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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 o. (Round your answer to five decimal places.) S= Interpret this estimate. s is the typical amount by which the depression score change value differs from ✓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.)

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 o. (Round your answer to five decimal places.) S= Interpret this estimate. s is the typical amount by which the depression score change value differs from ✓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.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2AGP
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A paper gives data on x = change in Body Mass Index (BMI, in kilograms/meter2) 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 0.1 0.7 0.8 1 1.5 1.2 1 0.4 0.4 Depression Score Change -1 9 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 20 S 5.26270 R-Sq 27.16% R-Sq (adj) 19.88% 15- : 10- -0.5 0.0 1.5 Ⓡ S 5.26270 Coefficients Term Coef VIF SE Coef 2.26 T-Value 2.88 P-Value 0.0164 Constant 6.512 BMI 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 o. (Round your answer to five decimal places.) S = Interpret this estimate. s is the typical amount by which the depression score change value differs from 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.) Depression score change 品と 0.5 BMI change R-sq 27.16 % 1.0
Transcribed Image Text:A paper gives data on x = change in Body Mass Index (BMI, in kilograms/meter2) 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 0.1 0.7 0.8 1 1.5 1.2 1 0.4 0.4 Depression Score Change -1 9 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 20 S 5.26270 R-Sq 27.16% R-Sq (adj) 19.88% 15- : 10- -0.5 0.0 1.5 Ⓡ S 5.26270 Coefficients Term Coef VIF SE Coef 2.26 T-Value 2.88 P-Value 0.0164 Constant 6.512 BMI 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 o. (Round your answer to five decimal places.) S = Interpret this estimate. s is the typical amount by which the depression score change value differs from 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.) Depression score change 品と 0.5 BMI change R-sq 27.16 % 1.0
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