这是一篇来自澳洲的**线性模型代写**

**Instructions: **

This is an individual assessment task. Your results and writing up must be your own work.

Your assignment must be word processed and converted to a single pdf file for online submission in iLearn using **Assignment 1 Submission **in the **Assessments **section.

The following file is available from the **Assignment 1 **folder in the **Assessments **section on the iLearn site:

SecondHandCars.csv

This assignment has 7 questions to answer. The end of your solutions should include the requested appen dices. These will be marked.

This assignment is worth 15%.

1**Second Hand Cars **

The file SecondHandCars.csv contains data collected for estimating the price of second hand cars. The following table contains a list of all variables in this file.

**Variable Description **

brand Manufacturer.

model Model of car.

year Year of first registration of car.

price Price in Pounds Sterling.

mileage Total distance (in miles) covered by the car.

tax Annual cost of vehicle tax.

mpg Miles per gallon, a measure of fuel efficiency.

engineSize Size of engine in litres.

- Read the data file SecondHandCars.csv into R calling it cars. Use a scatterplot matrix to have a look at the data on all numerical variables. Add a loess curve to each sub-plot to help to see possible relationships. On the basis of the scatterplots, which variables do you think will best predict the price of used cars?

Any R output produced to answer this question along with the R commands should be placed in

**Appendix 1 **which should be the first appendix at the end of all of your solutions.

- Obtain the regression of price on all the numerical predictor variables, including confidence intervals for the parameters. Is the overall regression significant, and what does this say about the situation?

Are predictors significant in the model? (Please save the model you fit in R as m1.)

Any R output produced to answer this question along with the R commands should be placed in

**Appendix 2 **which should be the second appendix at the end of all of your solutions.

- Is the variable mileage significant? What hypotheses are implied by this question, and what is the result of the analysis? Give a 95% confidence interval for the associated parameter and an interpretation of what it means. What about the variable mpg?

- We would like to investigate whether the regression on the two variables mpg and mileage is adequate,or whether the full set of variables is needed. What null and alternative hypotheses are we considering?

Using an F-test, set up an anova table to carry out the test. Report the p-value and your conclusion in statistical terms and in plain English. (Please save the reduced model you fit in R as mred and the full model you fit in R as mfull.)

Any R output produced to answer this question along with the R commands should be placed in

**Appendix 4 **which should be the third appendix at the end of all of your solutions. **There is no **

**Appendix 3**.

5.Compute two regressions:

a.price vs mpg

b.price vs mileage

What are your conclusions for models a and b regarding the significance of mpg and mileage and their

*R*2 ? (Please save the model fitted in R for part a. as ma and the model you fitted for part b. as mb.)

Any R output produced to answer this question along with the R commands should be placed in

**Appendix 5 **which should be the fourth appendix at the end of all of your solutions.

- Now compute a regression with mpg and mileage as predictors. What is your conclusion? Explain

what has happened. (Please save the model fitted in R as m2.)

Any R output produced to answer this question along with the R commands should be placed in

**Appendix 6 **which should be the fifth appendix at the end of all of your solutions.

What do the normal probability plot and the residual plot in first model, m2, say about the success of the regression?

Any R output produced to answer this question along with the R commands should be placed in **Appendix 7 **which should be the sixth appendix at the end of all of your solutions.

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