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Owner: ssansass
Created: Feb 24, 2013
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Views: 1543
Tags: SCP, #2, |, Markas, Sergalis

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SCP #2 | Markas Sergalis | Car weight vs. mileage

Are you affected by the gas price fluctuations? Of course you are! The more you pay for gas, the less you have, the less you can spend on other product. Yet, to counter this, people buy more economic cars that spend less fuel in them. One of the factors that influence gas consumption of a vehicle is a car's weight. This is the primary reason why in this report I analyzed the car's weight versus mileage in order to see trends and variables.

Based on the Scatter Plot (Result 1), it can be seen that weight of a car and its mileage is negatively associated. So, as the weight of a car rises, the mileage decreases instead. And it does make sense; the heavier the object you want to move, the more energy it will require to do so. Furthermore, the critical value for correlation coefficient (n=11) is .601, while the correlation between Weight and Miles Per Gallon is: -0.9640858, or its absolute value: 0.9640858. This proves that the data is linear related, as critical value correlation coefficient is less then then correlation between the two data sets analyzed.

The linear equation that best describes the data is the least squares regression line: ABX = -0.007036322x + 44.87933, whereas the x is the weight. To explain this, if the weight of a vehicle increases by 1 lbs. then the mileage per gallon is going to drop by around 0.007 on average. It is really not realistic for the weight of a vehicle to be o lbs. yet, what does the slope of around 44.9 tell us is that if a vehicle would weigh around 0 lbs. its mileage would be considered to be around 44.9 miles per gallon. Yet, this is out of scope of this model.

The coefficient of determination of this data is around 0.9294615, which means that around 93% of variability of mileage per gallon is explained by the least squares regression line. Is the data is worth to trust? Probably, yet, it is subjecive. One might need 95% explanation of variability, for others 93% is very close and trustworthy. Bottom line, I think this data is valid to make predictions in the future vehicles.

Based on the residual plot, showing no discernable pattern, a linear model is appropriate. Is seems that the residuals display constant error variance, and no outliers seems to appear in the boxplot of the residuals. There are no outliers seen, so there are no major harsh influences on the data. Yet, as there might be car models that are heavier, yet, more economic, the data turns out to be familiar with other makes.

As a result, this data can be a good reference in a subject study of the economy of the vehicles compared to their weight. Even though, we are affected by gas price fluctuations, this data seems to be resistant to it, as there are no observable outliers. Pick a car, which weigh less!

Result 1: SC#2 | Markas Sergalis | Scatter Plot   [Info]

Result 2: SC#2 | Markas Sergalis | Correlation   [Info]
 Correlation between Weight and Miles Per Gallon is: -0.9640858

Result 3: SC #2 | Simple Linear Regression   [Info]
Simple linear regression results:
Dependent Variable: Miles Per Gallon
Independent Variable: Weight
Miles Per Gallon = 44.87933 - 0.007036322 Weight
Sample size: 11
R (correlation coefficient) = -0.9641
R-sq = 0.9294615
Estimate of error standard deviation: 1.0331218

Parameter estimates:
 Parameter Estimate Std. Err. Alternative DF T-Stat P-Value Intercept 44.87933 2.1487117 ≠ 0 9 20.886623 <0.0001 Slope -0.007036322 6.461331E-4 ≠ 0 9 -10.889895 <0.0001

Analysis of variance table for regression model:
 Source DF SS MS F-stat P-value Model 1 126.57575 126.57575 118.58982 <0.0001 Error 9 9.606067 1.0673407 Total 10 136.18182

Result 4: SC #2 | Markas Sergalis | Simple Linear Regression   [Info]

Result 5: SC #2 | Markas Sergalis | Boxplot   [Info]

Data set 1. SC #2 | Weight of a Car versus Miles per Gallon   [Info]