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β1=SxySxxbeta 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
| Concept | Formula | |---------|---------| | | ( \sum (x_i - \barx)^2 ) | | Sample variance | ( s^2 = \fracS_xxn-1 ) | | Population variance | ( \sigma^2 = \fracS_xxn ) | | Computational Sxx | ( \sum x_i^2 - \frac(\sum x_i)^2n ) | | Regression slope | ( \hat\beta 1 = \fracS xyS_xx ) | | Correlation | ( r = \fracS_xy\sqrtS_xxS_yy ) | Sxx Variance Formula
Elara pressed the heels of her palms into her eyes until she saw starbursts. "It’s not working, Jonah. The regression model is a mess. The residuals look like a Rorschach test." β1=SxySxxbeta sub 1 equals the fraction with numerator
the fraction with numerator cap S sub x x end-sub and denominator cap N end-fraction Used when you have data for the entire group. Sample Variance ( The residuals look like a Rorschach test
( \barx = 26 / 5 = 5.2 )
[ \hat\beta 1 = \fracS xyS_xx ]
Let’s take a small dataset: ( x = [4, 8, 6, 5, 3] )
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