(a) What percentage of observed variation in depression score change can be explained by the simple linear regression model? We wish to determine the percentage of variation in depression score change that can be explained by the simple linear regression model.
(a) What percentage of observed variation in depression score change can be explained by the simple linear regression model? We wish to determine the percentage of variation in depression score change that can be explained by the simple linear regression model.
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Transcribed Image Text:(a) What percentage of observed variation in depression score change can be explained by the simple linear regression model?
We wish to determine the percentage of variation in depression score change that can be explained by the simple linear regression model.
First,
recall the given Minitab output.
Fitted Line Plot
Depression score change = 6.826 + 4.802 BMI change
15-
:
Ø
10-
5-
0-
0.0
0.5
1.0
BMI change
Depression score change
20
-0.5
S
5.38140
R-sq
21.45%
Coefficients
Term Coef SE Coef
Constant 6.826
2.32
BMI change 4.802
2.91
1.5
T-Value
2.95
1.65
S
R-Sq
21.45%
R-Sq (adj) 13.59%
Ⓡ
P-Value
0.015
0.129
5.38140
Regression Equation
Depression score change = 6.826+ 4.802 BMI change
VIF
1.00
Recall that the value describes the percentage of variation in y that can be explained by x in the simple linear regression model. According to the Minitab output, to two decimal places, ² =
regression model, to two decimal places, is
%.
%, so the percentage of variation in depression score change that can be explained by the simple linear
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