Recall that the deviations of the y values about the estimated regression line are called residuals. Estimate of σ 2įrom the regression model and its assumptions we can conclude that σ 2, the variance of e, also represents the variance of the y values about the regression line. Both require an estimate of σ 2, the variance of e in the regression model. Thus, to test for a significant regression relationship, we must conduct a hypothesis test to determine whether the value of β 1 is zero. Alternatively, if the value of β 1 is not equal to zero, we would conclude that the two variables are related. In this case, the mean value of y does not depend on the value of x and hence we would conclude that x and y are not linearly related. If the value of β 1 is zero, E(y) = β 0 + (0)x = b 0.
In a simple linear regression equation, the mean or expected value of y is a linear function of x: E(y) = β 0 + β 1x.
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