A nutritionist, studying the relationship between mean calorie intake per day and weight loss per week, collected the following data from a sample of 8 weight watcher's club members.

CALORIE INTAKE/DAY (x) WEIGHT LOSS (gram)/week (y)

600 890

2000 270

1200 340

1700 260

800 620

1500 380

2300 120

1000 490

sum of x values = 11100

sum of y values= 3370

SSxx=2468750

SSyy=411887.5

SSxy= -919875

a) Find the values of a and b in the least square line y= a+bx for predicting the Weight Loss per week (y) as a function of Calorie Intake/day (x). (Answers within two decimal places).

b) Use the equation of regression line in part a to predct "Weight Loss/week" if the "Calorie Intake/day" is 900. Round to two decimal places.

c) Compute the linear correlation of coefficient between Weight loss/week (y) and Calorie Intake/day (x). Round to 2 decimal places.

d) Test at proportional to =0.1 level of significance whether the correlation coefficient, p, is negative. Find the Critical value of t, Test statistic value, and whether or not you reject H0. Round answers to three decimal places.

e) Find a 90% prediction interval for the predicted weight loss per week for a randomly selected club member whose daily intake is 900. Find lower and upper limit to four decimal places of accuracy. Assume Se = 109.1892