Scatter Plot Matrix of all the Variables - Multiple Regression Analysis - Statistics Assessment Answer

Statistics Assessment Task

Questions 1.

Produce a scatterplot matrix of all the variables in the shellfish data. I recommend using the psych::pairs.panels() function or some other that also provides univariate histograms.

2. Referring to the scatterplot matrix, comment on the relationships between

(a) the response the variable MMass and the predictor variables, and

(b) among the predictor variables. Discuss the implications of your observations for the likely success of a multiple regression analysis.

3. Using histograms and scatterplots as a guide, find some transformations of the response and/or predictor variables that result in linear relationships between MMass and the predictors. List your chosen transformations, and produce a scatterplot matrix of the updated dataset.

4. Using the post-transformation dataset, fit the full multiple-regression model of MMass using all four predictor variables. Call the model m1. Use R to calculate the Variance Inflation Factors for this model and interpret the values.

Now use a stepwise regression procedure to choose an optimal set of variables to include in the model. Call the new model m2. Show your R code and output of the stepwise procedure and briefly describe the rationale for the steps that occurred.

6. Write down the final predictive equation for the model m2. Take care to include any transformations in the equation.

7. Calculate the Variance Inflation Factors for m2 and compare them with those from m1. Have they changed? If so, why?

8. Produce the standard set of diagnostic plots for model m2 and comment on what you see. In particular, does the model appear to violate any of the assumptions of linear regression?

9. Apply the summary() function to m2. Referring to the output, summarise the main conclusions that can be made from this model. [4 marks] 10. In R, use m2 to predict the muscle mass for a shellfish with the following measurements.

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