By Bouchaud J.-P.
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We make two important assumptions concerning the errors. First, we assume that E(ei |xi ) = 0, so if we could draw a scatterplot of the ei versus the xi , we would have a null scatterplot, with no patterns. The second assumption is that the errors are all independent, meaning that the value of the error for one case gives Applied Linear Regression, Third Edition, by Sanford Weisberg ISBN 0-471-66379-4 Copyright 2005 John Wiley & Sons, Inc. 19 20 SIMPLE LINEAR REGRESSION 3 Y b1 2 1 1 b0 = intercept 1 2 3 X FIG.
19) F is just a rescaled version of SSreg = SYY − RSS, with larger values of SSreg resulting in larger values of F . 19), 1 and n − 2 for simple regression. This is written F ∼ F (1, n − 2). 144 We obtain a signiﬁcance level or p-value for this test by comparing F to the percentage points of the F (1, n − 2)-distribution. 4. The p-value is shown as “approximately zero,” meaning that, if the NH were true, the change of F exceeding its observed value is essentially zero. This is very strong evidence against NH and in favor of AH.
786. Compute estimates of the slope and the intercept for the regression of Y on X. Draw the ﬁtted line on your scatterplot. 3. Obtain the estimate of σ 2 and ﬁnd the estimated standard errors of βˆ0 and βˆ1 . Also ﬁnd the estimated covariance between βˆ0 and βˆ1 . Compute the t-tests for the hypotheses that β0 = 0 and that β1 = 0 and ﬁnd the appropriate p-values using two-sided tests. 4. Obtain the analysis of variance table and F -test for regression. 3 for testing β1 = 0. 2. More with Forbes’ data An alternative approach to the analysis of Forbes’ experiments comes from the Clausius–Clapeyron formula of classical thermodynamics, which dates to Clausius (1850).
An introduction to statistical finance by Bouchaud J.-P.