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

question 127

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 x1 and the cost of raw materials x2 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
$\begin{array}{llllll} & d f & \text { SS } & \text { MS } & F & \text { Significance } F \\\hline \text { Regression } & 2 & 577.9903614 & 288.9952 & 205.717 & 0.004837532 \\\text { Residual } & 2 & 2.809638554 & 1.404819 & & \\\text { Total } & 4 & 580.8 & & & \\\hline\end{array}$

$\begin{array}{lllllll}\hline & \text { Coefficients } & \text { Standard Error } & \text { tStat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -26.48433735 & 3.674668773 & -7.20727 & 0.018713 & -42.29517198 & -10.67350271 \\\text { Time } & -2.168674699 & 4.11406532 & -0.52714 & 0.650732 & -19.8700814 & 15.532732 \\\text { Materials } & 8.142168675 & 1.094681583 & 7.437933 & 0.0176 & 3.432130693 & 12.85220666 \\\hline\end{array}$
a. What is the least squares prediction equation? b. Identify the SSE from the printout. c. Find the estimator of σ2 for the model.

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Definitions:

Jeremy Bentham

An English philosopher and legal theorist known for founding the philosophy of utilitarianism, emphasizing the greatest happiness principle.

John Locke

A 17th-century British philosopher known for his works on liberalism, political theory, and his ideas about natural rights and government.

Unpleasantness

The quality of being disagreeable or difficult to endure, often used to describe undesirable experiences or sensations.

Deserved

Warranted or merited due to actions or qualities.