The 95% prediction interval of the forecasted value ŷ 0 for x 0 is Here we look at any specific value of x, x 0, and find an interval around the predicted value ŷ 0 for x 0 such that there is a 95% probability that the real value of y (in the population) corresponding to x 0 is within this interval (see the graph on the right side of Figure 1).
There is also a concept called a prediction interval. any of the lines in the figure on the right above). Thus there is a 95% probability that the true best-fit line for the population lies within the confidence interval (e.g. The confidence interval consists of the space between the two curves (dotted lines). In the graph on the left of Figure 1, a linear regression line is calculated to fit the sample data points.
This means that there is a 95% probability that the true linear regression line of the population will lie within the confidence interval of the regression line calculated from the sample data.įigure 1 – Confidence vs. The 95% confidence interval for the forecasted values ŷ of x is
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