Clough Company Is Interested in Establishing the Relationship Between Utility

question 21

Essay

Clough Company is interested in establishing the relationship between utility costs and machine hours. Data have been collected and a regression analysis prepared using Excel. The monthly data and the regression output follow:
$\begin{array}{llll}&&\text { Utility } \\\text { Month } & \text { Machine Hours } & \text { Costs }\\\text { January } & 3,250& \$ 2,080 \\\text { February } & 3,77 0 & 25,200 \\\text { March } & 2,470 & 16,200 \\\text { April } & 4,030 & 27,600 \\\text { May } & 4,940 & 33,900 \\\text { June } & 4,290 & 26,400 \\\text { July } & 5,330 & 29,700 \\\text { August } & 4,550 & 27,300 \\\text { September } & 2,600 & 18,600 \\\text { October } & 4,810 & 31,200 \\\text { November } & 6,110 & 37,200 \\\text { December } & 5,460& 33,300\end{array}$

$$\begin{array}{c}\text { SUMMMARY OUTPUT}\\\text { Regression Statistics}\\\begin{array} { l r } \text { Multiple R } &96.5 \% \\\text { R Square } &93.2 \% \\\text { Adjusted R-Square } &92.5 \% \\\text { Starndard Eror } & 1,710.21\\\text { Obserrations } & 12.00 \\\end{array}\end{array}$$
$\begin{array}{|l|r|r|r|r|r|r|}\hline && \text { Standard } & && \text { Lower } & \text { Upper } \\&\text { Coefficients } & \text { Error } & \text { t Stat } & \text { P-value } & 95 \% & 95 \% \\ \hline \text { Intercept } & 4,472.26 & 2,019.39 & 2.21 & 0.051 & -27.23 & 8971.74 \\\hline \text { Machine } & 5.329 & 0.455 & 11.70 & 3.69 \mathrm{E}-07 & 4.314 & 6.343 \\\hline \end{array}$


Required:
(a.) What is the equation for utility costs using the regression analysis?
(b.) Does the variable "machine hours" have statistical significance? Explain.
(c.) Prepare an estimate of utility costs for a month when 3,000 machine hours are worked.

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Definitions:

Developmental Explanation

An account of how particular traits or behaviors emerge and change over an organism's lifespan.

Song Learning

The process through which birds acquire their vocalizations by listening to and imitating the songs of conspecifics, primarily during a sensitive phase early in life.

Environment Influence

Environment influence refers to the impact that surroundings and conditions have on the development, behavior, and survival of organisms.

Population Differences

Variations between groups of organisms of the same species, which may be due to genetic factors, environmental conditions, or both, and can lead to adaptations.