Maintaining a healthy weight can help improving the overall lifestyle and reducing the risk of hearth diseases, high blood pressure, stroke, and diabetes, and hence help main- taining good health overall.
Through this case study, we aims at studying association between weights and eating habits as well as physical conditions. We will study a dataset relating to 2111 individuals ages 14 to 61 from Mexico, Peru and Columbia. The data includes atributes such as gender, weight, height, attributes related to eating habits, and atributes related to physical condition. We will use this data to answer the following question
Whether there is an association between frequency of exercise and weight? Does weight has a signficant relationship with weight, and how the relationship between exercise and weight is when controlled for height.
What is the relationship between weight and gender+ the use of technological devices.
The data is downloaded from UCLA machine learning database https://archive-beta. ics.uci.edu/dataset/544/estimation+of+obesity+levels+based+on+eating+habits+ and+physical+condition. The data is available on our SAS server as mydata.Obesity.
Q1 (55 marks)
(a) (20 marks) Carry out a one-way analysis of variance (ANOVA) relating weight to frequency of exercise FAF. 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) (10 marks) If the assumptions for ANOVA is not satisfied, use a non- parametric method to validate the results in question ((a)).
(c) (25 marks) Use SAS to perform a one-way ANCOVA relating weight to FAF and height with height 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 considerations (report and comments only on the parts of the output most directly relevant to condition check- ing):
– Independence of the covariate and the treatment e↵ect (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.
Q2 (30 marks)
Perform and analyse a factorial ANOVA model to determine whether there is sta- tistically significant di↵erence in weight by Gender and the use of technological devices TUE. Carry out to test whether there is evidence of interaction between Gender and TUE. Examine and comment on residuals. Carry out appropriate follow-up analysis and discuss your results. Test the following a-priori hypotheses:
mean weight for male with TUE=1 is the same as mean weight for female with TUE=1.
State and test two other a-priori hypotheses of your choice.
Q3 (15 marks)
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.
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