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

question 29

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.
ANOVA
$\begin{array}{llllll}\hline & d f & S S & M S & F & \text { Significance F } \\\hline \text { Regression } & 2 & 1293.125328 & 646.5626641 & 21.27366772 & 2.35769 \mathrm{E}-05 \\\text { Residual } & 17 & 516.6746719 & 30.39262776 & & \\\text { Total } & 19 & 1809.8 & & & \\\hline\end{array}$

$\begin{array}{lllllll}\hline & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -4.409686163 & 16.72267106 & -0.263695085 & 0.795184685 & -39.69148734 & 30.87211502 \\\text { Test 1 } & 0.397435806 & 0.343012569 & 1.158662514 & 0.262611745 & -0.326258467 & 1.121130079 \\\text { Test 2 } & 0.638805278 & 0.224623383 & 2.843894834 & 0.011217936 & 0.164890704 & 1.112719852 \\\hline\end{array}$
Is there evidence of multicollinearity in the printout? Explain.

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Definitions:

Prolonged Stimulation

Continuous or extended exposure to a stimulus over a considerable period of time.

Neurotransmitter

Chemical messengers that transmit signals across a chemical synapse, from one neuron (nerve cell) to another 'target' neuron, muscle cell, or gland cell.

Amplitude

Amplitude refers to the magnitude or strength of a fluctuating signal, such as sound, light, or electrical signal, often measured from its baseline to its peak.

Brightness

The perception of how luminous an object appears, measured in lumens or subjective visual assessment.