An experiment was conducted to investigate the relationship between the dose of a pain medication and the number of hours of pain relief. Twenty individuals with chronic pain were randomly assigned to one of five doses-0.0, 0.5, 1.0, 1.5, 2.0-in milligrams (mg) of medication. The results are shown in the scatterplot below. 14- 12 10- Pain Relief (hours) 0.0 0.5 1.0 1.5 2.0 Dose (mg) The data were used to fit a least-squares regression line to predict the number of hours of pain relief for a given dose. Which of the following would be revealed by a plot of the residuals of the regression versus the dose? (A) The sum of the residuals is less than 0. (B) The sum of the residuals is greater than 0. (C) There are outliers associated with the lower doses. (D) The variation in the hours of pain relief is not the same across the doses. (E) There is a positive linear relationship between the residuals and the dose.

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Author:Amos Gilat
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Chapter1: Starting With Matlab
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why the correct answer is letter D and why the letters C and E are wrong?

An experiment was conducted to investigate the relationship between the dose of a pain medication and the
number of hours of pain relief. Twenty individuals with chronic pain were randomly assigned to one of
five doses 0.0, 0.5, 1.0, 1.5, 2.0-in milligrams (mg) of medication. The results are shown in the
scatterplot below.
Pain Relief (hours)
14-
12-
10-
8.
+
2
0.0
0.5
1.0
Dose (mg)
1.5
2.0
The data were used to fit a least-squares regression line to predict the number of hours of pain relief for a given
dose. Which of the following would be revealed by a plot of the residuals of the regression versus the dose?
(A) The sum of the residuals is less than 0.
(B) The sum of the residuals is greater than 0.
(C) There are outliers associated with the lower doses.
(D) The variation in the hours of pain relief is not the same across the doses.
(E) There is a positive linear relationship between the residuals and the dose.
Transcribed Image Text:An experiment was conducted to investigate the relationship between the dose of a pain medication and the number of hours of pain relief. Twenty individuals with chronic pain were randomly assigned to one of five doses 0.0, 0.5, 1.0, 1.5, 2.0-in milligrams (mg) of medication. The results are shown in the scatterplot below. Pain Relief (hours) 14- 12- 10- 8. + 2 0.0 0.5 1.0 Dose (mg) 1.5 2.0 The data were used to fit a least-squares regression line to predict the number of hours of pain relief for a given dose. Which of the following would be revealed by a plot of the residuals of the regression versus the dose? (A) The sum of the residuals is less than 0. (B) The sum of the residuals is greater than 0. (C) There are outliers associated with the lower doses. (D) The variation in the hours of pain relief is not the same across the doses. (E) There is a positive linear relationship between the residuals and the dose.
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