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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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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12.10 Confidence Interval for Beta0
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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)
12.10 Confidence Interval for
We have spent a lot of time working with the confidence interval for
We don’t typically create confidence intervals around F because the F-distribution is not symmetrical, making the confidence interval harder to interpret. But for any of the parameters we label with a
In the tipping study, we have put most of our emphasis on the confidence interval for the effect of smiley face on Tip
, represented as
The Tip
for the control group in the study. If we fit and then run confint()
on this model, we get 95% confidence intervals for both the
You’ve seen this output before when we used confint()
to get the confidence interval for
2.5 % 97.5 %
(Intercept) 22.254644 31.74536
ConditionSmiley Face -0.665492 12.75640
This time we will focus on the line labeled (Intercept)
, because that shows us the confidence interval for Tip
when
What if you wanted to find the confidence interval for Tip
? In other words, what would be the average percentage tipped by all tables (both control and smiley face) in the DGP? What is the confidence interval for this average tipping percentage? Again, we can use confint()
, which can take in any type of model.
2.5 % 97.5 %
(Intercept) 26.58087 33.46459
In the table below we show the confint()
output for both the condition model and the empty model.
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The condition model had two parameters (confint()
will calculate the confidence intervals for each parameter in the model so it will return different lines of output depending on the number of parameters.
Notice that the confidence interval around Condition
model (22.25 and 31.75).