Data
CH01PR19.txt
Exercise 1
Start by reading in the data.
read.table("data/CH01PR19.txt", col.names = c("Y", "X"))
And fit a simple linear regression model with \(Y\) as the response and \(X\) as the predictor.
- Look at the regression model with
summary(), write what you see.
- Use the
confint() function to get the confidence interval of the two parameter estimates. What happens to the width of the interval if we set level = 0.99. Explain.
- Use the predict function to predict the expected value of \(Y\) when \(X = 3\). Also obtain the confidence interval and prediction interval.
- Extract the regression residuals and confirm that \(\sum^n_{i = 1} \varepsilon_i = 0\) and \(\sum^n_{i = 1} \left(\varepsilon_i X_i\right) = 0\)
- Perform an Analysis of Variance (ANOVA). Explain what you see, does it match up with what we saw earlier?