Statistical analysis of automobile performance using R
##Overview AutosRUs' new MechaCar is "suffering from production troubles" and the company is hoping that an analytical review may help provide some insight. The goal of this project is to:
- Analyize and discuss any variables that could predict the MPG for new prototype design
- Show summary stats on the PSI of suspension coils
- Determine if manufacturing, and then a closer look at lots groups to report if they are statistically different from the mean population
- Design a study to compare the MechaCar performance with competitive manufacturers
Using the data set with nomimal data for the MechaCar prototypes, RStudio, Linear Regression model, and finally summary statistics the following analysis was performed.
In the summary output, each Pr(>|t|) value represents the probability that each coefficient contributes a random amount of variance to the linear model.
- Which variables/coefficients provided a non-random amount of variance to the mpg values in the dataset?
According to the results, vehicle length and ground clearance (as well as intercept) are statistically unlikely to provide random amounts of variance to the linear model. In other words the vehicle length and ground clearance have a significant impact on miles per gallon.
- Is the slope of the linear model considered to be zero? Why or why not?
H0 : The slope of the linear model is zero, or m = 0
Ha : The slope of the linear model is not zero, or m ≠ 0
From the linear regression model, the r-squared value is 0.70, which means that roughly 70% of the variablilty of the dependent variable (miles per gallon predictions) is explained using this linear model.
In addition, the p-value of the linear regression analysis is 5.35 x 10-11, which is much smaller than our assumed significance level of 0.05%. Therefore, we can state that there is sufficient evidence to reject our null hypothesis, which means that the slope of our linear model is not zero.
- Does this linear model predict mpg of MechaCar prototypes effectively? Why or why not?
When an intercept is statistically significant, it means that the intercept term explains a significant amount of variability in the dependent variable when all independent vairables are equal to zero. Depending on our dataset, a significant intercept could mean that the significant features (such as lenth and ground clearance) may need scaling or transforming to help improve the predictive power of the model. Alternatively, it may mean that there are other variables that can help explain the variability of our dependent variable that have not been included in our model, therefore this is not the most effective model to predict mpg for the MechaCar
- While the overall variance, as shown in the Total Summary data above, is under 100 PSI and meets specifications, there is a problem with one of the individual lots. Delving into the summary statistics further and grouping by Manufactured Lots; the variance for Lot 3 is well over the acceptable threshold, at 170.28.
H0 : There is no statistical difference between the observed sample mean and its presumed population mean. Ha : There is a statistical difference between the observed sample mean and its presumed population mean.
The t-test analysis for the entire data set analysis; Assuming our significance level was the common 0.05 percent, our p-value is above our significance level. Therefore, we do not have sufficient evidence to reject the null hypothesis, and we would state that the two means are statistically similar.
In looking further at all the Lots; the same conclusion can be drawn for Lot 1 & Lot 2; however the p-value returned for Lot 3 is 0.042 which is lower than the significance level, therefore there is sufficient evidence to reject the null hypothesis and state that the two means are statistically different.
Always a concern for parents is vehicle saftey. There are a number of ways beyond consumer preference and marketing perceptions to determine safety ratings. A couple of metrics could be vehicle breaking distance in weather conditions, transmission type, vehicle size (weight, tire length, axle length), and type of car (AWD, front, rear).
Null Hypothesis: The slope of the linear model is 0.
Alternate Hypothesis: The slope of the linear model is not 0.
Using linear regression and focusing on the significant coefficients. A correlation matrix once the rsquared and p-values are returned could be an easy way to show and report.