STATZIKI

Input

Y-values      X1-values     X2-values

1 1 1 2 2 2 3 3 3

Summary

Sum Y	3
Sum X1	6
Sum X2	9
Sum Y^2	3
Sum X1^2	12
Sum X2^2	27
Sum X1Y	6
Sum X2Y	9
Sum X1*X2	18
Mean Y	1
Mean X1	2
Mean X2	3

Coefficients

Y	0.07143
X1	0.14286
X2	0.21429

Formulas and Output

\[\begin{cases}intecept = \bar{y} - b_{1}\times \bar{x}_{1} - b_{2}\times \bar{x}_{2} \\\sum (x_{1}-\bar{x}_{1})(y-\bar{y}) = b_{1}\sum (x_{1}-\bar{x}_{1})^{2}+{b}_{2}\sum (x_{1}-\bar{x}_{1})(x_{2}-\bar{x}_{2}) \\\sum (x_{2}-\bar{x}_{2})(y-\bar{y}) = b_{1}\sum (x_{1}-\bar{x}_{1})(x_{2}-\bar{x}_{2})+{b}_{2}\sum (x_{2}-\bar{x}_{2})^{2}\end{cases}\] \[\sum (x_{1}-\bar{x}_{1})(y-\bar{y}) = \sum X_{1} Y - \frac{\sum x_{1}\sum y}{n} = 6 - \frac{ 6 \times 3 }{n} = 0.0\] \[\sum (x_{2}-\bar{x}_{2})(y-\bar{y}) = \sum X_{2} Y - \frac{\sum x_{2}\sum y}{n} = 9 - \frac{ 9 \times 3 }{n} = 0.0\] \[\sum (x_1-\bar{x}_1)(x_2-\bar{x}_2) =\sum X_1X_2 - \frac{\sum X_1 \sum X_2}{n} = 18 - \frac{ 6 \times 9 }{n} = 0.0\] \[\sum (X_1-\bar{X}_1)^{2}= \sum X_1^{2}-\frac{(\sum X_1)^{2}}{n} = 12 - \frac{ 6^{2} } {n} = 0.0\] \[\sum (X_2-\bar{X}_2)^{2}=\sum X_2^{2}-\frac{(\sum X_2)^{2}}{n} = 27 - \frac{ 9^{2} } {n} = 0.0\] \[\begin{cases} 0.0 = b_{1} \times 0.0 + b_{2} \times 0.0\\ 0.0 = b_{1} \times 0.0 + b_{2} \times 0.0\end{cases}\] \[\begin{eqnarray*} \textrm{Now solve for } b_1 \textrm{ & } b_2 \end{eqnarray*}\] \[b_1 = 0.14286\] \[b_2 = 0.21429\] \[intercept = \bar{Y} - b_1 \times \bar{X}_1 - b2 \times \bar{X}_2 = 1 - 0.14286 \times 2 - 0.21429 \times 3 = 0.07143\]

ANOVA

Goodness-of-fit

R2	0.02040816326530612
Adj. R2	-inf

Correlation Matrix

Variance Inflation Factors

Residual Plot

Normal Q-Q