The Printout Below Shows Part of the Least Squares Regression $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$

question 66

Essay

The printout below shows part of the least squares regression analysis for the model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 }$ fit to a set of data. The model attempts to predict a score on the final exam in a statistics course based on the scores on the first two tests in the class. $$\begin{array}{l}\text { ANOVA }\\\begin{array} { l l l l l l } \hline & d f & \text { SS } & \text { MS } & F & \text { Significance F } \\\hline \text { Regression } & 2 & 1293.125328 & 646.5626641 & 21.27366772 & 2.35769 \mathrm { E } - 05 \\\text { Residual } & 17 & 516.6746719 & 30.39262776 & & \\\text { Total } & 19 & 1809.8 & & & \\\hline\end{array}\\\begin{array} { l l l l l l l } \hline & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & - 4.409686163 & 16.72267106 & - 0.263695085 & 0.795184685 & - 39.69148734 & 30.87211502 \\\text { Test 1 } & 0.397435806 & 0.343012569 & 1.158662514 & 0.262611745 & - 0.326258467 & 1.121130079 \\\text { Test 2 } & 0.638805278 & 0.224623383 & 2.843894834 & 0.011217936 & 0.164890704 & 1.112719852 \\\hline\end{array}\end{array}$$ Is there evidence of multicollinearity in the printout? Explain.

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