The data below shows the gas mileage and respective car weights for 9 randomly s
ID: 458621 • Letter: T
Question
The data below shows the gas mileage and respective car weights for 9 randomly selected 2002 automobiles. a)Do you suspect there will be a strong correlation between the weight of an automobile and the gas mileage of the automobile? What other factors would also affect a particular automobile's gas mileage? b)Sketch a scatterplot of the data using weight as the independent variable and gas mileage as the dependent variable. c)Find a linear regression model for the data. What is the coefficient of determination? d)The Honda Insight is a hybrid (gas/electric) model car. Notice that it lies significantly away from the rest of the data. Remove this point from the data and find a new regression line and coefficient of determination. Is this new regression model a better predictor for gas mileage than the original? e)Use this regression line to predict the gas mileage for a car that has the same weight of the Honda Insight, 1847 pounds. What is the improvement in gas mileage of the Insight over gas models of the same weight according to the regression equation?Explanation / Answer
The correlation Co efficient between weight and gas mileage can be calculate with the help of MS Excel by using the Formula
= Correl(C4:C12,D4:D12)
The calculated value of Correlation Co efficient = -0.916, Means there is high negative correlation between Weight of the vehicle and gas mileage. As the the weight increase mileage will decrease.
What other factors are affecting the mileage.
No clear information on this is given in the proble. But these are general factors. Some of them are Speed, Driving Style, Number of passengers inside, offroad, onroad, Etc.
b) Drwaing is not possible here but You can do it with folowing guide line
Mark weight of X axis and Mileage on Y axis. and Connects these
c)
XY=ax+bx2
The calculation are shown Below
The Co efficent of determniation r2 = (-0.919)2 = 0.839.
The amount of variation = 83.9% . This means 83.9 percentage of changes in mileage is affected by the weight of the vehicle.
Model Weight (Pounds) Gas Mileage (Hwy) Chrylser Concorde 3479 28 Lexus Ls 430 3955 25 Honda Insight 1847 68 Subaru Legacy Wagon 3345 27 Toyota Camry 3086 32 Chevrolet Silverdado 4910 18 Ford Explorer 4159 21 Volkswagen Eurovan 4288 20 Cadillac Seville 3992 27 Correlation Co efficient -0.916577066Related Questions
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