Comparing randomization CIs and t-based CIs
As with hypothesis testing, if technical conditions hold (technical conditions are discussed more in the next chapter), the CI created for the slope parameter in the t-distribution setting should be in line with the CI created using bootstrapping. Create a CI for the slope parameter and compare it to the one created using the bootstrap percentile interval from the previous chapter.
Note that the bootstrap and t-intervals will not be exactly the same because they use different computational steps to arrive at the interval estimate.
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Inference for Linear Regression in R
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alpha <- 0.05
# Calculate the confidence level
confidence_level <- ___
# Calculate lower percentile cutoff
p_lower <- ___
# ... and the upper one
p_upper <- ___