ΣX | ΣY | Σ(x-x̅)² | Σ(y-ȳ)² | Σ(x-x̅)(y-ȳ) | |
total sum | 3450.00 | 33700.00 | 93750.00 | 5708333.3 | 712500.0 |
mean | 575.00 | 5616.67 | SSxx | SSyy | SSxy |
a)
Sample size, n = 6
here, x̅ = Σx / n= 575.000
ȳ = Σy/n = 5616.667
SSxx = Σ(x-x̅)² = 93750.0000
SSxy= Σ(x-x̅)(y-ȳ) = 712500.0
estimated slope , ß1 = SSxy/SSxx =
712500/93750= 7.6000
intercept,ß0 = y̅-ß1* x̄ = 5616.6667- (7.6
)*575= 1246.6667
Regression line is, Ŷ= 1246.67 +
( 7.600 )*x
b) $7.60
c) R² = (SSxy)²/(SSx.SSy) =
0.949
Approximately 94.9% of variation in observations
of variable Y, is explained by variable x
d)
Predicted Y at X= 650 is
Ŷ= 1246.66667 +
7.60000 *650= 6186.67
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