Prompt: The company expected fuel efficiency (miles per gallon) and weight of the car (often measured in thousands of pounds) to be correlated. The company also expects cars with higher horsepower to be less fuel efficient than cars with lower horsepower.
In your follow-up posts to other students, review your peers’ results and provide some analysis and interpretation:
POST # 1 😊 😊 😊
1) Do the scatterplots show any trend if yes, is the trend expected?
The first scatter plot shows a downward trend or negative plot, if you follow the data points from left to right they start from the top left then as you move further right, the dotes get closer to the x axis. The x-axis is labeled weight and the y-axis is miles per gallon, as the weight of the vehicle goes up the miles per gallon decreases. This is a expected trend the heavier a vehicle is the less miles per gallon you would get.
The second scatter plot shows a downward trend or negative plot as well. The x-axis for this plot is labeled horsepower, and the y-axis is mpg, this scatter plot is comparing horsepower to mpg, as you can see, as the horsepower goes up the mpg goes down like the first plot. This is also an expected trend the more powerful an engine is the fuel it takes to make it go.
mpg wt hp mpg 1.000000 -0.873635 -0.766214 wt -0.873635 1.000000 0.641488 hp -0.766214 0.641488 1.000000
What are the coefficients of correlation between miles per gallon and horsepower?
Using the correlation matrix above we can see that the correlation coefficient between miles per gallon and horsepower is -0.766214. This coefficient indicates a moderate negative correlation. In a negative correlation as one variable increases the response variable decreases, like when horse power increases the miles per gallon decreases because that is the response variable. In order to find the power of correlation between variables, take the absolute value of the correlation coefficient 0.40<0.76≤0.80
What are the coefficients of correlation between miles per gallon and the weight of the car?
The coefficient of correlation between miles per gallon and the weight of the car is -0.873635. This coefficient indicates a strong negative correlation. In order to find for the strength of this correlation is 0.80<0.87≤1.00
OLS Regression Results ============================================================================== Dep. Variable: mpg R-squared: 0.835 Model: OLS Adj. R-squared: 0.823 Method: Least Squares F-statistic: 68.42 Date: Mon, 05 Oct 2020 Prob (F-statistic): 2.69e-11 Time: 23:12:21 Log-Likelihood: -67.484 No. Observations: 30 AIC: 141.0 Df Residuals: 27 BIC: 145.2 Df Model: 2 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ Intercept 36.3849 1.540 23.624 0.000 33.225 39.545 wt -3.8046 0.597 -6.376 0.000 -5.029 -2.580 hp -0.0291 0.008 -3.434 0.002 -0.047 -0.012 ============================================================================== Omnibus: 6.483 Durbin-Watson: 1.634 Prob(Omnibus): 0.039 Jarque-Bera (JB): 4.801 Skew: 0.911 Prob(JB): 0.0907 Kurtosis: 3.721 Cond. No. 592. ============================================================================== 3) Write the multiple regression equation for miles per gallon as the response variable. Use weight and horsepower as predictor variables. The multiple regression equation for this discussion is E(Y)=B0+B1X1+B2X2 B0=36.3849B1=−3.8046B2=−0.0291 B0 represents the response variableB1 and B2 are the predictor variables
When you plug the coefficients in to the equation the equation is Yˆ=36.3849−3.8046(X1)−0.0291(X2)X1 represents the weight X2represents the horse power
How might the car rental company use this model?
A car rental company could use a model like this to high light its fleet, learning which vehicles have the best gas mileage while still having a decent amount of power, they could advertise those models more. Another way they could use a model like this, is in expanding their fleet, they could use this model to find the best vehicle to buy in order to provide the customer the gas mileage and horsepower they want.
POST # 2 😊 😊 😊
In this discussion, I am using a multiple regression model to determine if there is a correlation between miles per gallon, weight of car, and horsepower of vehicle. I will be using thirty samples from an imported CSV file. A car dealership made speculations that there is a correlation with the weight of car and horsepower that affects the fuel efficiency of a car.
First, in comparing regression models of mpg and the weight of the car with mpg and horsepower, it is seen that the scatter plots are somewhat similar. As can be seen by the scatter plot, there already seems to be visual, statistical evidence to back up the rental car company’s assumptions.
My assumption before the scatter plot was calculated was that weight of car and horsepower both affect the fuel efficiency of a vehicle. My assumptions were that in order to have higher horsepower, the engine needs to be big. Vehicles that have 6 cylinders and more usually have a higher horsepower, and they are needed to be big to accommodate the cylinders. Thus, the higher the horsepower, the heavier the engine. Even though there seems to be a visual correlation between the weight and horsepower, it is best to calculate the correlation to verify how reliable the correlation is.
mpg wt hp
mpg 1.000000 -0.869561 -0.774481
wt -0.869561 1.000000 0.652838
hp -0.774481 0.652838 1.000000
As can be seen from the correlation coefficients, the correlation between mpg and the weight at 87%. Since this is above 80%, there stands to be a strong correlation between the two. As with mpg and horsepower, the correlation coefficient stands at 77%. This is below the 80% mark which indicates that there is a correlation, but it is barely strong. Both values are in a negative regression. As with my assumption of higher horsepower needing a heavier engine, there is a correlation of 65%, but it is not a strong correlation. This helps me to think that a car with a heavy engine and high horsepower can still be fuel efficient due to the size of the car. Compared to the same type of engine in a truck, it must pull a heavier frame with heavier tires, thus tying back to the stronger correlation to the weight of the vehicle.
The multiple regression model is used to help me figure out an equation that the car company can use to determine how the weight of a car with the horsepower may affect miles per gallon. By using the calculations in the coef column, I was able to produce an equation:
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