All data analysis in this section is using the output from our multiple linear regression model in Fig 1.
- Which variables/coefficients provided a non-random amount of variance to the mpg values in the dataset?
From our multiple linear regression model, we found that vehicle length and ground clearance provided a significant, or non-random, amount of variance toward mpg values in our MechaCar dataset.
- Is the slope of the linear model considered to be zero? Why or why not?
While the slope of the linear models testing against vehicle weight, spoiler angle, and all-wheel drive(AWD) are not exactly zero, they can be considered zero as they have no significant impact on MPG values. The slope of the linear models against vehicle length and ground clearance cannot be considered zero as they have a significant impact on MPG values, with vehicle length having a positive impact on MPG (slope = 6.27) and AWD having a negative impact on MPG values (slope = -3.41).
- Does this linear model predict mpg of MechaCar prototypes effectively? Why or why not?
To understand if the linear model predicts MPG of MechaCar prototypes, effectively we need to look at our r-squared value. Depending on field standards, the level of correlation being considered "high" can be subjective. The R-squared value for our multiple linear regression model was 0.71 (adjusted R-squared = 0.68), for our model we are considering an R-squared of >= 0.9 as a good predictor. Therefore, our linear model of predicting mpg of MechaCar prototypes not the most effective.
The design specifications for the MechaCar suspension coils dictate that the variance of the suspension coils must not exceed 100 pounds per square inch. Does the current manufacturing data meet this design specification for all manufacturing lots in total and each lot individually? Why or why not?
The current manufacturing data for MechaCar suspension coils meets the design specification that the suspension coils must not exceed 100 pounds/sq. inch as the variance of all lots is 62.29 pounds/sq. inch (Fig 2.).
When parsing the data by lot, we found that while suspension coil manufacturing lots 1 and 2 meet the variance requirement, lot 3 suspension coils failed to meet design specifications with a variance of 170.29 pounds/sq. inch (Fig 3.).
To determine if the PSI across all manufacturing lots and each lot individually is statistically significant from the population mean of 1500 pounds/sq. inch, we utilized the t-test. Running a t-test comparing the PSI across all manufacturing lots to the population mean, we found that the combined manufacturing lot PSI mean (1498.78) was not significantly different from the population with a p-value = 0.06 (Fig 4.).
Next, when we compared each manufacturing lot individually against the mean PSI of the population, we found that only manufacturing lot 3 had a mean PSI statistically significant compared to the population with a mean PSI of 1496.14 and a p-value of 0.04 (Fig 5c.).
As we determined using our linear regression model, both vehicle length and ground clearance had a siginificant impact on MechaCar MPG performance. While these gave insight into MechaCar performance, other metrics may be beter to test as our statistical model was not great having an R-squared of 0.71. Other factors such as engine size, tire type, fuel type may impact a car's performance more. To see how MechaCar performs against the competition, we could test engine size, tire type, fuel type, and MPG against 4 other major car competitors. Our null hypothesis would be that engine size, tire type, an fuel type have no impact on MPG car performance and there is no difference in MPG. Our alternative hypothesis would be that engine size, tire type, and fuel type have a signifcant impact on MPG. First we would use a Shaprio-Wilk test on MPG data to make sure our data is normally distributed. Then, perform a ANOVA testing the MPG of all samples between MechaCar and each competitor to determine if there is a difference in mean MPG. IF there is no signifcant difference, we can accept our null hypothesis. Otherwise, going forward we can run two-way ANOVAS to test car brand and each variable against MPG to see if there are signifcant differences in each metric between car brands on MPG performance.