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

question 25

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


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

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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Definitions:

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Lemon Test

A three-part test developed by the Supreme Court to evaluate whether a government's action is in violation of the Establishment Clause of the First Amendment.

Purpose

The reason for which something is done or created or for which something exists.

McCarthyism

The practice of making accusations of subversion or treason without proper regard for evidence, especially during the early 1950s in the United States.