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 { Mear } & \text { StDev } & \text { SE Mear } \\\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}

$Oil Quality and Price Quality of oil is measured in API gravity degrees--the higher the degrees API,the higher the quality.The table shown below is produced by an expert in the field who believes that there is a relationship between quality and price per barrel. \begin{array} { | c | c | } \hline \text { Oi degrees API } & \text { Price per barrel (in \$) } \\ \hline 27.0 & 12.02 \\ 28.5 & 12.04 \\ 30.8 & 12.32 \\ 31.3 & 12.27 \\ 31.9 & 12.49 \\ 34.5 & 12.70 \\ 34.0 & 12.80 \\ 34.7 & 13.00 \\ 37.0 & 13.00 \\ 41.0 & 13.17 \\ 41.0 & 13.19 \\ 38.8 & 13.22 \\ 39.3 & 13.27 \\ \hline \end{array} A partial Minitab output follows: \begin{array}{l} \text { Dascriptive atafistics }\\ \begin{array} { l l l l l } \text { Variable } & \mathrm { N } & \text { Mear } & \text { StDev } & \text { SE Mear } \\ \text { Degrees } & 13 & 34.60 & 4.613 & 1.280 \\ \text { Price } & 13 & 1270 & 0.757 & 0.127 \end{array} \end{array} \begin{array}{l} \begin{array} { l l } \text { Covariances }&&\\ &\text { Degeres } & \text { Price } \\ \text { Degeres } &21.281667 & \\ \text { Price } &2.026750 & 0.208933 \end{array} \end{array} \begin{array}{l} \text { Analysis of Variance }\\ \begin{array} { l l r r r } \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text {p}\\ \text { Regeression } & 1 & 2.3162 & 2.3162 & 134.24&0.000 \\ \text { Resichul Entar } & 11 & 0.1898 & 0.0173 & \\ \text { Total } & 12 & 2.5060 & & \end{array} \end{array} -In a simple linear regression model,testing whether the slope \beta <sub>1</sub> of the population regression line could be zero is the same as testing whether or not the population coefficient of correlation \rho equals zero.$

\begin{array}{l}\text { Analysis of Variance }\\\begin{array} { l l r r r } \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text {p}\\\text { Regeression } & 1 & 2.3162 & 2.3162 & 134.24&0.000 \\\text { Resichul Entar } & 11 & 0.1898 & 0.0173 & \\\text { Total } & 12 & 2.5060 & &\end{array}\end{array}

-In a simple linear regression model,testing whether the slope

\beta

₁ of the population regression line could be zero is the same as testing whether or not the population coefficient of correlation

\rho

equals zero.

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