Sxx Variance Formula 〈REAL × Pick〉

If (S_xx) is random (random (x)), the of (\hat\beta 1) involves the expectation of (1/S xx). But conditionally on (x), (S_xx) is constant.

There are 4 data points, so $n = 4$.

This version is the most intuitive because it shows exactly what the "Sum of Squares" means: sxx variance formula

s2=Sxxn−1s squared equals the fraction with numerator cap S sub x x end-sub and denominator n minus 1 end-fraction To find the , you take the square root of that result:

. Both lead to the same result, but the second one is usually much easier for manual calculations. If (S_xx) is random (random (x)), the of

Substitute the values: $$S_xx = 120 - \frac(20)^24$$ $$S_xx = 120 - \frac4004$$ $$S_xx = 120 - 100$$ $$S_xx = 20$$

b1=SxySxxb sub 1 equals the fraction with numerator cap S sub x y end-sub and denominator cap S sub x x end-sub end-fraction Sxxcap S sub x x end-sub This version is the most intuitive because it

The variance of the slope estimator (\hat\beta_1) in simple linear regression is:

If (x_i \sim \texti.i.d. N(\mu_x, \sigma_x^2)):

s2=Sxxn−1s squared equals the fraction with numerator cap S sub x x end-sub and denominator n minus 1 end-fraction 💡 Why use Dividing by instead of

In Simple Linear Regression ($y = \beta_0 + \beta_1x$), $S_xx$ is required to find the slope ($\beta_1$).