# How to compute a confidence interval for a regression coefficient (in R)

## Task

Say we have a linear regression model, either single variable or multivariate. How do we compute a confidence interval for the coefficient of one of the explanatory variables in the model?

Related tasks:

- How to compute a confidence interval for a mean difference (matched pairs)
- How to compute a confidence interval for a population mean
- How to compute a confidence interval for a single population variance
- How to compute a confidence interval for the difference between two means when both population variances are known
- How to compute a confidence interval for the difference between two means when population variances are unknown
- How to compute a confidence interval for the difference between two proportions
- How to compute a confidence interval for the expected value of a response variable
- How to compute a confidence interval for the population proportion
- How to compute a confidence interval for the ratio of two population variances

## Solution

We’ll assume that you have fit a single linear model to your data, as in the code below, which uses fake example data. You can replace it with your actual data.

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x <- c(34, 9, 78, 60, 22, 45, 83, 59, 25)
y <- c(126, 347, 298, 309, 450, 187, 266, 385, 400)
model <- lm(y ~ x)

We can use R’s `confint()`

function to find the confidence interval for the model coefficients. You can change the `level`

parameter to specify a different confidence level. Note that if you have a multiple regression model, it will make confidence intervals for all of the coefficient values.

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confint(model, level = 0.95) # or choose any confidence level; here we use 0.95

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2.5 % 97.5 %
(Intercept) 172.638075 535.526421
x -4.491961 2.473935

The 95% confidence interval for the regression coefficient is $[-4.491961, 2.473935]$.

Content last modified on 24 July 2023.

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Contributed by Elizabeth Czarniak (CZARNIA_ELIZ@bentley.edu)