546 views

### Why are the ends of the prediction interval wider in the regression? [duplicate]

Usually, the prediction interval has this shape in the image. I don't know why the end of the interval is wider than the center.
751 views

### Finding the the Confidence Interval with Linear Extrapolation [duplicate]

Suppose I have some slightly messy data with an r squared of 0.9, and so fits a line pretty well. If I were to extrapolate based on the slope and intercept of the fit, I would expect my y values to ...
48 views

### Standard error of linear regression fit [duplicate]

I have a naive question about regression. How does R function predict.lm compute the 95% confidence interval of the fitted line? In particular why is this not a straight line? ...
26 views

### computing confidence curves around the fitting line [duplicate]

I am reading a book about linear regression in which there is a plot showing the regression line and two curves they call a confidence band (also can be seen here). As I learn something last week that ...
22 views

### How to intuitively understand the shapes of confidence and prediction intervals in simple linear regression [duplicate]

Assume the linear regression $Y=b_{0}+b_{1}X$ The $100(1-a)$% prediction interval for $x=x_{*}$ is given by whereas the The $100(1-a)$% confidence interval for $E(Y|X=x_{*})$ is given by What I don'...
31k views

### Understanding shape and calculation of confidence bands in linear regression

I am trying to understand the origin of the curved shaped of confidence bands associated with an OLS linear regression and how it relates to the confidence intervals of the regression parameters (...