In statistics, Sxxcap S sub x x end-sub (also known as the sum of squares of
$$s^2 = \fracS_xxn - 1$$
The Sxx variance formula has numerous applications in statistics, data analysis, and engineering. Some of the key applications include: Sxx Variance Formula
Regression slope:
First, ( S_xy = \sum (x_i - \barx)(y_i - \bary) ).
( \bary = (60+70+80+90+100)/5 = 80 ).
Deviations: (2-6)(60-80)=(-4)(-20)=80; (4-6)(70-80)=(-2)(-10)=20; (6-6)0=0; (8-6)(90-80)=210=20; (10-6)(100-80)=4*20=80.
Sum ( S_xy = 80+20+0+20+80 = 200 ).
Thus, ( b_1 = 200 / 40 = 5 ).
Interpretation: each extra hour studied increases score by 5 points.
[ \boxedS_xx = \sum_i=1^n (x_i - \barx)^2 ] In statistics, Sxxcap S sub x x end-sub
| Student | Score | Deviation from mean | Squared deviation | | --- | --- | --- | --- | | 1 | 80 | 0 | 0 | | 2 | 70 | -10 | 100 | | 3 | 90 | 10 | 100 | | 4 | 85 | 5 | 25 | | 5 | 75 | -5 | 25 |
[ S_xx = (n-1) \cdot s_x^2 ]
To avoid rounding errors or needing to calculate ( \barx ) first, use:
[ S_xx = \sum_i=1^n x_i^2 - \frac(\sum_i=1^n x_i)^2n ] Interpretation: each extra hour studied increases score by