Answer Happy

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 0.1 0.7 0.8 1 1.5 1.2 1 0.2 0.2 Depression Score Change -1 9 4 4 5 8 13 14 16 18 12 14 The accompanying computer output is from Minitab. Fitted Line Plot Depression score change = 7.090 + 4.615 BMI change 20 5.37139 R-S 21.31% 15- R-Sq (adj) 13.44% Depression score change 10-1 0- -0.5 0.0 0.5 1.0 1.5 BMI change S 5.37139 R-sq 21.31% Coefficients VIF Term Constant BMI change Coef 7.090 4.618 SE Coet 2.20 2.80 T-Value 3.22 1.65 P-Value 0.0092 0.1308 1.00 Regression Equation Depression score change = 7.090 + 4.615 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.) X % (b) Give a point estimate of o. (Round your answer to five decimal places.) s = x 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.) X (d) Calculate a point estimate of the mean depression score change for a patient whose BMI change was 1.2 kg/m². (Round your answer to three decimal places.) ỹ = x