Question

A new drug is tested for serum cholesterol-lowering properties on six randomly selected volunteers. The serum cholesterol values are given in the following table.

         

(a) At 95% confidence level, test whether X and Y are independent.

(b) FInd the p-value.

(c) Calculate the least-squares regression line for these data.

(d) Interpret the usefulness of the model.

(e) State any assumptions you have made in solving the problem.

Answer 1

Solution

The given data:

             

(a) At 95% condence interval, test whether X and Y are independent.

Since the test statistic value is included in rejection region, Hence we reject null hypothesis.

Therefore, X and Y are linearly related.

(b) Find p-value.

Therefore, p-value = 0:0373

(c) Calculate the least-squares regression line for these data.

For the given data we have:

(d) Interpret the usefulness of the model.

The least-squares regression line was selected as one that seems to fit the data reasonably well, and it minimizes the sum of squared errors.

(e) State any assumptions you have made in solving the problem.

We assumed that the pair (X; Y ) has bivariate normal probability distribution.