Introduction

There are total of three questions worth 8 + 18 + 14 = 40 marks in this assignment.
This assignment is worth a total of 20% of your final mark, subject to hurdles and any other matters (e.g., late penalties, special consideration, etc.) as specified in the FIT2086 Unit Guide or elsewhere in the FIT2086 Moodle site (including Faculty of I.T. and Monash University policies).

Submission: No files are to be submitted via e-mail. Correct files are to be submitted to Moodle, as given above. You must submit the following three files:

1. One PDF file containing non-code answers to all the questions that require written answers. This file should also include all your plots.

2. The two required R script files containing R code answers as discussed in Question 2 and 3.
Please read these submission instructions carefully and take care to submit the correct files in the correct places.

Question 1 (8 marks)

This question will require you to analyse a regression dataset. In particular, you will be looking
at trying to predict the compressive strength of concrete from various measurements of the various components used in the concrete mixture. Obviously this is an extremely important problem as concrete is the single most important material in civil engineering and construction. The file concrete.ass3.2021.csv contains the data you will be analysing. There are n = 250 observations on p = 8 predictors, seven of which measure the amount of various component substances within the concrete mixture. The target is the compressive strength of the resulting concrete mixture in megapascals (MPa). The higher the compressive strength, the better the concrete mixture is. The data dictionary for this dataset is given in Table 1. Provide working/R code/justifications for each of these mquestions as required.

1. Fit a multiple linear model to the concrete data using R. Using the results of fitting the linear
model, which predictors do you think are possibly associated with compressive strength, and
why? Which three variables appear to be the strongest predictors of compressive strength, and
why? [2 marks]

2. How would your assessment of which predictors are associated change if you used the Bonferroni procedure with α = 0.05? [1 marks]

3. Describe what eﬀect cement (Cement) in the concrete mix appears to have on the mean compressive strength. Describe the effect that the Age variable has on the mean compressive strength of the concrete. [2 marks]

4. Use the stepwise selection procedure with the BIC penalty to prune out potentially unimportant variables. Write down the final regression equation obtained after pruning. [1 mark]

5. Imagine that a civil engineer proposes to use a new mix of concrete for a project with the mixture given in Table 2. The engineer asks you to predict the mean compressive strength of this new concrete mix after it has set for 28 days.

(a) Use the model found in Q1.4 to predict the mean compressive strength for this mix. Provide
a 95% confidence interval for this prediction. (you may use R to answer this question) [1
mark]

(b) The mix of concrete that the engineer is currently using has a mean compressive strength
of 52.35mPa after setting for 28 days. Does your model suggest that the newly proposed
mix is better than the current mix? [1 mark]

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