simple linear regression

# simple linear regression - t = estimate hypothesized...

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simple linear regression E follows a normal distribution, mean 0 E~N(0,sigma^2) E(y) = B0 + B1 X + E(E) error is the difference btwn the point and the true line(Y(hat) = B0(hat) + B1(hat) X) Error is something you do not observe The distance between the point and the imaginary true line residual is the difference between the point and the fitted line minimize sum of square error to obtain the fitted line The residuals are centered around 0 (summation of all the residuals is 0) lm(y var ~ x var, data=fuel) lm = linear model abline() a + bx line SS residual sigma(yi - yi(hat)) / (n-k-1) where k is how many variables you have --------- Simple regression 4.1 - 4.6 Multiple regression 5.1 - 5.4 Epsilon is assumed to be independent and follow N(0, sigma^2) standard error → S(Bhat)

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Unformatted text preview: t = estimate - hypothesized value [mean] / standard error of the estimate In a regression setting, if you don’t reject H0 you will actually accept it Different than in hypothesis testing when you do not accept H0 R^2 tells you the proportion of total variability explained by your linear regression model F test is to test is B1=0 or not testing the overall usefulness of the model credit scores → log(x+1) because some people have 0 savings so you cannot do log(0) but log(1) = 0 *** btwn -% and .1% error ** btwn .1% and 1% error * btwn 1% and 5% error . btwn 5% and 10% The lower p value, the better degrees of freedom n - 2 → simple regression n-k-1 → multiple regression; k = number of variables...
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