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Cut Calibri E Copy . a.?.! ???Merge aste·Format Painter B 1 u. Alignment Font Clipboard G19 Question 3: The editors of a national automotive magazine recently studied 30 different automobiles sold in the United States with the intent of seeing whether they could develop a multiple regression model to explain the variation in highway mileage per gallon. A number of different independent variables were collected. 2 The following correlation matrix was developed: mile ape higtway Curb Weigsylinders Horse Power Torgue 0 to 60mt Price as Tested Displacem 4 mileage, highway 5Curb Weight 6 Cylinders 7.1 Horse Power 0.7391.000 0.6950.596 1000 0.549 0293 0840 1.000 0.67905020.9320931 1.000 0.3380.053 0.637 0.860 -0.7171.000 0 392 0.030 0.457 0766 0.566 0 819 0.674 0510 0.9120 789 0915 0.555 Torque 0 to 60 mph 9 Price as Tested 10Displacement 1.000 0.350 1.0 12 If only one variable were to be brought into the model, which variable should it be if the goal is to explain the highest possible percentage of variation in the 13 dependent variable? 16 Question 1Question 2Questlon 3Question 4 1| Question 5 3 Chinese differences -From the rExplanation / Answer
R2 = coefficient of determination
R = correlation coefficient
Suppose that the correlation coefficient of dependent variable with two different independent variables are R1 and R2
The maximum value of | R1 | and |R2 | is the strogest correlation coefficient between the corresponding variables.
From the above correlation matrix ,the correlation between the "Highway mileage" and "curb weight" is strongest than others.
Therefore curb Weight should be include in the model to explain the highest possible percentage of variation in the dependent variable ( that is in the Highway mileage).
So answer is " Curb Weight"
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