Using data for a large sample of cars (n = 93), a statistics student calculated a matrix of correlation coefficients for selected variables describing each car. (a) In the spaces provided, write the two-tailed critical values of the correlation coefficient for α = .05 and α = .01 respectively. Show how you derived these critical values. (b) Mark with * all correlations that are significant at α = .05, and mark with ** those that are significant at α = .01. (c) Why might you expect a negative correlation between Weight and HwyMPG? (d) Why might you expect a positive correlation between HPMax and Length? Explain your reasoning. (e) Why is the matrix empty above the diagonal?
Correlation Matrix (

n = 93

cars)

\begin{array}{|c|c|c|c|c|c|c|}\text { MidPr}&\text { CityMPG}&\text { HwyMPG}&\text { EngSize}&\text { HPMax}&\text {Length}& \text {Weight }\\\hline \text { MidPr}&1.000 & & & & & & \\\hline\text { CityMPG}&-0.595 & 1.000 & & & & & \\\hline\text { HwyMPG}&-0.561 & 0.944 & 1.000 & & & & \\\hline\text { EngSize}&0.597 & -0.710 & -0.627 & 1.000 & & & \\\hline \text { HPMax}&0.788 & -0.673 & -0.619 & 0.732 & 1.000 & & \\\hline \text {Length}& 0.504 & -0.666 & -0.543 & 0.780 & 0.551 & 1.000 & \\\hline \text {Weight }&0.647 & -0.843 & -0.811 & 0.845 & 0.739 & 0.806 & 1.000 \\\hline\end{array}

MidPr = midrange price (in

\$ 1,000 )

- average of min and max prices
CityMPG = city MPG (miles per gallon by EPA rating)
HwyMPG highway MPG
EngSize = engine size (liters)
HPMax = horsepower (maximum)
Length

=

length (inches)
Weight = weight (pounds)
Critical value for

.05

Critical value for .01

Which Estimated Multiple Regression Has Nonlinearity Tests? A) y^=−92−5x1+6x12+18x2−12x22\hat { y } = - 92 - 5 x _ { 1 } + 6 x _ { 1 } ^ { 2 } + 18 x _ { 2 } - 12 x _ { 2 } ^ { 2 }y^​=−92−5x1​+6x12​+18x2​−12x22​

Multiple Choice

Correct Answer:VerifiedShow Answer

Which Estimated Multiple Regression Has Nonlinearity Tests?
A) $\hat { y } = - 92 - 5 x _ { 1 } + 6 x _ { 1 } ^ { 2 } + 18 x _ { 2 } - 12 x _ { 2 } ^ { 2 }$

Correct Answer:
Verified