# Confidence Limits and Significance Tests for Sample Regression Lines

## Abstract

A regression line calculated from sample data may well be affected by sampling error. Even if the sampling is random, the line is unlikely to be precisely the same as the regression line of the population from which the sample is taken. The equation Ŷ = a + bX of the sample regression line is only an estimate of the equation μ = α + βX of the regression line of the population.^{l} It may be a bad estimate, especially if the sample is small or non-random. The regression coefficient b of the sample may differ greatly from the coefficient β of the population and a, the Y-intercept of the sample regression line, may be very different from α, the Y-intercept of the population regression line.

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