In a recent commercial, a weight

-loss company featured testimonials touting their "miracle shake" nutritional

supplement

.

Satisfied Customer

Time (days)

Weight Loss (kg)

Sarah, from Toronto

30

11

Zack, from New York

45

16

Eli, from Detroit

90

36

Yvette, from Montral

10

4.5

Lynn, from San Diego

30

8.5

Kulwinder, from Vancouver

60

20

The commercial claims that the miracle shake will provide guaranteed weight loss when you follow its dietary

program. A message in small print adds "Individual results may vary."

a) Use the company's data to calculate

the correlation between time on the miracle

-shake diet and weight loss. Classify the correlation.

b)

Based on a linear model, how much weight loss would you expect after 120 days? Is this prediction

likely to be accurate?

c) Does the observed correlation imply that the miracle shakes cause weight loss? Identify any possible

extraneous variables.

d) Are there any problems with the sampling technique? Explain.