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Stats Week11 - Coggle Diagram
Stats Week11
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questions
when more points are added to a parabola (when r = 0), r will still remain 0... week 9 extra qn 2b
degree of freedom depends on the context and situation: the main idea is that you take the total number of ways the data can be "changed" and subtract away its constraints
for chi squared test, m-1, for all others its n-1 / n-2
where m = no of categories
where n = no of data values
regression line in class = y hat = r * x after we standardise the data where yhat = the fitted values and r = the correlation coefficient ... RMBR that multicollinearity means high correlation between x variables, and that is bad. if we say y is highly correlated to x, then it is good.
1 sided confidence intervals correct, lower and upper bound respectively.
the t distribution converges to a z distribution when n is large
s is a good estimator for sigma when n is large
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residuals (e = difference between the yi - yhat) --> can plot a QQ plot to check if they are actually normal--> are the approximations to the actual error (epsilon)
important points
ANOVA F p value = p value for beta1hat IF only 1 predictor variable, as the hypothesis test is the same (testing if beta1 = 0). the F statistic is the square of the t statistic
if the p value is less than the t crit value, reject null hypothesis
if the confidence interval doesnt contain 0, reject null hypothesis
for prediction intervals, you need to use t inv (the t crit), and you use the n-2 and df BEFORE you add the new "prediction in"
We can assume (and prove) that y_i bar is an unbiased estimator for mu_i. However it is not straightforward to test for the equality of the mu_i’s using y_i bar directly, due to an issue known as multiple testing.
proofs
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sum of (xi - xbar) (xi - xbar) = sum of (xi-xbar)(xi) cos the last term goes to 0 = sum of (xi - xbar)^2 = (n-1)s^2
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