Course Outline
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segmentGetting Started (Don't Skip This Part)
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segmentStatistics and Data Science: A Modeling Approach
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segmentPART I: EXPLORING VARIATION
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segmentChapter 1 - Welcome to Statistics: A Modeling Approach
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segmentChapter 2 - Understanding Data
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segmentChapter 3 - Examining Distributions
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segmentChapter 4 - Explaining Variation
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segmentPART II: MODELING VARIATION
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segmentChapter 5 - A Simple Model
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segmentChapter 6 - Quantifying Error
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segmentChapter 7 - Adding an Explanatory Variable to the Model
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7.6 Graphing Residuals From the Model
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segmentChapter 8 - Digging Deeper into Group Models
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segmentChapter 9 - Models with a Quantitative Explanatory Variable
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segmentPART III: EVALUATING MODELS
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segmentChapter 10 - The Logic of Inference
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segmentChapter 11 - Model Comparison with F
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segmentChapter 12 - Parameter Estimation and Confidence Intervals
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segmentChapter 13 - What You Have Learned
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segmentFinishing Up (Don't Skip This Part!)
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segmentResources
list High School / Advanced Statistics and Data Science I (ABC)
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 Gender. Try modifying it to generate histograms of Gender_resid in a facet grid by Gender. Compare the histograms of residuals from the Gender_model with histograms of thumb length.
require(coursekata)
# this creates the residuals from the Gender_model
Gender_model <- lm(Fingers$Thumb ~ Fingers$Gender)
Fingers$Gender_resid <- resid(Gender_model)
# this creates histograms of Thumb for each Gender
# modify it to create histograms of Gender_resid for each Gender
gf_histogram(~Thumb, data = Fingers) %>%
gf_facet_grid(Gender ~ .)
# this creates the residuals from the Gender_model
Gender_model <- lm(Fingers$Thumb ~ Fingers$Gender)
Fingers$Gender_resid <- resid(Gender_model)
# this creates histograms of Thumb for each Gender
# modify it to create histograms of Gender_resid for each Gender
gf_histogram(~Gender_resid, data = Fingers) %>%
gf_facet_grid(Gender ~ .)
ex() %>% {
check_or(.,
check_function(., "gf_histogram") %>% {
check_arg(., "object") %>% check_equal()
check_arg(., "data") %>% check_equal()
},
override_solution(., "gf_histogram(Fingers, ~ Gender_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 `Gender`")
}Here we’ve depicted the histograms of Thumb by Gender (in teal) next to the histograms of Gender_resid by Gender (in darker gray).
Thumb
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Gender_resid
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The residuals of the Gender_model represent the variation leftover after taking out the part of the variation that can be explained by Gender. The figures below show the mean Thumb length and mean Gender_resid of the two Gender groups.
mean Thumb of each group
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mean Gender_resid of each group
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