### Epidemiology, population health and public health Epidemiology, population health and public health

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pectoris before and 4 weeks after once-daily dosing with an
experimental anti-anginal medication. The investigator wanted to
know if the improvement in exercise duration is related to the
patient’s disease history. Disease duration since initial diagnosis (in
years) and percent-improvement in treadmill walking times are
shown below for a study with 20 patients enrolled. Is there a
significant linear relationship between improvement on medication
and disease duration?

Patient# Duration(Yrs) %improvement
1 1 40
2 1 90
3 3 30
4 2 30
5 1 80
6 5 60
7 1 10
8 4 -10
9 2 50
10 6 40
11 1 60
12 4 0
13 2 50
14 2 110
15 3 20
16 3 70
17 5 -30
18 3 20
19 1 40
20 6 0

The regression slope, which represents the average change in y for a one-unit
change in x, is the best estimate of the rate of improvement in treadmill
performance for each one-year increase in disease duration,
The statistical significance is determined by the t-test, summarized
as follows:
Regression Equation:
NULL Hypothesis:
Alt. Hypothesis:
Test statistic:
Decision Rule:
p-value:
Conclusion:

12). In a regression analysis involving 30 observations, the following estimated regression equation was obtained.
y = 17.6 + 3.8X1 + 2.3X2 + 7.6X3 + 2.7X4
For this estimated regression equation SS(Total)= 1805 and SSR = 1760. Construct the ANOVA table.
SS df MS F-ratio p-value
Regression
Res Error
Total R-sq=

a. At a = .05, is the F test significant?

Suppose variables X1 and X4 are dropped from the model and the following estimated regression equation is obtained.
y = 12 + 5.3X2 + 9.6X3 SS df MS F p-value
For this model SS(Total)= 1805 and SSR = 1705. Regression
b. Compute SSE( with x1, x2, x3, x4). Res Error
Total
c. Compute SSE(with x2, x3). R-sq:

d. Use an F test and a .05 level of significance to determine whether X1 and X4 contribute significantly to the model.

13). Complete all the missing cells in the following Regression Output:

SUMMARY OUTPUT

Regression Statistics
Multiple R
R Square
Standard Error 0.573
Observations 20

ANOVA
df SS MS F Significance F
Regression
Residual 2.299
Total 11.985

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -0.869 0.952
Miles 0.061 6.182
Deliveries 0.221 4.176

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