(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.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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| 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 |
Answer d,e,f
(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.
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