The Quality of Oil Is Measured in API Gravity Degrees

question 108

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 Minitab 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 $$\begin{array} { | l | r | r | r | r | } \hline \text { Predictor } & \text { Coef } & \text { StDev } & \mathrm { T } & \mathrm { P } \\\hline \text { Constant } & 9.4349 & 0.2867 & 32.91 & 0.000 \\\hline \text { Degrees } & 0.095235 & 0.008220 & 11.59 & 0.000 \\\hline\end{array}$$ S = 0.1314 R-Sq = 92.46% R-Sq(adj) = 91.7%
Analysis of Variance $$\begin{array} { | l | r | r | r | r | r | } \hline \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\\hline \text { Regression } & 1 & 2.3162 & 2.3162 & 134.24 & 0.000 \\\hline \text { Residual Error } & 11 & 0.1898 & 0.0173 & & \\\hline \text { Total } & 12 & 2.5060 & & & \\\hline\end{array}$$ a. Draw a scatter diagram of the data to determine whether a linear model appears to be appropriate to describe the relationship between the quality of oil and price per barrel.
b. Determine the least squares regression line.
c. Redraw the scatter diagram and plot the least squares regression line on it.
d. Interpret the value of the slope of the regression line.

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Definitions:

Tax Cuts

Reductions in the amount of taxes imposed by a government, often aimed at stimulating economic growth by increasing disposable income or encouraging investment.

Labor Supplied

The overall time period that workers consent to and can offer to work, in exchange for an established rate of pay.

Laffer Curve

A theoretical representation of the relationship between government revenue raised by taxation and all possible rates of taxation, suggesting that higher tax rates beyond a certain point actually decrease total revenue.

Elasticities

Measures of how much the quantity demanded or supplied of a good responds to changes in price, income, or other factors.