Course Outline

list High School / Advanced Statistics and Data Science I (ABC)

Book
  • High School / Advanced Statistics and Data Science I (ABC)
  • High School / Statistics and Data Science I (AB)
  • High School / Statistics and Data Science II (XCD)
  • High School / Algebra + Data Science (G)
  • College / Introductory Statistics with R (ABC)
  • College / Advanced Statistics with R (ABCD)
  • College / Accelerated Statistics with R (XCD)
  • CKHub: Jupyter made easy

7.6 Graphing Residuals From the Model

You might wonder, why are we bothering to generate and save residuals? There are a lot of reasons but one short answer is: it helps us to understand the error around our model, and can suggest ways of improving the model.

Just as the first thing we do when looking at a data set is to examine the distributions of the variables, it is good to get in the habit of examining the distributions of residuals after we fit a new model.

In the following window, we have provided the code to create histograms of Thumb in a facet grid by Sex. Try modifying it to generate histograms of Sex_resid in a facet grid by Sex. Compare the histograms of residuals from the Sex_model with histograms of thumb length.

require(coursekata) # this creates the residuals from the Sex_model Sex_model <- lm(Fingers$Thumb ~ Fingers$Sex) Fingers$Sex_resid <- resid(Sex_model) # this creates histograms of Thumb for each Sex # modify it to create histograms of Sex_resid for each Sex gf_histogram(~Thumb, data = Fingers) %>% gf_facet_grid(Sex ~ .) # this creates the residuals from the Sex_model Sex_model <- lm(Fingers$Thumb ~ Fingers$Sex) Fingers$Sex_resid <- resid(Sex_model) # this creates histograms of Thumb for each Sex # modify it to create histograms of Sex_resid for each Sex gf_histogram(~Sex_resid, data = Fingers) %>% gf_facet_grid(Sex ~ .) ex() %>% { check_or(., check_function(., "gf_histogram") %>% { check_arg(., "object") %>% check_equal() check_arg(., "data") %>% check_equal() }, override_solution(., "gf_histogram(Fingers, ~ Sex_resid)") %>% check_function("gf_histogram") %>% { check_arg(., "object") %>% check_equal() check_arg(., "gformula") %>% check_equal() } ) check_function(., "gf_facet_grid") %>% check_arg("...") %>% check_equal(incorrect_msg = "Make sure you keep the code to create a grid faceted by `Sex`") }

Here we’ve depicted the histograms of Thumb by Sex (in teal) next to the histograms of Sex_resid by Sex (in darker gray).

Thumb Sex_resid

On the left, a faceted histogram of Thumb faceted by Sex (female and male), in teal. The distributions are both roughly normal but the male group is distributed slightly more to the right.

On the right, a faceted histogram of Sex_resid faceted by Sex (female and male), in gray. The distributions are both roughly normal and are mostly overlapping.


The residuals of the Sex_model represent the variation leftover after taking out the part of the variation that can be explained by Sex. The figures below show the mean Thumb length and mean Sex_resid of the two Sex groups.

mean Thumb of each group mean Sex_resid of each group

A faceted histogram of the distribution of Thumb by Sex on the left with vertical lines showing the mean for each Sex group. The mean for the male group is higher than the mean for the female group.

A faceted histogram of the distribution of Sex_resid by Sex on the right with vertical lines showing the mean for each Sex_resid group. The means for both the male group and the female group are 0.


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