6 a)
i)
n = 8
linear regression equation
Y = b0 + b1 * X
Slope b1 = SSxy / SSxx
SSxx = SUM of X^2 - (SUM of x)^2/n = 325751 - 941^2/8 = 215065.9
SSxy = SUM of xy - (SUM of x * SUM of y)/n = 3271030 - (941*9570)/8 = 2145359
Slope b1 = 2145359/215065.9 = 9.9754
Intercept b0 = Mean Y - Mean X * Slope
Mean X = SUM of X / n = 941/8 = 117.625
Mean Y = SUM of Y / n = 9570/8 = 1196.25
Intercept b0 = 1196.25-117.625*9.9754 = 22.8936
Y = 22.8936 + 9.9754 * X
ii)
Coefficient of correlation r = SSxy/SQRT(SSxx*SSyy)
SSyy = SUM of y^2 - (SUM of y)^2/n = 32849700 - (9570^2)/8 = 21401588
r = 2145359/SQRT(215065.9*21401588) = 0.99998 (neraly 1)
Coefficient of determination r^2 = 0.999959 (nearly 1)
100% of variation in Y variable is explained by regression analysis
or
100% of variation in Y variable is explained by variation in X variable
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