AE 09: Dental visits and health in North Carolina

Application exercise

The data for this application exercise come from the CDC PLACES 2025 county release. PLACES provides model-based local health estimates for every U.S. county.

We will model the relationship between the estimated percentage of adults who visited a dentist during the previous year and the estimated percentage reporting fair or poor health across the 100 North Carolina counties.

Getting started

Packages

We will use the tidyverse package for data visualization and wrangling and the tidymodels package for modeling.

library(tidyverse)
library(tidymodels)
library(scales)

Data

The data can be found in the data folder; the file is called nc-places.csv.

nc_places <- read_csv("data/nc-places.csv")

The variables used in this exercise are:

Variable name	Description
`county`	North Carolina county name
`dental_visit`	Percentage of adults who visited a dentist or dental clinic during the previous year
`fair_or_poor_health`	Percentage of adults reporting fair or poor general health

The percentage variables are age-adjusted, model-based estimates.

Visualizing the relationship

Create an appropriate plot to investigate the relationship between dental_visit and fair_or_poor_health. Put the predictor on the (x)-axis and the outcome on the (y)-axis. Add appropriate labels.

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Describe the form, direction, and strength of the relationship. Note any unusual observations.

Add your response here.

If you were to draw a straight line that best represents this relationship, where would it go? Why?

Add your response here.

Now let R draw the line. Use geom_smooth() with method = "lm" and set se = FALSE.

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What types of questions can this plot help answer?

Add your response here.

Model fit and summary

Fit a linear regression model that predicts fair-or-poor-health prevalence from dental-visit prevalence.

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Display the model summary and extract the slope and intercept estimates.

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Write the fitted model using mathematical notation.

Add your response here.

Interpret the slope in context.

Add your response here.

Interpret the intercept in context. Is this interpretation meaningful for these data?

Add your response here.

Correlation

Calculate the correlation between dental-visit prevalence and fair-or-poor-health prevalence. Interpret its sign and magnitude.

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Add your response here.

Predictions and residuals

Use the model to predict fair-or-poor-health prevalence for a county where 60% of adults visited a dentist during the previous year.

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Add your response here.

Use augment() to add predictions and residuals to the county data.

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Durham County

Durham County has a dental-visit prevalence of 68.2% and an observed fair-or-poor-health prevalence of 16.5%. Use the augmented data frame to identify the predicted value and residual for Durham County.

# add code here

Add your response here.

Verify this residual by calculating the predicted value using the model and comparing it to the observed value. If your calculation doesn’t exactly match the residual returned by augment(), explain why.

Add your response here.

Identifying potential outliers

Identify the counties with the five highest absolute residuals. Report their observed values, predicted values, and residuals.

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Mark these counties on the scatterplot. Do they appear to be outliers?

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Add your response here.

Interpreting responsibly

Does this analysis establish that increasing dental visits causes better general health? Explain.

Add your response here.