MET CS 555 Assignment 6 - 20 points

The data in this document consists of body temperature measurements and heart rate measurements for 65 men and 65 women. Save the data to a file, and read the data file into R.Use this data to address the following questions.

(1) We are interested in whether the proportion of men and women with body temperatures greater than or equal to 98.6 degrees Fahrenheit are equal. Therefore, we need to dichotomize the body temperature variable. Create a new variable, called "temp_level" in which temp_level = 1 if body temperature >= 98.6 and temp_level=0 if body temperature < 98.6. (2 points)

(2) Summarize the data relating to body temperature level (i.e., the variable you created above) by sex. (2 points)

(3) Calculate the risk difference for high body temperature level between men and women.Formally test (at the alpha=0.05 level) whether the proportion of people with higher body temperatures (greater than or equal to 98.6) is the same across men and women based on this effect measure. You should be showing all 5 steps in the 5-step recipe for testing. (4 points)

(4) Perform a logistic regression with sex as the only explanatory variable.Formally test (at the alpha=0.05 level) if the odds of having a temperature greater than or equal to 98.6 is the same between males and females.Again, please show all 5 steps. Additionally, include the odds ratio for sex and the associated 95% confidence interval in your summary, and interpret the value of the odds ratio.Lastly, what is the c-statistic for this model? (5 points)

(5) Perform multiple logistic regression predicting body temperature level from sex and heart rate.Briefly summarize the output from this mode (no need to go through all 5 steps).Give the odds ratio for sex. Also, report the odds ratio for heart rate (for a 10-beat increase).What is the c-statistic of this model?(5 points)

(6) Which model fit the data better?Support your response with evidence from your output.Present the ROC curve for the model you choose. (2 points)

Dataset

Data (1=males, 2 =females)

temp sex Heart rate

96.3 1 70

96.7 1 71

96.9 1 74

97 1 80

97.1 1 73

97.1 1 75

97.1 1 82

97.2 1 64

97.3 1 69

97.4 1 70

97.4 1 68

97.4 1 72

97.4 1 78

97.5 1 70

97.5 1 75

97.6 1 74

97.6 1 69

97.6 1 73

97.7 1 77

97.8 1 58

97.8 1 73

97.8 1 65

97.8 1 74

97.9 1 76

97.9 1 72

98 1 78

98 1 71

98 1 74

98 1 67

98 1 64

98 1 78

98.1 1 73

98.1 1 67

98.2 1 66

98.2 1 64

98.2 1 71

98.2 1 72

98.3 1 86

98.3 1 72

98.4 1 68

98.4 1 70

98.4 1 82

98.4 1 84

98.5 1 68

98.5 1 71

98.6 2 77

98.6 1 78

98.6 1 83

98.6 2 66

98.6 1 70

98.6 1 82

98.7 2 73

98.7 1 78

98.8 1 78

98.8 1 81

98.8 2 78

98.9 1 80

99 2 75

99 2 79

99 1 81

99.1 1 71

99.2 1 83

99.3 1 63

99.4 1 70

99.5 1 75

96.4 2 69

96.7 2 62

96.8 1 75

97.2 1 66

97.2 2 68

97.4 2 57

97.6 1 61

97.7 2 84

97.7 1 61

97.8 2 77

97.8 2 62

97.8 2 71

97.9 1 68

97.9 2 69

97.9 2 79

98 2 76

98 1 87

98 2 78

98 2 73

98 2 89

98.1 2 81

98.2 2 73

98.2 2 64

98.2 2 65

98.2 2 73

98.2 2 69

98.2 2 57

98.3 2 79

98.3 2 78

98.3 2 80

98.4 2 79

98.4 2 81

98.4 2 73

98.4 2 74

98.4 2 84

98.5 2 83

98.6 2 82

98.6 2 85

98.6 2 86

98.6 2 77

98.7 2 72

98.7 2 79

98.7 2 59

98.7 2 64

98.7 2 65

98.7 2 82

98.8 2 64

98.8 2 70

98.8 2 83

98.8 2 89

98.8 2 69

98.8 2 73

98.8 2 84

98.9 2 76

99 2 79

99 2 81

99.1 2 80

99.1 2 74

99.2 2 77

99.2 2 66

99.3 2 68

99.4 2 77

99.9 2 79

100 2 78

100.8 2 77