The paper referenced in Exercise 13.9 (?Depression, Body Mass Index, and Chronic Obstructive Pulmonary Disease?A Holistic Approach,? International Journal of COPD [2016]: 239?249) gave data on

x = Change in body mass index (BMI in kg/m²)

and

y = Change in a measure of depression

for patients suffering from depression who participated in a pulmonary rehabilitation program. JMP output for these data is shown below.

a. What does the scatterplot suggest about the relationship between depression score change and BMI change?

b. What is the equation of the estimated regression line?

c. Is there a useful linear relationship between the two variables? Carry out an appropriate test using a significance level of ? = 0.05.

Transcribed Image Text:

Bivariate Fit of Depression score change By BMI Change 20 15 10 -0.5 0.5 1.5 BMI change Depression: score change Linear Fit Depression score change = 6.8725681 + 5.077821*BMI Change %3D Summary of Fit RSquare 0.234828 RSquare Adj 0.158311 Root Mean Square Error Mean of Response 5.365593 9.75 Observations (or Sum Wgts) 12 Analysis of Variance Source DF Sum of Squares Mean Square F Ratio Model 88.35409 88.3541 3.0690 Error 10 287.89591 28.7896 Prob > F C. Total 11 376.25000 0.1104 Parameter Estimates Term Estimate Std Error t Ratio Prob> t Intercept 6.8725681 2.257651 3.04 0.0124* BMI Change 5.077821 2.898557 1.75 0.1104