a.
Sum of X = 58
Sum of Y = 210
Mean X = 9.6667
Mean Y = 35
Sum of squares (SSX) = 173.3333
Sum of products (SP) = 762
Regression Equation = ŷ = bX + a
b = SP/SSX = 762/173.33 =
4.3962
a = MY - bMX = 35 -
(4.4*9.67) = -7.4962
ŷ = 4.3962X - 7.4962
b. For x=15,
ŷ = (4.3962*15) - 7.4962=58.4468
c.
X Values
∑ = 58
Mean = 9.667
∑(X - Mx)2 = SSx = 173.333
Y Values
∑ = 210
Mean = 35
∑(Y - My)2 = SSy = 3548
X and Y Combined
N = 6
∑(X - Mx)(Y - My) = 762
R Calculation
r = ∑((X - My)(Y - Mx)) /
√((SSx)(SSy))
r = 762 / √((173.333)(3548)) = 0.9717
As r is near 1 and it is positive
So there is strong positive correlation between x and y
d. Here r=0.9717, so r^2=0.9717^2=0.9442
Hence 94.42% of variation in y is explained by x
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