Compare your data, and then your peers data, and answer the questions below: My data: The coefficients of correlation between miles per gallon and horsepower is -0.786323. The correlation value is close to –1 and the direction is negative with strong strength. There is a strong negative linear association between miles per gallon and horsepower. As the horsepower increases the miles per gallon decreases and as the horsepower decreases the miles per gallon increases. The coefficients of correlation between miles per gallon and the weight of the car is –0.871156. The correlation value is close to –1 and the direction is negative with strong strength. There is a strong negative linear association between miles per gallon and weight of the car. As the weight of the car increases the miles per gallon decreases and as the weight of the car decreases the miles per gallon increases. mpg wt hp
Compare your data, and then your peers data, and answer the questions below:
My data:
The coefficients of
The coefficients of correlation between miles per gallon and the weight of the car is –0.871156. The correlation value is close to –1 and the direction is negative with strong strength. There is a strong negative linear association between miles per gallon and weight of the car. As the weight of the car increases the miles per gallon decreases and as the weight of the car decreases the miles per gallon increases.
mpg wt hp
mpg 1.000000 -0.871156 -0.786323
wt -0.871156 1.000000 0.656837
hp -0.786323 0.656837 1.000000
The intercept is 37.6181, the coefficient for wt is –3.8709, and the coefficient for hp is –0.0334. Thus, the multiple regression equation for miles per gallon as the response variable is, mpg = 37.6181 – 3.8709 wt – 0.0334 hp.
It can be said that, if weight of the car increases by 1 unit the mpg is decreases by 3.8709 units when the horsepower is constant, and if horsepower increases by 1 unit the mpg is decreases by 0.0334 units when the weight of the car is constant. Moreover, the coefficient of determination of the model is 0.840. That is, 84% variation of mpg can be explained by the variations of weight and horsepower of the car. Thus, the car rental company can use the model to predict the mileage of the car using the weight and horsepower of the car.
My Peer's data:
Correlation Matrix:
mpg wt hp
mpg 1.000000 -0.856762 -0.777679
wt -0.856762 1.000000 0.657360
hp -0.777679 0.657360 1.000000
The coefficient of correlation between mpg and horsepower is -0.777679, the sign is negative, and the strength is moderate: 0.40 < |-0.777679| <= 1.00. The coefficient of correlation between mpg and weight is -0.856762, the sign is also negative, and the strength is strong: 0.80 < |-0.856762| <= 1.00. This tells us there is a moderate
The multiple regression equation is: mpg = 37.4790 + (-3.9252*wt) + (-0.0322*hp)
The car rental company might use this model to determine the most fuel-efficient vehicles for their customers as well as how much to charge for vehicles. With vehicles like sportscars that may not have a lot of weight but do have more than average horsepower, calculating weight alone might make it appear to use less fuel, but including horsepower, they have a better picture of true fuel efficiency and overall costs for their vehicles.
Now, answer the following, provide analysis and interpretation:
- Review your peer's multiple regression model. What is the predicted value of miles per gallon for a car that has 2.78 (2,780 lbs) weight and 225 horsepower? Suppose that this car achieves 18 miles per gallon, what is the residual based on this actual value and the value that is predicted using the regression equation?
- How do the plots and
correlation coefficients of your peers compare with yours? - Would you recommend this regression model to the car rental company? Why or why not?
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 2 images
