Using the variables listed in the table above, Describe each variable. (b) State for each variable whether it is qualitative or quantitative; if it is qualitative, state whether it is nominal or ordinal, and if it is quantitative, state whether it is discrete or continuous.
A lecturer at college wanted to know if he can predict student’s quiz results by asking them to
complete a simple survey. The result of the survey is given below:
| Quiz Results | EQR | Study Hrs | Age | Sex | BBT | MB | MC | AuHS | LM |
| 15 | 10 | 3 | 19 | 0 | 0 | 1 | 1 | 0 | 1 |
| 14 | 15 | 4 | 24 | 0 | 0 | 1 | 0 | 0 | 1 |
| 9 | 15 | 1 | 20 | 0 | 10 | 1 | 0 | 0 | 1 |
| 6 | 10 | 3 | 21 | 0 | 0 | 1 | 1 | 0 | 1 |
| 14 | 15 | 4 | 21 | 0 | 9 | 1 | 0 | 0 | 1 |
| 12 | 10 | 6 | 21 | 0 | 2 | 0 | 1 | 0 | 1 |
| 12 | 13 | 2 | 21 | 1 | 8 | 1 | 0 | 0 | 0 |
| 15 | 15 | 0 | 20 | 0 | 8 | 1 | 0 | 0 | 1 |
| 12 | 15 | 3 | 20 | 0 | 10 | 1 | 0 | 0 | 1 |
| 13 | 15 | 0.2 | 19 | 0 | 8 | 1 | 0 | 0 | 1 |
| 15 | 15 | 2 | 20 | 0 | 6 | 1 | 0 | 1 | 1 |
| 12 | 14 | 5 | 20 | 0 | 5 | 1 | 1 | 1 | 1 |
| 14 | 15 | 7 | 22 | 0 | 8 | 0 | 0 | 0 | 0 |
| 7 | 7 | 10 | 21 | 1 | 7 | 0 | 0 | 1 | 0 |
| 11 | 15 | 5 | 24 | 0 | 0 | 1 | 0 | 0 | 1 |
| 10 | 10 | 3 | 22 | 1 | 0 | 1 | 0 | 0 | 1 |
| 13 | 11 | 3 | 23 | 1 | 1 | 1 | 1 | 1 | 1 |
| 13 | 15 | 2 | 22 | 1 | 8 | 0 | 0 | 0 | 0 |
| 13 | 12 | 4 | 20 | 1 | 7 | 1 | 0 | 1 | 0 |
| 13 | 10 | 3 | 20 | 1 | 0 | 1 | 0 | 0 | 1 |
| 8 | 13 | 5 | 20 | 1 | 8 | 0 | 0 | 0 | 0 |
| 12 | 13 | 5 | 22 | 0 | 5 | 0 | 0 | 0 | 1 |
| 13 | 15 | 8 | 22 | 0 | 5 | 0 | 1 | 0 | 1 |
| 10 | 13 | 4 | 23 | 1 | 7 | 1 | 0 | 0 | 1 |
| 13 | 13 | 0.5 | 20 | 1 | 0 | 0 | 0 | 0 | 0 |
| 12 | 13 | 0.5 | 20 | 1 | 0 | 1 | 0 | 0 | 0 |
| 15 | 15 | 2 | 21 | 0 | 10 | 1 | 0 | 0 | 1 |
| 10 | 13 | 6 | 22 | 0 | 6 | 1 | 1 | 0 | 1 |
| 11 | 8 | 5 | 20 | 0 | 10 | 0 | 0 | 1 | 0 |
| 12 | 10 | 4 | 19 | 1 | 0 | 1 | 0 | 0 | 1 |
| 8 | 5 | 2 | 20 | 1 | 0 | 1 | 0 | 1 | 0 |
| 11 | 13 | 6 | 20 | 1 | 7.5 | 1 | 1 | 1 | 1 |
| 10 | 3 | 12 | 21 | 0 | 4 | 1 | 0 | 1 | 0 |
| 8 | 11 | 2 | 19 | 0 | 0 | 1 | 0 | 0 | 1 |
| 15 | 15 | 3 | 23 | 1 | 2 | 1 | 0 | 0 | 1 |
| 11 | 14 | 1 | 23 | 0 | 10 | 1 | 1 | 1 | 1 |
| 13 | 14 | 4 | 21 | 1 | 8 | 1 | 0 | 1 | 1 |
| 9 | 15 | 3 | 22 | 0 | 5 | 1 | 0 | 0 | 0 |
| 13 | 14 | 4 | 21 | 0 | 9 | 1 | 0 | 0 | 1 |
| 13 | 15 | 4 | 20 | 0 | 5 | 1 | 0 | 0 | 1 |
| 11 | 13 | 5 | 20 | 1 | 8 | 0 | 0 | 0 | 0 |
| 7 | 10 | 3 | 24 | 1 | 5 | 1 | 0 | 1 | 1 |
| 14 | 15 | 3 | 20 | 0 | 6 | 1 | 0 | 0 | 1 |
| 13 | 15 | 3 | 20 | 0 | 8 | 0 | 0 | 0 | 0 |
