Question: Is it possible to predict an American female‘s actual weight from what she considers to be her ideal weight? The scatterplot below displays the results of a study that asked females to write down what they considered to be their "ideal weight". After writing them down, the females were weighed and the data was plotted. As it turns out, 69.45% of the variability in actual weight could be explained by the linear relationship with ideal weight.

1. Which of the following do you think best represents the correlation between the variables ideal weight and actual weight?

1. 0.3945
2. -0.6945
3. -0.8334
4. 0.8334
5. approximately 1.

B. A linear regression was performed, and the least squares line was calculated to be \(\mathrm{y}=-11.198+1.1789 \mathrm{x}\). Which of the following best interprets the slope of the regression line?

1. A 1 pound increase in actual weight tends to result in a 1.1789 pound increase in ideal weight.
2. A 1 pound increase in ideal weight tends to result in an 11.198 pound increase in actual weight.
3. A 1 pound decrease in ideal weight tends to result in an 11.198 pound decrease in actual weight.
4. A 1 pound increase in ideal weight tends to result in a 1.1789 pound increase in actual weight.
5. An ideal weight of zero pounds (which is clearly impossible) would correspond to an actual weight of -11.198 pounds (also clearly impossible).

C. Suppose we randomly select a female that was not a part of this study and try to predict her actual weight from her ideal weight. Given that this female's ideal weight was 135 , which of the following can you conclude?

1. We would predict her actual weight to be approximately 148 pounds
2. We would predict her actual weight to be approximately 159 pounds
3. We should not be predicting anything for this female because she was not a part of the original group of women in the study.
4. We should not be predicting anything for this female's weight because of extrapolation.
5. Choices \(\mathrm{C}\) and \(\mathrm{D}\) are both valid responses.

D. On the scatterplot above, circle the female that would have the largest positive residual value and also circle the female that would have the largest negative residual value.

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