The Printout Shows the Results of a First-Order Regression Analysis $y$

question 12

Essay

The printout shows the results of a first-order regression analysis relating the sales price $y$ of a product to the time in hours $x _ { 1 }$ and the cost of raw materials $x _ { 2 }$ needed to make the product.
SUMMARY OUTPUT
$\begin{array}{ll}\hline \text { Regression Statistics } & \\\hline \text { Multiple R } & 0.997578302 \\\text { R Square } & 0.995162468 \\\text { Adjusted R Square } & 0.990324936 \\\text { Standard Error } & 1.185250723 \\\text { Observations } & 5 \\\hline\end{array}$

ANOVA
$\begin{array}{llllll}\hline & d f & \text { SS } & \text { MS } & \text { F } & \text { Significance } F \\\hline \text { Regression } & 2 & 577.9903614 & 288.9952 & 205.717 & 0.004837532 \\\text { Residual } & 2 & 2.809638554 & 1.404819 & & \\\text { Total } & 4 & 580.8 & & &\end{array}$

$\begin{array}{llllllll}\hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -26.48433735 & 3.674668773 & -7.20727 & 0.018713 & -42.29517198 & -10.67350271 \\\text { Time } & -2.168674699 & 4.11406532 & -0.52714 & 0.650732 & -19.8700814 & 15.532732 & 12.85220666 \\\text { Materials } & 8.142168675 & 1.094681583 & 7.437933 & 0.0176 & 3.432130693 & 12.05 \\\hline\end{array}$


a. What is the least squares prediction equation?
b. Identify the SSE from the printout.
c. Find the estimator of $\sigma ^ { 2 }$ for the model.

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