| 8 | 12 | 0.5 | 22 | 1 | 2 | 1 | 1 | 0 | 1 |
| 8 | 10 | 4 | 19 | 1 | 7 | 0 | 0 | 1 | 1 |
| 15 | 15 | 3 | 20 | 0 | 7 | 1 | 0 | 0 | 1 |
| 14 | 14 | 3 | 19 | 0 | 8 | 1 | 0 | 0 | 1 |
| 7 | 10 | 3 | 21 | 1 | 0 | 0 | 0 | 1 | 0 |
| 11 | 13 | 2 | 21 | 0 | 7 | 1 | 1 | 0 | 1 |
| 14 | 15 | 6 | 22 | 0 | 6 | 1 | 0 | 0 | 1 |
| 9 | 12 | 3 | 21 | 1 | 0 | 1 | 0 | 0 | 1 |
| 14 | 15 | 2 | 22 | 0 | 5 | 1 | 0 | 0 | 1 |
| 9 | 8 | 4 | 21 | 0 | 7 | 1 | 0 | 1 | 1 |
| 15 | 15 | 7 | 20 | 0 | 6 | 1 | 0 | 0 | 1 |
| 13 | 14 | 3 | 23 | 1 | 4 | 0 | 1 | 0 | 0 |
| 14 | 15 | 5 | 21 | 0 | 5 | 1 | 0 | 0 | 1 |
| 12 | 13 | 5 | 19 | 1 | 6 | 1 | 0 | 0 | 0 |
| 14 | 12 | 2 | 22 | 1 | 10 | 1 | 0 | 0 | 1 |
| 14 | 13 | 2 | 22 | 0 | 10 | 1 | 0 | 0 | 0 |
| 11 | 12 | 3 | 22 | 0 | 8 | 1 | 0 | 1 | 1 |
| 4 | 1 | 9 | 30 | 0 | 10 | 1 | 0 | 1 | 1 |
| 14 | 15 | 3 | 21 | 1 | 8 | 1 | 0 | 0 | 1 |
| 15 | 15 | 3 | 20 | 0 | 0 | 0 | 0 | 0 | 0 |
| 13 | 15 | 3 | 19 | 1 | 7 | 1 | 0 | 0 | 1 |
| 14 | 15 | 2 | 21 | 1 | 6 | 1 | 0 | 0 | 1 |
| 8 | 5 | 3 | 20 | 0 | 0 | 1 | 0 | 1 | 1 |
| 7 | 10 | 9 | 21 | 1 | 0 | 1 | 1 | 0 | 1 |
| 12 | 14 | 4 | 20 | 0 | 0 | 1 | 0 | 0 | 0 |
| 6 | 8 | 4 | 21 | 0 | 1 | 1 | 1 | 0 | 0 |
| 9 | 10 | 5 | 20 | 0 | 2 | 0 | 0 | 1 | 0 |
| 10 | 13 | 2 | 20 | 1 | 6 | 1 | 1 | 1 | 0 |
| 10 | 12 | 1 | 25 | 1 | 5 | 1 | 0 | 1 | 1 |
| 13 | 15 | 2 | 21 | 1 | 3 | 1 | 0 | 0 | 1 |
| 9 | 8 | 1 | 29 | 0 | 0 | 0 | 1 | 0 | 0 |
| 12 | 13 | 2 | 19 | 0 | 0 | 1 | 0 | 0 | 1 |
| 12 | 15 | 3 | 20 | 0 | 0 | 1 | 0 | 0 | 1 |
| 14 | 12 | 7 | 19 | 0 | 3 | 1 | 0 | 1 | 1 |
| 8 | 7 | 1 | 19 | 1 | 0 | 0 | 1 | 0 | 0 |
| 14 | 12 | 1 | 23 | 1 | 6 | 1 | 0 | 1 | 1 |
| 11 | 9 | 3 | 20 | 1 | 5 | 0 | 1 | 1 | 1 |
| 13 | 15 | 2 | 21 | 1 | 0 | 1 | 0 | 0 | 1 |
| 14 | 11 | 2 | 19 | 1 | 9 | 0 | 0 | 0 | 0 |
| 11 | 14 | 4 | 22 | 1 | 10 | 0 | 0 | 0 | 1 |
| 10 | 8 | 5 | 20 | 1 | 5 | 0 | 0 | 1 | 1 |
| 11 | 13 | 1 | 22 | 1 | 2 | 0 | 0 | 0 | 0 |
| 14 | 15 | 0.5 | 20 | 0 | 8 | 1 | 0 | 0 | 0 |
| 12 | 14 | 15 | 23 | 0 | 0 | 1 | 1 | 0 | 1 |
| 10 | 12 | 4 | 19 | 1 | 0 | 0 | 1 | 1 | 1 |
| 14 | 12 | 0 | 20 | 1 | 3 | 1 | 0 | 1 | 1 |
| 13 | 10 | 2 | 19 | 1 | 0 | 1 | 0 | 1 | 0 |
| 15 | 12 | 2 | 20 | 1 | 3 | 1 | 0 | 1 | 1 |
| 8 | 10 | 3 | 19 | 1 | 1 | 1 | 0 | 1 | 1 |
| 14 | 12 | 5 | 21 | 0 | 0 | 1 | 0 | 0 | 1 |
| 6 | 10 | 2 | 21 | 1 | 8 | 1 | 0 | 0 | 1 |
| 8 | 8 | 2 | 21 | 1 | 1 | 1 | 0 | 1 | 1 |
| 12 | 10 | 2 | 20 | 0 | 7 | 1 | 0 | 1 | 1 |
| 9 | 6 | 3 | 20 | 0 | 1 | 1 | 1 | 1 | 1 |
| 7 | 8 | 4 | 19 | 1 | 9 | 1 | 1 | 1 | 0 |
