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.

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
• No

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

Explain your reasoning.

Assume that before/after weights result in a correlation coefficient of r=0.087. Is there correlation at the 5% significance level?

• Yes
• No

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

a) We are given the correlation coefficient value here as 0.876. As it is more than 0.304 which is the critical value at 5% level of significance, therefore the test is significant here and we have sufficient evidence here that there is a linear correlation coefficient between the two variables at 5% level of significance.

As the correlation coefficient is significant here, therefore the predicted value for 200 pounds of weight is computed here as:

y = 0.802x + 30.27 = 190.67
Therefore 190.67 is the predicted value here.

b) As the correlation coefficient here is 0.087 < 0.304 which is the critical value here, therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence here that the linear correlation coefficient is significant at 5% level of significance here.

As the linear correlation is not significant here, the regression equation is not valid here and therefore the best predicted value here would be given as the mean weight after one year that is the mean of the dependent variable which is given as: 178.2
Therefore 178.2 is the predicted value here.