I need the completew working solutions and accurate answers to this question. Th

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I need the completew working solutions and accurate answers to this question. Thank you.

(1.5 pts. + 1 pt. BONUS) 3. Some physicians use the cholesterol ratio (CR = total cholesterol/HDL cholesterol) as a measure of a patient's risk of heart disease. In addition, the triglyceride concentration (TG) is associated with coronary artery disease in many patients. In a study of the relationship between these two variables, a random sample of adults was obtained, and the triglyceride level denoted as X1 in mg/dl and cholesterol ratio (y) was obtained for each person. The scatterplot and regression line of In(triglyceride level - 129) denoted as x2 vs. cholesterol ratio is beloww. y -0.8059 + 1.5603x, The ANOVA summary table is Source of Variation Sum of Squares Degrees of freedom Mean Square Regression Error Total 103.16 103.16 3.20 106.36 1 23 24 0.14 (0.5 pt.) a) What is the coefficient of determination? (1 pt.) b) Do you think that an increase in the triglyceride level causes an increase in the cholesterol level? Please explain your answer. (1 pt.) BONUS: c) Why do you think that they had to take the logarithm of the triglyceride level? Additional Problems: Note, the book gives the sums so that you can use the computing method to calculate the estimated value of the parameters, not Sxy and Sxx. 12.19, 12.21, 12.23

Explanation / Answer

Result:

a).

coefficient of determination = 103.16/106.36 =0.969914

96.99% of variation in y is explained by x2.

b).

calculated F =103.16/0.14 =736.8571

calculated F= 736.8571 > critical F=4.28, Regression is significant.

since the regression coefficient is positive, there is positive correlation between y and x2.

Therefore increase in the triglyceride level causes an increase in the cholesterol level.

c).

The log transformation can be used to make highly skewed distributions less skewed.

Since the distribution of triglyceride level is skewed, log transformation is taken.

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