x | y | (x-x̅)² | (y-ȳ)² | (x-x̅)(y-ȳ) |
3 | 4 | 6.25 | 5.06 | 5.63 |
5 | 6 | 0.25 | 0.06 | 0.13 |
7 | 7 | 2.25 | 0.56 | 1.13 |
7 | 8 | 2.25 | 3.06 | 2.63 |
ΣX | ΣY | Σ(x-x̅)² | Σ(y-ȳ)² | Σ(x-x̅)(y-ȳ) | |
total sum | 22 | 25 | 11 | 8.750 | 9.500 |
mean | 5.500 | 6.250 | SSxx | SSyy | SSxy |
sample size , n = 4
here, x̅ = Σx / n= 5.50 ,
ȳ = Σy/n = 6.25
SSxx = Σ(x-x̅)² = 11.0000
SSxy= Σ(x-x̅)(y-ȳ) = 9.5
estimated slope , ß1 = SSxy/SSxx = 9.5
/ 11.000 = 0.86364
intercept, ß0 = y̅-ß1* x̄ =
1.50000
so, regression line is Ŷ = 1.50
+ 0.8636*x
estimated coefficient b = 0.8636
-------------
estimated std error of slope =Se(ß1) = Se/√Sxx = 0.522 /√ 11.00 = 0.1575
estimated std error of intercept =Se(ßo) = Se*√(1/n+x̅²/Sxx)= 0.905
R² = (Sxy)²/(Sx.Sy) = 0.9377
Anova table | |||||
variation | SS | df | MS | F-stat | p-value |
regression | 8.2045 | 1 | 8.2045 | 30.08 | 0.0317 |
error, | 0.5455 | 2 | 0.2727 | ||
total | 8.7500 | 3 |
F value = 30.08
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