Question

the graph shows the relationship between nonexercise activity change (nea) and fat gain (kg). the red line represents the regression model, and the blue point represents a subject with nea=-47. assume the blue point( actual data data point) is lower than its fat gain prediction on the red line. based on the graph, which of the following statements are correct? (select all that apply.) a. the regression line predicts a fat gain of approximately 3.7 kg for this subject. b. the subjects observed fat gain is smaller than the predicted value. c. the residual for this subject is negative. d. the model overestimated the subjects fat gain. e. the point representing the subject lies above the regression line.

Explanation:

Step1: Analyze option a

From the graph, when NEA = - 47, the value on the regression - line for fat gain is approximately 3.7 kg. So option a is correct.

Step2: Analyze option b

It is given that the blue point (actual data point) is lower than its fat - gain prediction on the red line. So the observed fat gain is smaller than the predicted value, and option b is correct.

Step3: Analyze option c

Residual = Observed value - Predicted value. Since the observed value is lower than the predicted value, the residual is negative. Option c is correct.

Step4: Analyze option d

Since the observed fat gain is smaller than the predicted value, the model overestimated the subject's fat gain. Option d is correct.

Step5: Analyze option e

The point representing the subject lies below the regression line as the actual fat gain is lower than the predicted fat gain. So option e is incorrect.

Answer:

A. The regression line predicts a fat gain of approximately 3.7 kg for this subject.
B. The subject's observed fat gain is smaller than the predicted value.
C. The residual for this subject is negative.
D. The model overestimated the subject's fat gain.