Both of the following questions from Hassard, Thomas H. 1991. Understanding Bios

Question

Both of the following questions from Hassard, Thomas H. 1991. Understanding Biostatistics. St. Louis: Mosby Year Book, p0. 148-149. The following data gives weight (in lbs) and cholesterol (in mg/dl) measurements collected from 14 adult males as part of a coronary disease study. (none of the subjects were known to have experienced a coronary incident within the 10 years before the study.) Calculate a linear regression to determine if there is any evidence of a relationship between the two variables. The researchers for this study would like to know if weight affects cholesterol. Identify the following:

1. The independent and dependent variable

2. The coefficients (slope and intercept) of the regression

3. The hypothesis of the experiment.

4. The p-value obtained from the t-test

5. A conclusion about the hypothesis (whether or not you reject the null) Weight Cholesterol 168 135 175 403 173 294 158 312 154 311 214 222 176 302 262 269 181 311 143 286 140 403 187 244 163 353 164 252 In an initial trial of a newly developed anesthetic, the time (in min) from administration of the anesthetic until induction of anesthesia was recorded for 10 patients, and the effective dosage rate used in (µg/kg) was calculated from the patient's weight. The researchers would like to know how disease affects induction time. Identify the following:

1. The independent and dependent variable

2. The coefficients (slope and intercept) of the regression

3. The hypothesis of the experiment.

4. The p-value obtained from the t-test

5. A conclusion about the hypothesis Dose Induction time 1.3 25 1.9 13 1.5 19 1.1 23 1.0 26 1.3 21 2.1 11 0.7 31 1.6 14 0.9 24 Please submit work in EXCEL only. Work done by hand will not be accepted.

Explanation / Answer

first part)

1. The independent variable is weight and dependent variable cholestrol

As here we want to know the effect of weight on cholestrol

2. The coefficients (slope and intercept) of the regression

the regression line y(cholestrol)=a+b(weight)=415.86+0.7018*x

3. The hypothesis of the experiment.

null hypothesis H0: b=0 and

alternate hypothesis H1: b is not = 0

4. The p-value obtained from the t-test=0.2776

5. A conclusion about the hypothesis (whether or not you reject the null)

not reject null hypothesis , as p-value is more than alpha=0.05 ( generally level of significance of alpha=0.05)

follwoing information has been generated using regression anlaysis in ms-excel

(second par)

1. The independent variable is dose and

induction time is dependent variable

2. The coefficients (slope and intercept) of the regression

y(induction time)=a+b*dose=39.14-13.76

3. The hypothesis of the experiment.

null hypothesis H0: b=0 and

alternate hypothesis H1: b is not = 0

4. The p-value obtained from the t-test is less than 0.001

5. A conclusion about the hypothesis : reject null hypothesis and conclude that there is significant relation between y and x ( as p-value is less than alpha=0.05)

following information has been generate using ms-excel command for regression

SUMMARY OUTPUT Regression Statistics Multiple R 0.311918466 R Square 0.097293129 Adjusted R Square 0.022067557 Standard Error 69.16963033 Observations 14 ANOVA df SS MS F Significance F Regression 1 6187.96117 6187.961 1.293352 0.277630422 Residual 12 57413.25312 4784.438 Total 13 63601.21429 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 415.8606841 109.912361 3.783566 0.002607 176.382222 655.3391461 176.3822 655.3391 X Variable 1 -0.701810243 0.617108271 -1.13726 0.27763 -2.046373659 0.642753173 -2.04637 0.642753

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