

    patterns, such as increasing residuals with increasing fits

    Residuals versus order. This is a plot of all residuals in the order that the data was collected and can be used to find non-random error, especially of time-related effects. A positive correlation is indicated by a clustering of residuals with the same sign. A negative correlation is indicated by rapid changes in the signs of consecutive residuals.

    Four in one. Select this option to produce a normal plot of residuals, a histogram of residuals, a plot of residuals versus fits, and a plot of residuals versus order in one graph window.

    Residuals versus other variables. This is a plot of all residuals versus another variable. Plot the residuals against:

    Each predictor to look for curvature or differences in the magnitude of the residuals

    Important variables left out of the model to see if they have critical additional effects on the response.

If certain residual values are of concern, you can brush your graph to identify them. See graph brushing.

 

Residual

The difference between an observed value (y) and its corresponding fitted value (ŷ). For example, the scatterplot below plots men's weight against their height; the regression line plots the fitted values of weight for each observed value of height. Suppose a man is 6 feet tall and the fitted value of his weight is 190 lbs. If his actual weight is 200, the residual is 10.  If his actual weight is 175, the residual is -5.

 

weight
	height

Residual values are especially useful in regression and ANOVA procedures because they indicate the extent to which a model accounts for the variation in the observed data.