## Course Outline

• segmentGetting Started (Don't Skip This Part)
• segmentStatistics and Data Science: A Modeling Approach
• segmentPART I: EXPLORING VARIATION
• segmentChapter 1 - Welcome to Statistics: A Modeling Approach
• segmentChapter 2 - Understanding Data
• segmentChapter 3 - Examining Distributions
• segmentChapter 4 - Explaining Variation
• segmentPART II: MODELING VARIATION
• segmentChapter 5 - A Simple Model
• segmentChapter 6 - Quantifying Error
• segmentChapter 7 - Adding an Explanatory Variable to the Model
• segmentChapter 8 - Digging Deeper into Group Models
• segmentChapter 9 - Models with a Quantitative Explanatory Variable
• segmentPART III: EVALUATING MODELS
• segmentChapter 10 - The Logic of Inference
• segmentChapter 11 - Model Comparison with F
• segmentChapter 12 - Parameter Estimation and Confidence Intervals
• segmentFinishing Up (Don't Skip This Part!)
• segmentResources

### 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)
• College / Statistics and Data Science (ABC)
• College / Advanced Statistics and Data Science (ABCD)
• College / Accelerated Statistics and Data Science (XCDCOLLEGE)
• Skew the Script: Jupyter

## 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

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