The Quality of Oil Is Measured in API Gravity Degrees

question 53

Essay

The quality of oil is measured in API gravity degrees - the higher the degrees API, the higher the quality. The table shown below is produced by an expert in the field, who believes that there is a relationship between quality and price per barrel. $$\begin{array} { | c | c | } \hline \text { Oil degrees API } & \text { Price per barrel (in } \$ \text { ) } \\\hline 27.0 & 12.02 \\\hline 28.5 & 12.04 \\\hline 30.8 & 12.32 \\\hline 31.3 & 12.27 \\\hline 31.9 & 12.49 \\\hline 34.5 & 12.70 \\\hline 34.0 & 12.80 \\\hline 34.7 & 13.00 \\\hline 37.0 & 13.00 \\\hline 41.0 & 13.17 \\\hline 41.0 & 13.19 \\\hline 38.8 & 13.22 \\\hline 39.3 & 13.27 \\\hline\end{array}$$ A partial computer output follows.
Descriptive Statistics $$\begin{array} { | l | r | r | r | r | } \hline \text { Variable } & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } \\\hline \text { Degrees } & 13 & 34.60 & 4.613 & 1.280 \\\hline \text { Frice } & 13 & 12.730 & 0.457 & 0.127 \\\hline\end{array}$$ Covariances $$\begin{array} { | l | r | r | } \hline & \text { Degrees } & \text { Price } \\\hline \text { Degrees } & 21.281667 & \\\hline \text { Price } & 2.026750 & 0.208833 \\\hline\end{array}$$ Regression Analysis $$\begin{array} { | l | r | r | r | r | } \hline \text { Fredictor } & \text { Coef } & \text { StDev } & \mathrm { T } & \mathrm { P } \\\hline \text { Constant } & 9.4349 & 0.2867 & 32.91 & 0.000 \\\hline \text { Degrees } & 0.095235 & 0.008220 & 11.59 & 0.000 \\\hline\end{array}$$ se = 0.1314 R2 = 92.46% R2(adjusted) = 91.7%
Analysis of Variance $$\begin{array} { | l | r | r | r | r | r | } \hline \text { Source } & \text { DF } & \text { SS } & \text { MS } & \mathrm { F } & \mathrm { P } \\\hline \text { Regression } & 1 & 2.3162 & 2.3162 & 134.24 & 0.000 \\\hline \text { Residual Error } & 11 & 0.1898 & 0.0173 & & \\\hline \text { Total } & 12 & 2.5060 & & & \\\hline\end{array}$$ a. Determine the standard error of estimate and describe what this statistic tells you.
b. Determine the coefficient of determination and discuss what its value tells you about the two variables.
c. Calculate the Pearson correlation coefficient. What sign does it have? Why?

Analyze funding models for public goods, such as parks, and their effects on service quality and availability.

Understand the economic implications of environmental laws and policies on property rights, conservation efforts, and resource allocation.

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Analyze the implications of cost allocations on product profitability.

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Definitions:

Unit Costs

The expenses a company faces to manufacture, warehouse, and market a single unit of a specific product or service.

Outliers

Data points that lie significantly outside the range of the rest of the data, often indicating a variance from the norm that could warrant further investigation.

Missing Data

Refers to the absence of data points or information in datasets, which can lead to challenges in analysis and decision-making.

Fixed Fee

A pricing strategy where a single fixed amount is charged for a service regardless of usage or time required.