5. [-17 Points] DETAILS PODSTAT6 13.2.026. A papert gave data on x = change in Body Mass Index (BMI in kilograms/meter)

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5 17 Points Details Podstat6 13 2 026 A Papert Gave Data On X Change In Body Mass Index Bmi In Kilograms Meter 1 (65.87 KiB) Viewed 23 times

5. [-17 Points] DETAILS PODSTAT6 13.2.026. A papert gave 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. JMP output for these data is shown below. Bivariate Fit of Depression Score Change by BMI Change 20 15 - 10 - Depression score change 5 0 T -0.5 0 0.5 1 1.5 BMI change -Linear Fit Linear Fit Depression score change = 6.8725681 + 5.077821*BMI Change Summary of Fit RSquare RSquare Adj Root Mean Square Error Mean of Response Observations (or Sum Wots) 0.234828 0.158311 5.365593 9.75 12 F Ratio Prob > Analysis of Variance Sum of Source DF Squares Model 1 88.35409 Error 10 287.89591 C. Total 11 376.25000 Mean square 88.3541 28.7896 3.07 0.1104 Parameter Estimates Term Estimate Prob > lt Std Error 2.257651 2.898557 6.8725681 5.077821 t Ratio 3.04 1.75 Intercept BMI change 0.0124* 0.1104

Intercept BMI Change 6.8725681 5.077821 2.257651 2.898557 3.04 1.75 0.0124* 0.1104 (a) What does the scatterplot suggest about the relationship between depression score change and BMI change? The scatterplot suggests that there -Select--- a linear relationship between depression score change and BMI change because there is -Select--- trend in the plot. (b) What is the equation of the estimated regression line? Ý = (c) Is there is a useful linear relationship between the two variables? Carry out an appropriate test using a significance level of a = 0.05. State the null and alternative hypotheses. O HO: B = 0 versus Hy: B = 0 OHO: B = 0 versus Ha: ß < 0 OHO: < 0 versus Ha: ß > 0 O Ho: B = 0 versus H: B > 0 4a O Ho: B = 0 versus Hz: ß = 0 a Report the test statistic and its P-value for whether there is a useful linear relationship between the two sets of data. (Round your test statistic to two decimal places and your P-value to four decimal places.) t = P-value = Use the P-value to evaluate the statistical significance of the results at the 5% level. Ho is not rejected. There is not sufficient evidence of a useful linear relationship between depression score change and BMI change. Ho is rejected. There is sufficient evidence of a useful linear relationship between depression score change and BMI change. Ho is not rejected. There is sufficient evidence of a useful linear relationship between depression score change and BMI change. Ho is rejected. There is not evidence of a useful linear relationship between depression score change and BMI change.