Reference no: EM133157571 , Length: 25 pages

MATH 4044 Statistics for Data Sciences - University Of South Australia

To achieve maximum marks for each question, you should aim to:
- Complete the requested statistical analysis in SAS using appropriate tasks or procedures.
- Include only the output most relevant to the question and interpret all key results. Do not include every piece of output produced by SAS!
- Discuss the results more broadly in the context of the given scenario.

Introduction
Use the data to study the factors that affect the beneficiary's insurance charges.

Data Description
Machine Learning with R by Brett Lantz is a book that provides an introduction to ma- chine learning using R. The dataset is used as an example for regression in the book. The data is downloaded from Some post-processing was carried out for the purpose of the case study.
The data file for this case study is called insurancev2.sas7bdat. The dataset con- tains insurance charges to the beneficiary, together with their demographic information. Variables in that file are as follows:

Assignment Tasks

Question 1
(a) Carry out a one-way analysis relating log_charges to agegroup. Use contrasts to test at least one a-priori hypothesis of your choice. Examine and comment on residuals. Also carry out appropriate post-hoc comparisons and discuss your results.
(b) Use SAS to perform a one-way ANCOVA relating log_charges to agegroup and bmi with bmi as a covariate, including appropriate post-hoc comparisons:
- Confirm that there is a linear relationship between the response variable and the covariate (a scatterplot and correlation coefficient plus a comment will suffice);
- Check the two additional ANCOVA assumptions (report and comments only on the parts of the output most directly relevant to condition check- ing):
∗ Independence of the covariate and the treatment effect (perform a one-way ANOVA test);
∗ Equality of slopes (add and check significance of the interaction term);
- Report and briefly discuss your results.
Technical note: Make sure you obtain and examine Type III Sum of Squares (ss3). Also obtain estimates of 'least squares means' (lsmeans) which are means by treatment adjusted for the covariate.

Question 2
(a) Carry out a one-way analysis of variance relating log_charges and weight_range. Examine and comment on residuals. Use contrast to test at least one a-priori hypothesis of your choice. Also carry out appropriate post-hoc comparison and discuss your results.
(b) Extend your analysis in part a to test whether there is evidence of interaction between weight_range and smoker. Examine and comment on residuals. Carry out appropriate post-hoc comparisons and discuss your results.

Question 3 Carry out an additional ANCOVA or factorial ANOVA of your choice to find other factors that may have significant impact on insurance charges.

Question 4 Write a summary of your findings from Questions 1-3. Keep the technical details of the analyses that led you to these conclusions to the absolute minimum. Rather, focus on practical significance and present your findings in non-specialist terms. One to two paragraphs (up to a page) will be sufficient.

Attachment:- Statistics for Data Sciences.rar