Course : Analysis of experience plans MAT3378 Question: A study wanted to show that taking calcium moderate amount has an impact on the reduction of cholesterol levels. We have therefore selected a sample of 10 random people on whom we measured these two variables.

Calcium (mg)	81.4	32.3	27.3	51.9	37.9	54.7	40.1	39.6	18.9	68.1
Cholesterol (Mmol/l)	5.99	6.44	6.32	6.77	5.55	5.78	6.89	6.25	6.45	6.24

(A) Which of these two variables must be an independent variable?

(B) Determine the equation of linear regression between these two variables.

(C) Interpret the estimators a and b of your equation.

(D) Determine the linear correlation and determination coefficients and interpret them in the context of this exercise.

(E) Determine the residues associated with this model.

(F) Deduce a point estimator of the standard deviation of the error associated with this model.

(G) Put on the same graph the point cloud, the regression line, the coefficient of linear correlation and determination as well as the 95% level confidence interval for the expectation of Y knowing X=x.

(H) Make a general conclusion to confirm or refute the objective initial of the study.