A paper gives data on x- change in Body Mass Index (BMI, in kilograms/meter*) and y- change in a measure of depression for patients suffering from depression who participated in a pulmonary rehabilitation program. The table below contains a subset of the data given in the paper and ar approximate values read from a scatterplot in the paper. BMI Change (kg/m²) -0.5 0 0.1 0.7 0.8 1 1.5 1.2 1 0.4 0.4 0.5 Depression Score Change -1 4 4 58 8 13 14 17 18 12 14 The accompanying computer output is from Minitab. Fitted Line Plot Depression score change 6.512 + 5.472 BMI change 20 5.26270 27.16% R-Sq (adj) 19.88% R-Sa 15- 8 10- 5- 0- -0.5 0.0 0.5 1.0 1.5 BMI change R-ag 27.16 5.26270 Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 6.512 2.26 2.88 0.0164 EMI change 5.472 2.83 1.93 0.0823 1.00 Regression Equation Depression score change - 6.512 - 5.472 BMI change (a) What percentage of observed variation in depression score change can be explained by the simple linear regression model? (Round your answer to two decimal places.) (b) Give a point estimate of a. (Round your answer to five decimal places.) Interpret this estimate. s is the typical amount by which the -Select-- v value -Select v what is predicted using the least squares regression line. (c) Give an estimate of the average change in depression score change associated with a 1 kg/m? increase in BMI change. (Round your answer to three decimal places.) (d) Calculate a point estimate of the mean depression score change for a patient whose BMI change was 1.2 kg/m. (Round your answer to three decimal places.)
A paper gives data on x- change in Body Mass Index (BMI, in kilograms/meter*) and y- change in a measure of depression for patients suffering from depression who participated in a pulmonary rehabilitation program. The table below contains a subset of the data given in the paper and ar approximate values read from a scatterplot in the paper. BMI Change (kg/m²) -0.5 0 0.1 0.7 0.8 1 1.5 1.2 1 0.4 0.4 0.5 Depression Score Change -1 4 4 58 8 13 14 17 18 12 14 The accompanying computer output is from Minitab. Fitted Line Plot Depression score change 6.512 + 5.472 BMI change 20 5.26270 27.16% R-Sq (adj) 19.88% R-Sa 15- 8 10- 5- 0- -0.5 0.0 0.5 1.0 1.5 BMI change R-ag 27.16 5.26270 Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 6.512 2.26 2.88 0.0164 EMI change 5.472 2.83 1.93 0.0823 1.00 Regression Equation Depression score change - 6.512 - 5.472 BMI change (a) What percentage of observed variation in depression score change can be explained by the simple linear regression model? (Round your answer to two decimal places.) (b) Give a point estimate of a. (Round your answer to five decimal places.) Interpret this estimate. s is the typical amount by which the -Select-- v value -Select v what is predicted using the least squares regression line. (c) Give an estimate of the average change in depression score change associated with a 1 kg/m? increase in BMI change. (Round your answer to three decimal places.) (d) Calculate a point estimate of the mean depression score change for a patient whose BMI change was 1.2 kg/m. (Round your answer to three decimal places.)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter5: A Survey Of Other Common Functions
Section5.3: Modeling Data With Power Functions
Problem 3TU
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Transcribed Image Text:A paper gives data on x = change in Body Mass Index (BMI, in kilograms/meter?) and y = change in a measure of depression for patients suffering from depression who participated in a pulmonary rehabilitation program. The table below contains a subset of the data given in the paper and are
approximate values read from a scatterplot in the paper.
BMI Change (kg/m²)
0.5
-0.5
0.1
0.7 0.8
1
1.5
1.2 1
0.4
0.4
Depression Score Change
-1
4
4
5
8
13
14
17
18
12
14
The accompanying computer output is from Minitab.
Fitted Line Plot
Depression score change = 6.512 + 5.472 BMI change
5.26270
20-
R-Sq
R-Sq (adj) 19.88%
27.16%
15-
10-
5-
0-
-0.5
0.0
0.5
1.0
1.5
BMI change
R-są
5.26270
27.16%
Coefficients
Term
Coef
SE Coef
T-Value
P-Value
VIF
6.512
5.472
Constant
2.26
2.88
0.0164
BMI change
2.83
1.93
0.0823
1.00
Regression Equation
Depression score change = 6.512 + 5.472 BMI change
(a) What percentage of observed variation in depression score change can be explained by the simple linear regression model? (Round your answer to two decimal places.)
%
(b) Give a point estimate of a. (Round your answer to five decimal places.)
s =
Interpret this estimate.
s is the typical amount by which the -Select---
v value ---Select---
v what is predicted using the least squares regression line.
(c) Give an estimate of the average change in depression score change associated with a 1 kg/m2 increase in BMI change. (Round your answer to three decimal places.)
(d) Calculate a point estimate of the mean depression score change for a patient whose BMI change was 1.2 kg/m?. (Round your answer to three decimal places.)
Depression score change
•.
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