The following table gives information on the amount of sugar (in grams) and the calorie count in one serving of a sample of 13 different varieties of cereal.

Sugar (gms) Calories

4 120

15 200

12 140

11 110

8 120

6 80

7 190

2 100

7 120

14 190

20 190

3 110

13 120

(a)Find thecorrelation coefficientandcoefficient of determination.What can youconcludefrom their values?

(b)Testat a 1% significance level whether the linear correlation coefficient between the two variables listed in the table is positive. Useboththe p-value and critical value (including reject and non-reject regions) approaches.