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 inthe paper.BMI Change (kg/m2)0.7 0.8 11.5 1.210.4 0.40.5-0.50.1Depression Score Change-1| 4581314| 17| 18| 1214The accompanying computer output is from Minitab.Fitted Line PlotDepression score change = 6.512 + 5.472 BMI change5.2627020 -R-SqR-Sq (adj) 19.88%27.16%15-10-.5--0.50.00.51.01.5BMI change5.2627027.166CoefficientsTermCoefSE CoefT-ValueP-ValueVIFConstant6.5122.262.880.0164BMI change5.4722.831.930.08231.00Regression EquationDepression score change = 6.512 + 5.472 EMI 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.)27.16(b) Give a point estimate of o. (Round your answer to five decimal places.)s = 5.26270Interpret this estimate.s is the typical amount by which the depression score change vvalue differs fromvV 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.)5.472(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.)ŷ = 5.586Depression score change

a) Percentage of the observed variation in depression score is R^2=27.16% b) Point Estimate of sigma…

A paper gives data on change in Body Mass Index (BM. in kilegrams/meter and y- the paper 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 scatterp 0.5 -0.5 0.1 0.7 0.0 1. 1.a: 0.4 0.4 14 17 1 12 14 BHI Change (kg/m²) Depression Score Change -: The accompanying computer eutput is from Minitab . Fitted Line Plot Depression score change 6312 + 3472 BMI change 5.2620 27.1% R-Sa (adi) 19.88% 20- 15 10 .. -0.5 0.0 0.5 1.0 15 BMI change Coettieients Term Ceet E Cont T-Value p-Value VIr a. Censtant 4.a 0.044 t change .a a. 2.12 1.9 0.0sas 1.00 Regression Equation Depeien e hange e.1a s.47a I hange (a) what percentage of observed variation in depression score change can be explained by the simple linear regression model? (Round your ansver to two decimal places.) 27.10 (b) Give a point estimate of d. (Round your anser to five decimal places.) Interpret this estimate. sis the typical ameunt by which the cepresson score enange y value es rom v swhat is predicted using the least squares regression line. (e) Give an estimate of the average change in depression score change associated with a kg/m inerease in BMI change. (Round your anser to three decimal places.] ) 3472 (4) 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.)

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.7: More On Inequalities

Problem 44E