Statistical Modelling - Multiple Linear Regression - Statistics Assignment Help

Assignment Task:

Task. 
You need to ?nd the best (most parsimonious) multiple linear regression model for the response variable in a chosen dataset and write a short technical report on your ?ndings.

Instructions. 
The work should be done individually or in groups of 2 students. You need to join “Assignment Groups” on Canvas. You can work together in practical classes. If your group partner is from a di?erent class, you can arrange to come to the same class. You should complete the assignment by 30 March. You can collaborate using Canvas Chat, Messenger or Skype, share ?les using Dropbox or Github.

Evaluation. 
This assignment will contribute 10% to your overall module score. The R work is worth 5%, and the report is worth 5%. You will need to present your work in class. The presentations will take place during practical classes. You will need to explain to the lecturer (in front of your computer) your R code and your ?ndings. Your work will not be awarded any score without a presentation.

R work.
The analysis should be conducted using RStudio. You need to write an R script and upload it to Canvas. You can use all built-in statistical functions or compute the necessary values manually. Your R script should:
1. Be well-written, i.e. easy to read and understand to a person with a good knowledge of R, but not familiar with the problem you are solving.

2. The data should be read from a csv ?le using read.csv().

3. Visually inspect the data and make suitable transformations of variables if necessary. Inspect the data for outliers (use both a scatterplot matrix and a boxplot for visual inspection). You should only remove “obvious” outliers that are clearly out of the way and do not ?t the remaining data. (Once you have completed steps 5 through 11 you might need to revisit step 4 and make necessary adjustments to the data; then repeat steps 5 through 11 once again.)

4. Inspect the scatterplot matrix and choose a “full model” for the response variable. Conduct the overall F-test and individual t-tests on your full model. Find the residual standard error S, the coe?cient of determination R2 and the adjusted coe?cient of determination R2adj. 

5. By inspecting the results of the individual t-tests on the full model, choose a “reduced model” for your response variable. Conduct the overall F-test and individual t-tests on your reduced model. Find S, R2 and R2adj. Then compare the reduced model and the full model using the partial F-test and the values of S, R2 and R2adj.

6. If your reduced model is better (more parsimonious) than the full model, choose a “further reduced model” and repeat the analysis outlined in step 7.

7. If your full model is better than the reduced model, choose a di?erent “intermediate reduced model” and repeat analysis outlined in step 7.

8. Determine which of your models is the “best model”, i.e. has the smallest S, the biggest R2adj, and all (or most) of its regressor are signi?cant (P-values < 0.01). Then compare your best model against the best model according to the Akaike information criterion. (This test was explained in Sheet 6, Question 1.9.)

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