Using STATA obtain a multiple linear regression for the data set given above. Write the estimated multiple linear

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ANSWER ALL QUESTIONS

Contemporary Analytical Tools

1. Following are the weights (kg) and blood glucose levels (mg/100 ml) of 16 apparently healthy adult males:

Weight (x)	Glucose (y)
64.0 75.3 73.0 82.1 76.2 95.7 59.4 93.4 82.1 78.9 76.7 82.1 83.9 73.0 64.4 77.6	108 109 104 102 105 121  79 107 101  85  99 100 108 104 102  87

Please download the STATA data file– PUBH810_assignment3_q1.dta from Canvas and save the STATA data file as on your flash drive. Please don’t change the name of the file.

A. Write the estimated simple linear regression equation of Y on X and interpret the results in terms of intercept and regression coefficient (slope). Can you conclude that the regression coefficient for variable weight (X) is not equal to zero by performing t-test and F-test? State your null and alternative hypotheses? (3+3+3+2+2+2 points)

B. Write and interpret the 95% confidence interval for regression coefficient (β) for weight. (3+3 points)

C. How much variation is not explained by this regression model? (2 points)

D. How much variation is explained by this regression model? (2 points) 

2. The following are the gender and blood glucose levels (mg/100 ml) of 16 apparently healthy adult males and females:

Please download the STATA data file– PUBH810_assignment3_q2.dta from Canvas and save the STATA data file as on your flash drive. Please don’t change the name of the file.

Using STATA, answer the following questions:

A. Estimate the simple linear regression equation of Y on X. Write the estimated regression equation and interpret the results in terms of intercept and regression coefficient (slope). Test the hypothesis that the population regression coefficient for female is not zero (β≠0) using t-test. State your null and alternative hypotheses. (4+2+2+2+2 points)

B. What is the value of the regression coefficient for the males? (2 points)

C. What is the predicted value of glucose (y) for the males? (3 points)

D. What is the predicted value of glucose (y) for the females? (3 points)

3. The following data were collected on a simple random sample of 20 patients with hypertension. The variables are:

Y  = mean arterial blood pressure (mm Hg)

X1 = age (years)

X2 = weight (kg)

X3 = body surface area (sq m)

X4 = duration of hypertension (years)

X5 = basal pulse (beats/min)

X6 = measures of stress

Please download the STATA data file– PUBH810_assignment3_q3.dta from Canvas and save the STATA data file as on your flash drive. Please don’t change the name of the file.

A. Using STATA obtain a multiple linear regression for the data set given above. Write the estimated multiple linear regression equation of y on x1, x2, x3, x4, x5, and x6. (6 points)

B. Comment on all the regression coefficients regarding statistical significance using the p value. (6 points)

C. Test the hypothesis that the population regression coefficient for age (X1) is not zero. State your null and alternative hypotheses. State your conclusion. (4+2 points)

4. The following data were obtained on 12 males between the ages of 12 and 18 years (all measurements are in centimeters)

Please download the STATA data file– PUBH810_assignment3_q4.dta from Canvas and save the STATA data file as on your flash drive. Please don’t change the name of the file.

A. Using STATA, after running a multiple linear regression of y on x1 and x2,  obtain the multiple correlation coefficient and test the null hypothesis that  . State your null and alternative hypothesis. (6+3 points)

B. Using STATA obtain Pearson’s correlation coefficients between y and x1; between y and x2; and between x1 and x2. (4+4 points)

5. Researcher wished to study the effect of biofeedback and manual dexterity on the ability of patients to perform a complicated task accurately. Twenty-eight patients were randomly selected from those referred for physical therapy. The 28 were then randomly assigned to either receive or not receive biofeedback. The dependent variable is the number of consecutive repetitions of the task completed. The following are the data:

Please download the STATA data file– PUBH810_assignment3_q5.dta from Canvas and save the STATA data file as on your flash drive. Please don’t change the name of the file.

Number of repetitions y	Manual dexterity score x1	Biofeed-back x2	Number of repetitions y	Manual dexterity score x1	Biofeed-back x2
88 102   73 105   51   52 106   76 100 112   89   52   49   75	225   88 162   90 245 150   87 212 112   77 137 171 199 137	yes yes no yes no yes yes yes yes yes no no no yes	50   75   75 112   55 115   50   87 106   91   75   70 100 100	149 251 102   90 180   25 142   88   87 101 211 136 100 100	no yes no yes no yes no no no no yes yes no yes

(a) Using STATA perform the regression analysis of y on x1 and x2 and write the estimated regression equation of y on x1 and x2. Interpret the estimated regression coefficients for x1 and for x2. (Hints: you need to create a dummy variable for x2). (5+3+3 points)

(b) Write the estimated regression equation of y for the biofeedback group (x2 = yes) (3 points)

(c) Write the estimated regression equation of y for the non-biofeedback group (x2 = no). (3 points)

(d) What is the estimated number of repetitions for a person with 100 manual dexterity score with the presence of biofeedback? (3 points)

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