As book I'm reading now shows, formula for the slope of the line in linear regression is
$\beta_1 = \dfrac{\displaystyle \sum_{i=1}^n(X_i - \bar{X_n})(Y_i - \bar{Y_n})}{\displaystyle \sum_{i=1}^n(X_i - \bar{X_n})^2}$
The other formula for the slope is $\dfrac{Cov(X,Y)}{Var(X,Y)} = \dfrac{\mathbf{E}((X-\mu_x)(Y-\mu_y))}{\mathbf{E}(X-\mu)^2}$
So as I can see those 2 formulas look really simillar. First uses Sums, second Expectations. First uses mean of samples, second mean of populations. But why are they equal? Expectation != Sum.
Also there is a third formula for the slope which I don't really understand :
$p\dfrac{\sigma_y}{\sigma_x}$
2026-03-25 23:10:09.1774480209
What is the difference between Expectation and Sum formula for the slope of line in regression?
50 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in EXPECTED-VALUE
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