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Statistics, multiple choice, regression equation  2nd question 
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#1
Jun2211, 04:58 PM

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1. The problem statement, all variables and given/known data
A regression equation was developed to predict gasoline mileage (mpg) for various car weights (pounds). The resultant equation was: Y = 35.2  .0034 X. Which two answers can be concluded? A. The explanatory variable is the mileage and the response variable is the weight. B. The explanatory variable is the weight and the response variable is the mileage. C. Heavier cars get lower mileage. D. Heavier cars get higher mileage. 2. Relevant equations y=mx+b 3. The attempt at a solution My answer is A and D, For they make the most sense to me, yet I am not sure:/ 


#2
Jun2211, 08:51 PM

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Hi Calculator14! Welcome to PF!
Do you have the definitions handy for the "explanatory variable" and the "response variable"? Those should tell you which is which.... In your expression X would be the weight. Suppose you fill in 2 values, say 1000 kg and 2000 kg, which result (mileage) would be the highest? (Note that this problem is not about what is intuitively likely, but about what the formula says.) 


#3
Jun2311, 11:50 AM

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Also since this is a statistics question, the very small slope, so close to zero, might give one pause concluding either C or D. You might take that into consideration if you are supposed to choose the "best" answer.



#4
Jun2311, 12:14 PM

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Statistics, multiple choice, regression equation  2nd question
In my opinion that makes this question a bad question. Because without information how accurate the slope is, I think we still need to choose either C or D. It's a trick question! 


#5
Jun2311, 01:29 PM

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This is a simple problem. The regression equation was developed to predict (key word) gas mileage (the number of miles traveled on a gallon of gas) for a given car knowing its weight. It's reasonable to conclude that 'gas mileage', being what is predicted, is the 'response'. Therefore, one also concludes that the 'weight' of the car is the 'explanatory' variable, since different mileage predictions, according to this equation, are a function solely of different car weights.
Based on these factors, would you like to change your answer? By looking at the slope of the curve, which in this case is negative, one concludes that a heavier car will have lower gas mileage. (Quick: what has higher gas mileage? A Toyota or a Tank?) 


#6
Jun2311, 07:26 PM

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The slope is not small when you consider that "x" is in pounds and that a typical car weighs around 3000+ pounds! If you were to take the weight of the car in tons then the slope would be about 7.6. For any linear equation you can make the slope as large or as small as you like, merely by choice of units. You cannot conclude the slope is small without considering the units involved. 


#7
Jun2311, 07:56 PM

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