| 13 | 11 | 6 | 19 | 1 | 6 | 1 | 0 | 0 | 1 |
| 13 | 10 | 2 | 25 | 1 | 0 | 1 | 0 | 0 | 1 |
| 14 | 14 | 2 | 25 | 1 | 5 | 1 | 0 | 0 | 0 |
Quiz Result Actual Mark (0-15) for quiz student attained
EQR Quiz score (0-15) expected to get before taking the quiz
Study Hrs. Number of hours per week (on average) spent studying for Statistics
Age Age (in years)
BBT Satisfaction rating of Big Bang Theory
Sex M=1 F=0
MB MB=1 for good math background, otherwise 0
MC MC= 1 if math centre is used regularly, otherwise 0
AuHS AuHS = 1 if student completed high school in Australia, otherwise 0
LM LM=1 if student likes math, 0 otherwise
Task 1: Variable List
(a) Using the variables listed in the table above, Describe each variable.
(b) State for each variable whether it is qualitative or quantitative; if it is qualitative, state
whether it is nominal or ordinal, and if it is quantitative, state whether it is discrete or
continuous.
Task 2: Histogram
Create a histogram showing the distribution of marks and study hours. Find the 5-number
summary of the distribution of marks and study hours. Comment on the shape of the
distribution: is it symmetrical? If it is not, is it positively or negatively skewed? Are there any
outliers present? If so, are they of particular interest?
Task 3:
(a) Run a regression of Quiz results on EQR. Formulate a hypothesis test to determine if EQR is
a significant factor in determining quiz results.
(b) Interpret the above regression
(c) Run a regression of Quiz results on EQR, study hours, age and sex. Is this a better or worse
model. Explain
(d) Are all variables significant determinants? Explain
(e) Interpret the regression from part c
(f) Run a regression of Quiz results on all the listed variables. Are they all statistically significant?
Determine the best model to help predict quiz results.
Task 5: Regression Analysis
The lecturer is interested to see what variables, if any will help determine the number of hours
spent on studying statistics. Test and find any regression models that can help determine the
number of hours spent on studying. (Hint run Study hrs. on…)
(a) On average, how much do males study more(less) than females?
(b) Do people who enjoy the Big Bang Theory impact on the number of hours studies?
(c) Is age a determining factor on the number of hours studied?
(d) Do students with a stronger math background study more or less? Also state how much more
or less
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