Quiz 16: Simple Linear Regression and Correlation

NARRBEGIN: Oil Quality and Price 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. $\begin{array} { | c | c | } \hline \text { Oil degrees API } & \text { Price per barrel (in \$) } \\\hline 27.0 & 12.02 \\28.5 & 12.04 \\30.8 & 12.32 \\31.3 & 12.27 \\31.9 & 12.49 \\34.5 & 12.70 \\34.0 & 12.80 \\34.7 & 13.00 \\37.0 & 13.00 \\41.0 & 13.17 \\41.0 & 13.19 \\38.8 & 13.22 \\39.3 & 13.27 \\\hline\end{array}$ A partial Minitab output follows: $\begin{array}{l}\text { Descriptive Statistics }\\\begin{array} { l l l l l } \text { Variable } & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } \\\text { Degrees } & 13 & 34.60 & 4.613 & 1.280 \\\text { Price } & 13 & 1270 & 0.757 & 0.127\end{array}\end{array}$ $\begin{array}{l}\text { Bavarifinces }\\\begin{array}{lll} & \text { Degrees } & \text { Price } \\\text { Degrees } & 21.281667 & \\\text { Price } & 2.026750 & 0.208833\end{array}\end{array}$ $\text { Regression Analysis }$ $\begin{array}{lllr}\text { Predictor } & {\text { Coef }} & \text { StDev } & \text { T } & \text { P } \\\text { Constant } & 9.4349 & 0.2867 & 32.91 &0.000\\\text { Degrees } & 0.095235 & 0.008220 & 11.59&0.000\\\end{array}$ $\mathrm{S}=0.1314 \quad \mathrm{R}-\mathrm{Sq}=92.46 \% \quad \mathrm{R}-\mathrm{Sg}(\mathrm{adj})=91.7 \%$ $\text { Analysis of Variance }$ $\begin{array}{llrrr}\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text {P } \\\text { Regression } & 1 & 2.3162 & 2.3162 & 134.24 &0.000\\\text { Residual Error } & 11 & 0.1898 & 0.0173 & \\\text { Total } & 12 & 2.5060\end{array}$ NARREND -{Oil Quality and Price Narrative} For what values of API gravity degrees do we feel comfortable making predictions for oil price?