STAT1070 - The Two Variables of Interest Here Are MPG City and DriveTrain - Statistics Assignment Help

Assignment Task

Question 1
The data file sample cars.omv contains information from the United States of America for 18 randomly sampled motor vehicles. The data was collected to investigate whether there are differences in fuel economy for motor vehicles with differing drive types.
The two variables of interest here are MPG City and DriveTrain. The MPG variable is a measure of distance travelled per gallon of fuel used when driving in a city environment. The larger this number the more fuel efficient the vehicle is. The drive train variable indicates what wheels of the vehicle are mechanically driven from the engine. It is expected that front wheel drives have the best fuel economy, followed by rear wheel drives and then all wheel drives. This is due to the mechanical losses in the drive train. For the following, use a significance level of 5%.

(a) Plot the data and provide a preliminary assessment of whether there appears to be differences between fuel efficiency based on drive type.
(b) Carry out an appropriate hypothesis test to for differences in fuel efficiency for the different drive types. Make sure to report the hypotheses tested, test statistic, null distribution, p-value and conclusion in plain language.
(c) If appropriate, carry out post-hoc tests and report the results of each comparison making sure you justify your conclusions. If post-hoc testing is not appropriate, explain the purpose of post-hoc tests and why they are not appropriate in this example.
(d) Assess the assumptions of the test you performed in part (b).

Question 2
In the previous question, researchers randomly collected data on motor vehicles from the United States of America. Another insight they are hoping to receive from the data is if there is a relationship between weight and the fuel economy of a vehicle.
The variables they are now interested in is are Weight which is measured in pounds (lb) and MPG Highway. The MPG variable is a measure of distance travelled per gallon of fuel used when driving on a highway. The data appear in the file sample cars.omv.

(a) A scatterplot is a useful graphical tool for investigating possible relationships between two numerical variables. Produce a scatterplot using the data provided ensuring that you place the appropriate variables on the x-axis and y-axis. Describe the relationship between the two variables.
(b) Provide the equation for the linear regression model of highway MPG and weight. Interpret the numbers (b0 and b1) in the regression equation.
(c) Use the regression equation to predict the highway MPG of a vehicle with a weight of 3,000lb.
(d) How much of the variation in highway MPG is accounted for in the linear regression with weight as a predictor?
(e) Test at the 5% significance level if there is a relationship between critical highway MPG and weight. Be sure to include the following in your answer:
- the null and alternative hypotheses
- the test statistic
- the null distribution
- the p-value
- your conclusion

(f) Provide a 95% confidence interval for the population slope parameter and interpret this interval.
(g) List the assumptions of your analysis. To what degree are these assumptions satisfied? Include output from jamovi where appropriate.

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