Out: 04/29 19:00
Due: 05/13 19:00
Collaboration:
Collaboration on solving the assignment is allowed, after you have thought about the problem sets on your own. It is also OK to get clarification (but not solutions) from online resources, again after you have thought about the problem sets on your own. There are two requirements:
Cite your collaborators fully and completely (e.g., “XXX explained to me what is asked in problem set 3”). Or cite online resources (e.g., “I got inspired by reading XXX”) that helped you.
Write your scripts and report independently - the scripts and report must come from you only.
Submitting your assignment:
Submit your R scripts and report to TA (12332275@mail.sustech.edu.cn)
Late Submission:
Late submissions will not receive any credit.
Hint: Please follow the general steps of hypothesis testing as introduced in the lecture.
Your professor wants to study the relationship between sitting duration and his blood pressure. In 13 days, he measured how long he sits (in hours) and his blood pressure (mm Hg) immediately after it. The data are sorted and listed in the table.
| Day | Sitting duration (hour) | Blood pressure (mm Hg) |
|---|---|---|
| 1 | 2.88 | 84 |
| 2 | 2.51 | 86 |
| 3 | 2.22 | 96 |
| 4 | 2.16 | 93 |
| 5 | 2.05 | 94 |
| 6 | 1.93 | 101 |
| 7 | 1.67 | 103 |
| 8 | 1.49 | 102 |
| 9 | 1.25 | 100 |
| 10 | 1.21 | 108 |
| 11 | 1.15 | 104 |
| 12 | 1.12 | 102 |
| 13 | 0.73 | 111 |
1.1 [5 points] Is there a linear relationship between sitting duration and blood pressure for your professor?
1.2 [5 points] On average, how high will your
professor’s blood pressure be after he sits for 1.80 hours
(give the 95% confidence interval)?
To investigate the influence factors of AQI near a highway, a researcher measured the air pressure (hPa), air temperature (degree), relative humidity (%), and traffic flow rate (cars per hour) in 15 days.
| Day | AQI | Pressure | Temperature | Humidity | Traffic |
|---|---|---|---|---|---|
| 1 | 367 | 999.9 | 20.2 | 44 | 357 |
| 2 | 307 | 999.4 | 21.1 | 56 | 256 |
| 3 | 280 | 999.1 | 19.3 | 20 | 270 |
| 4 | 388 | 999.6 | 17.5 | 31 | 541 |
| 5 | 268 | 998.5 | 16.9 | 60 | 254 |
| 6 | 347 | 1000.8 | 22.5 | 48 | 337 |
| 7 | 308 | 1002.0 | 13.6 | 76 | 411 |
| 8 | 247 | 999.4 | 21.2 | 62 | 280 |
| 9 | 289 | 1002.7 | 23.5 | 60 | 281 |
| 10 | 200 | 1003.2 | 18.6 | 74 | 88 |
| 11 | 329 | 996.6 | 25.0 | 68 | 275 |
| 12 | 385 | 1003.0 | 23.6 | 69 | 358 |
| 13 | 337 | 1004.3 | 17.0 | 50 | 380 |
| 14 | 337 | 1000.4 | 27.2 | 36 | 268 |
| 15 | 394 | 998.3 | 14.1 | 63 | 523 |
2.1 [5 points] Build a best model between
AQI and potential variables.
2.2 [10 points] Based on your best model, how high
will AQI be in this site at the specific conditions as follow? Provide
the 95% confidence interval.
Condition 1: Pressure 1003.0 hPa, temperature
25.0 °C, humidity 70%, and traffic flow rate
450 cars per hour.
Condition 2: Pressure 1001.0 hPa, temperature
15.0 °C, humidity 50%, and traffic flow rate
300 cars per hour.
In this problem set we use the in-built data set mtcars
to describe different models of a car with their various engine
specifications.
In mtcars data set, the transmission mode (automatic or
manual) is described by the column am, which is a binary
value (0 is automatic or 1 is manual).
Load the data via:
3.1 [5 points] Fit a logistic regression model
between the columns am and 3 other columns -
gross horsepower hp, weight wt (in
1000 lbs), and number of cylinders cyl.
3.2 [10 points] Which independent variable has a significant slope? Update your logistic regression model by excluding the independent variable(s) with insignificant slope. Compute McFadden’s R2 and the probability cutoff.
3.3 [10 points] Using the updated model from step
3.2, make predictions of am (automatic or
manual) for the following 2 cars:
Car 1: gross horsepower of 140, weight of
3000 lbs
Car 2: gross horsepower of 90, weight of
2000 lbs
4.1 [15 points] [SS], p38-39, Problem 1.2.
4.2 [15 points] [SS], p39, Problem 1.6.