Question

In a test of the Weight Watchers weight loss program, weights of 42 subjects are recorded before and after the program such that the x-value is an individual's weight at the start of the program and the y-value is the same person's weight after one year on the program. The mean of the starting weights was 192.7 pounds. The mean of the weights after one year was 178.2 pounds. The regression equation was found to be yˆ=.802x+30.27ŷ=.802x+30.27. The critical r-values at 5% significance are: r=±0.304.r=±0.304.

1a. Assume that before/after weights result in a correlation coefficient of r=0.876.r=0.876. Is there correlation at the 5% significance level? (Yes or No)

1b. If someone had a starting weight of 200 pounds, what would be your best prediction for their ending weight? ________ pounds.

Explain your reasoning.

1c. Assume that before/after weights result in a correlation coefficient of r=0.087.r=0.087. Is there correlation at the 5% significance level? (Yes or No)

1d. If someone had a starting weight of 200 pounds, what would be your best prediction for their ending weight? _______ pounds.

Explain your reasoning.

Answer 1

When calculated r value lies within the critical values of r then there is no correlation and we take average value of y as the best predicted value.

a) As r = 0.876 which is outside of critical value -0.304 and 0.304 hence at 5% level of significance there is correlation in before/after weights. yes

b) x = 200 then y = 0.802*200 + 30.27 = 190.67 pounds.

c) As r = 0.087 which is within the critical values -0.304 and 0.304 hence at 5% level of significance there is no correlation. no

d) Since there is no correlation hence we use mean of y to predict values for given x. Hence, the best prediction of their ending weight is 178.2 pounds.

I hope this will help. Thank you.