Below is a screenshot of the output of the linear regression as well as the summary stats:

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

• The Spoiler Angle and AWD variables were non-random.

2. Is the slope of the linear model considered to be zero? Why or why not?

• It is not for any of the variables tested in the mulitple regression model. Therefore, the slope cannot be considered zero for this model.

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

• It does because it returns an adjusted R-squared value of .6825.
  • This means there is a good probability there is a relationship between response variable (mpg) and the other predictor variables in the dataset.

In summary, the summary statistics from the dataset: Suspension_Coil.csv's 'PSI' column looks like this:

And the same dataset grouped by Manufacturing Lot:

• Based on these statistics, it looks like only Manufacturing Lot 3 does not the specs requirements for PSI. Its PSI variance stat is well over 100 at ≈ 170.
• The total variance for PSI looks good at ≈ 62 PSI, while the individual lots 1 and 2 are well below 100 at under 10 PSI respectively.

Here is a picture of the t-test output on the Suspension coil dataframe:

And here are two pictures showing the same test filtered for each Manufacturing Lot:

According to these outputs, we can safely conclude, based on the respective p-values of for each Manufacturing Lot, that only for the 3rd lot we can safely reject the null hypothesis. For the other ones we must certainly fail to reject the null hypothesis because their p-values are 100% and over 50% respectively.

The third lot's p-value is below 5%.

Using these variables:

• Vehicle weight
• fuel efficiency
• horsepower

We can conduct a mulitple linear regression test to find out if both vehicle weight and horsepower effect fuel efficiency across manufacturers.

We would conduct this test because:

• There are two independent variables that are both continuous tyopes.
• There is one continuous dependent metric.

The data we would need is located in both the MechaCar_dataframe and the Suspension Coil dataframe already:

1. the horsepower for each car across manufacturers
2. the fuel efficiency in miles/km per gallon/liter for every car
3. the horsepower in a floating point value.