Investigating the relationship between weight loss and triglyceride level

Investigating the relationship between weight loss and triglyceride level reduction

 
CASE PROBLEM IV
Investigating the relationship between weight loss and triglyceride level reduction
EC 580, Instructor: Asiye Aydilek
Epidemiological studies have shown that there is a relationship between raised blood levels of triglyceride and coronary heart disease but it is not certain how important a risk factor triglycerides are. It is believed that exercise and lower consumption of fatty acids can help to reduce triglyceride levels. (Triglycerides are lipids (fats) which are formed from glycerol and fatty acids. They can be absorbed into the body from food intake, particularly from fatty food, or produced in the body itself when the uptake of energy (food) exceeds the expenditure (exercise). Triglycerides provide the principal energy store for the body. Compared to carbohydrates or proteins, triglycerides produce a substantially higher number of calories per gram.)

In 1998 Knoll Pharmaceuticals received authorisation to market sibutramine for the treatment of obesity in the USA. One of their suite of studies involved 35 obese patients who followed a treatment regime comprising a combination of diet, exercise and drug treatment.

Each patient?s weight and triglyceride level were recorded at the start (known as baseline) and at week 8. The information recorded for each patient was:

Patient ID
Weight at baseline (kg)
Weight at week 8 (kg)
Triglyceride level at baseline (mg/dl)
Triglyceride level at week 8 (mg/dl)
1. Compute the Pearson correlation coefficient of weight loss and triglyceride level reduction and indicate whether and how the two variables are correlated.
Hint:
construct a column of weight loss, weight loss = weight at baseline- weight at week 8
construct a column triglyceride level reduction, triglyceride level reduction = Triglyceride level at baseline- Triglyceride level at week 8
Pearson correlation of weight loss and triglyceride level reduction = 0.464 . Thus, they are weakly and linearly correlated.

2. Provide the simple regression analysis of the data using Excel.
You need to provide Regression Statistics, ANOVA Table and coefficients.

Hint:
Click ?Data Analysis? first and then choose ?Regression.?
For the input Y range, choose the column of triglyceride level reduction.
For the input X range, choose the column of weight loss.
Click all the boxes in residuals.
3. Write the estimated regression equation.

4. Is the model significant at 5% significance level? In other words, does the weight loss significantly influence triglyceride level reduction?

Hint: Use the p-value in the ANOVA table. Remember if pvalue is less than a then we reject the null hypothesis of the coefficient being zero. It means the model is significant in that case.
5. How much of the variation in triglyceride level reduction is explained by the fitted model?
6. Provide the Residual plot.
7-Looking at the residual plot, can we say that our assumption that variance of E is same for all X values? (Hint: If there is a pattern such as increasing with X in the residual plot, then the assumption is violated)
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