Oil Quality and Price
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 { Oi degrees API } & \text { Price per barrel (in \$) } \\\hline 27.0 & 12.02 \\28.5 & 12.04 \\30.8 & 12.32 \\31.3 & 12.27 \\31.9 & 12.49 \\34.5 & 12.70 \\34.0 & 12.80 \\34.7 & 13.00 \\37.0 & 13.00 \\41.0 & 13.17 \\41.0 & 13.19 \\38.8 & 13.22 \\39.3 & 13.27 \\\hline\end{array}

A partial Minitab output follows:

\begin{array}{l}\text { Dascriptive atafistics }\\\begin{array} { l l l l l } \text { Variable } & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } \\\text { Degrees } & 13 & 34.60 & 4.613 & 1.280 \\\text { Price } & 13 & 1270 & 0.757 & 0.127\end{array}\end{array}

\begin{array}{l}\begin{array} { l l } \text {Covariances }\\&\text { Degeres } & \text { Price } \\\text { Degeres }&21.281667 & \\\text { Price } &2.026750 & 0.208933\end{array}\end{array}

\begin{array}{l}\begin{array} { l l l r } \text { Rederatian Antalyis } & & \\\text { predictor } & \text { Caef } & \text { StDev } & \text { T }&\text { P} \\\text { Cunstant } & 9.4349 & 0.2867 & 32.91&0.000 \\\text { Degrees } & 0.095235 &0 .008220 & 11.59&0.000\end{array}\\\\S =0 .1314 \quad R - S q = 92.46 \% \quad R - S q ( a dj ) = 91.7 \%\end{array}

\begin{array}{l}\text { Analysis of Variance }\\\begin{array} { l l r r r } \text { Surce } & \text { DF } & \text { SS } & \text { MS } & \text { F } &\text {P}\\\text { Regeression } & 1 & 2.3162 & 2.3162 & 134.24 &0.000\\\text { Residual Error } & 11 & 0.1898 & 0.0173 & \\\text { Total } & 12 & 2.5060 & &\end{array}\end{array}

-{Oil Quality and Price Narrative} Use the regression equation

\tilde { y } = 9.4349 + 0.095235 x

to determine the predicted values of y.

The Least Squares Method Requires That the Variance σz2\sigma _ { z } ^ { 2 }σz2​

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The Least Squares Method Requires That the Variance $\sigma _ { z } ^ { 2 }$

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