What does the scatterplot suggest about the relationship between depression score change and BMI change? The scatterplot suggests that there a linear relationship between depression score change and BMI change because there is trend in the plot. (b) What is the equation of the estimated regression line? Use the Parameter Estimates from the JMP Output for the Estimate of the Intercept and BMI Change. Use all decimals from the output in your answer. ŷ = + x (c) Is there is a significant linear relationship between the two variables? Carry out the Module Utility Test using a significance level of ? = 0.05. State the null and alternative hypotheses. H0: ? = 0 versus Ha: ? ≠ 0 H0: ? = 0 versus Ha: ? < 0 H0: ? ≤ 0 versus Ha: ? > 0 H0: ? = 0 versus Ha: ? > 0 H0: ? ≠ 0 versus Ha: ? = 0 Calculate the test statistic and its P-value for whether there is a useful linear relationship between the two sets of data. These values can be found in the Parameter Estimates of the JMP Output under the t-Ratio and Prob for the BMI Change. (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. H0 is not rejected. There is not sufficient evidence of a useful linear relationship between depression score change and BMI change.H0 is rejected. There is not evidence of a useful linear relationship between depression score change and BMI change. H0 is rejected. There is sufficient evidence of a useful linear relationship between depression score change and BMI change.H0 is not rejected. There is sufficient evidence of a useful linear relationship between depression score change and BMI change.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A paper† gave 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. JMP output for these data is shown below.

A scatterplot titled "Bivariate Fit of Depression Score Schange by BMI Change" has 12 points and a line plotted on it.

The horizontal axis is labeled "BMI change" and ranges from about −0.8 to about 1.8.
The vertical axis is labeled "Depression score change" and ranges from about −2 to 20.
The points are plotted from left to right in an upward, diagonal direction starting from the middle left of the diagram.
The points are very scattered and are between approximately −0.5 to 1.5 on the horizontal axis and between approximately −1 to 18 on the vertical axis.
A line with positive slope titled "Linear Fit" is drawn across the plot to approximate the trend of the points. The line enters the viewing window at about (−0.8, 3) and exits at about (1.8, 15).

Linear Fit

Depression score change = 6.8725681 + 5.077821*BMI Change

Summary of Fit

RSquare	0.234828
RSquare Adj	0.158311
Root Mean Square Error	5.365593
Mean of Response	9.75
Observations (or Sum Wgts)	12

Analysis of Variance

Source	DF	Sum of Squares	Mean Square	F Ratio	Prob > F
Model	1	88.35409	88.3541	3.0690	0.1104
Error	10	287.89591	28.7896
C. Total	11	376.25000

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

(a)

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

The scatterplot suggests that there a linear relationship between depression score change and BMI change because there is trend in the plot.

(b)

What is the equation of the estimated regression line? Use the Parameter Estimates from the JMP Output for the Estimate of the Intercept and BMI Change. Use all decimals from the output in your answer.

ŷ = +

(c)

Is there is a significant linear relationship between the two variables? Carry out the Module Utility Test using a significance level of

? = 0.05.

State the null and alternative hypotheses.

H₀: ? = 0 versus H_a: ? ≠ 0

H₀: ? = 0 versus H_a: ? < 0

H₀: ? ≤ 0 versus H_a: ? > 0

H₀: ? = 0 versus H_a: ? > 0

H₀: ? ≠ 0 versus H_a: ? = 0

Calculate the test statistic and its P-value for whether there is a useful linear relationship between the two sets of data. These values can be found in the Parameter Estimates of the JMP Output under the t-Ratio and Prob for the BMI Change. (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.

H₀ is not rejected. There is not sufficient evidence of a useful linear relationship between depression score change and BMI change.H₀ is rejected. There is not evidence of a useful linear relationship between depression score change and BMI change. H₀ is rejected. There is sufficient evidence of a useful linear relationship between depression score change and BMI change.H₀ is not rejected. There is sufficient evidence of a useful linear relationship between depression score change and BMI change.

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