A few weeks after starting his new role, Jeremy is approached by upper management about a special project. AutosRUs’ newest prototype, the MechaCar, is suffering from production troubles that are blocking the manufacturing team’s progress. AutosRUs’ upper management has called on Jeremy and the data analytics team to review the production data for insights that may help the manufacturing team.

Help Jeremy and the data analytics team do the following:

• Perform multiple linear regression analysis to identify which variables in the dataset predict the mpg of MechaCar prototypes
• Collect summary statistics on the pounds per square inch (PSI) of the suspension coils from the manufacturing lots
• Run t-tests to determine if the manufacturing lots are statistically different from the mean population
• Design a statistical study to compare vehicle performance of the MechaCar vehicles against vehicles from other manufacturers. For each statistical analysis, you’ll write a summary interpretation of the findings.

• Deliverable 1: Linear Regression to Predict MPG
• Deliverable 2: Summary Statistics on Suspension Coils
• Deliverable 3: T-Test on Suspension Coils
• Deliverable 4: Design a Study Comparing the MechaCar to the Competition

Identify the source of production manufacturing problem for AutosRUs’ newest prototype, the MechaCar.

• MechaCar_mpg.csv
• Suspension_Coil.csv

Resource: R, dplyr

Stated in 2. Identify the Datasource

NA

Only through subset tests are we able to identify Lot 3 as the source of problem for the manufacturing team.

NA

The "Proper" Conclusion is indicated below on Summary

1. Which variables/coefficients provided a non-random amount of variance to the mpg values in the dataset?

• H0 : The different variables in the dataset does not predict the mpg of MechaCar prototypes
• Ha : The different variables in the dataset predicts the mpg of MechaCar prototypes

The variables/coefficients below (each Pr(>|t|) value) provided a non-random amount of variance to the mpg values in the dataset.

LM

• vehicle_length : 2.60e-12 (2.60 x 10-12 = 0.00000000000260)
• vehicle_weight : 0.0776
• ground clearance : 5.21e-08b (5.21 x 10-8 = 0.0000000521)

According to results, these variables are statistically unlikely to provide random amounts of variance to the linear model. That means, vehicle_length, vehicle_weight and ground clearance vehicle have a significant impact on mpg.

2. 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

P-val

• p-value : 5.35e-11 (5.35 x 10-11 = 0.0000000000535)
• Assumed significance level is: 0.05%

The p-value is smaller than assumed significance level. 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.

3. Does this linear model predict mpg of MechaCar prototypes effectively? Why or why not?

From our linear regression model, the r-squared value is 0.71, which means that roughly 71% of the variability of our dependent variable (mpg predictions) is explained using this linear model, which suggests there is a strong positive correlation between MPG and the variables of vehicle length, vehicle weight, spoiler angle, ground clearance, and AWD.

1. 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?

Summarize

The total variance of the suspension coils is 62.29 for all manufacturing lots in total. This is within MechaCar design specifications.

Group_by

Variance of the suspension coils must not exceed 100 pounds per square inch. Lots 1 and 2 are within the design specifications. Lot 3 variance for suspension coils is 170.28, which exceeds 100 pounds per square inch. Therefore Lot 3 did not meet design specifications.

1. Determine if all manufacturing lots and each lot individually are statistically different from the population mean of 1,500 pounds per square inch.

• 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.

All Lots Graph

Normal distribution, or normality, is commonly referred to as "the bell curve," and describes a dataset where values farther from its mean occur less frequently than values closer to its mean. The distribution of the suspension coil is visualised with a density plot which assumes an approximate normal distribution with the bell curve.

5 assumptions:

1. The input data is numerical and continuous. This is because we are testing the distribution of two datasets.
2. The sample data was selected randomly from its population data.
3. The input data is considered to be normally distributed.
4. The sample size is reasonably large. Generally speaking, this means that the sample data distribution should be similar to its population data distribution.
5. The variance of the input data should be very similar.

If the p-value is greater than 0.05, the data is considered normally distributed. All models below are using One Sample t-test.

All Lots

• p-value : 0.06028
• mean: 1498.78 (against 1500)

The p-value is above our significance level. Therefore, we do not have sufficient evidence to reject the null hypothesis, and the two means are statistically similar.

Lot 1

• p-value : 1
• mean: 1500 (against 1500)

The p-value is above our significance level. Therefore, we do not have sufficient evidence to reject the null hypothesis, and the two means are statistically similar.

Lot 2

• p-value : 0.6072
• mean: 1500.2 (against 1500)

The p-value is above our significance level. Therefore, we do not have sufficient evidence to reject the null hypothesis, and the two means are statistically similar.

Lot 3

• p-value : 0.04168
• mean: 1496.14 (against 1500)

The p-value is below our significance level. Therefore, we have sufficient evidence to reject the null hypothesis, and the two means are statistically different.

Write a short description of a statistical study that can quantify how the MechaCar performs against the competition. In your study design, think critically about what metrics would be of interest to a consumer: for a few examples, cost, city or highway fuel efficiency, horse power, maintenance cost, or safety rating.

1. What metric or metrics are you going to test?

• Selling Price: Costs of buying the car
• Cost of Ownership (Maintenance Cost & Fuel Efficiency): Long term costs to owning the car for its estimated lifetime
• Safety Rating:
  • crashworthiness — how well a vehicle protects its occupants in a crash
  • crash avoidance and mitigation — technology that can prevent a crash or lessen its severity

2. What is the null hypothesis or alternative hypothesis?

• H0 : There is no difference in terms of selling price, costs of ownership and safety ratings between AutosRUs’ MechaCar and its competition in the same market segmentation.
• Ha : There is a difference in terms of either one or all for selling price, costs of ownership and safety ratings between AutosRUs’ MechaCar and its competition in the same market segmentation.

3. What statistical test would you use to test the hypothesis? And why?

Multiple linear regression since there are a few variables and this will give insights for all metrics above.

4. What data is needed to run the statistical test? Historical data of competitors for:

• sold price
• maintenance costs, frequency of maintenance vs car age, costs of spare parts, fuel consumption / km
• iihs (Insurance Institute for Highway Safety) ratings and evalutions data. (https://www.iihs.org/ratings/about-our-tests)

Hypothesis Testing in Five Steps

Regardless of the complexity of the dataset or the proposed question, hypothesis testing uses the same five steps:

1. Generate a null hypothesis, its corresponding alternate hypothesis, and the significance level.
2. Identify a statistical analysis to assess the truth of the null hypothesis.
3. Compute the p-value using statistical analysis.
4. Compare p-value to the significance level.
5. Reject (or fail to reject) the null hypothesis and generate the conclusion.
6. Keep in mind that the null and alternate hypotheses are used to explain one of two outcomes from our proposed question, and both are mutually exclusive and exhaustive.

In other words, no matter what, one of these statements must be used to explain our analysis results.