As an introduction, we would like to visualize the characteristics of the data set. The dataset includes data from 3 schools and contains 183 observations. The average study time is 8.9 hours, and the average test score is 44.77.
A table to visualize the data is:| School Full Name | School Short Name | Test Score | Study Time |
|---|---|---|---|
| Hillcrest High School | Hillcrest | 54.59454 | 13.092146 |
| Hillcrest High School | Hillcrest | 45.90443 | 7.285176 |
| Hillcrest High School | Hillcrest | 46.07368 | 10.068656 |
| Hillcrest High School | Hillcrest | 53.15568 | 10.877858 |
| Hillcrest High School | Hillcrest | 51.89308 | 10.192075 |
| Hillcrest High School | Hillcrest | 45.88416 | 8.660897 |
| Hillcrest High School | Hillcrest | 49.43284 | 13.513836 |
| Hillcrest High School | Hillcrest | 49.04923 | 8.695293 |
| Hillcrest High School | Hillcrest | 55.00619 | 15.034541 |
| Hillcrest High School | Hillcrest | 49.30719 | 8.791128 |
| Hillcrest High School | Hillcrest | 49.59065 | 12.893879 |
| Hillcrest High School | Hillcrest | 54.12954 | 15.839206 |
| Hillcrest High School | Hillcrest | 47.03255 | 4.812688 |
| Hillcrest High School | Hillcrest | 48.98281 | 8.142904 |
| Hillcrest High School | Hillcrest | 50.05463 | 8.579306 |
| Hillcrest High School | Hillcrest | 56.51023 | 10.887121 |
| Hillcrest High School | Hillcrest | 48.13828 | 8.126511 |
| Hillcrest High School | Hillcrest | 33.20910 | 1.009904 |
| Hillcrest High School | Hillcrest | 40.99077 | 1.657870 |
| Hillcrest High School | Hillcrest | 57.04151 | 12.939610 |
| Oakwood High School | Oakwood | 44.29733 | 8.059354 |
| Oakwood High School | Oakwood | 25.14011 | 3.635345 |
| Oakwood High School | Oakwood | 35.47447 | 8.463518 |
| Oakwood High School | Oakwood | 45.12912 | 12.623294 |
| Oakwood High School | Oakwood | 48.16753 | 14.664851 |
| Oakwood High School | Oakwood | 35.43849 | 7.687863 |
| Oakwood High School | Oakwood | 37.85879 | 8.207462 |
| Oakwood High School | Oakwood | 25.77590 | 3.689781 |
| Oakwood High School | Oakwood | 48.83004 | 10.359562 |
| Oakwood High School | Oakwood | 36.44190 | 7.059286 |
| Oakwood High School | Oakwood | 42.43892 | 10.345621 |
| Oakwood High School | Oakwood | 45.67442 | 11.093782 |
| Oakwood High School | Oakwood | 46.28141 | 12.084581 |
| Oakwood High School | Oakwood | 35.90872 | 7.152491 |
| Oakwood High School | Oakwood | 47.41863 | 10.494136 |
| Oakwood High School | Oakwood | 29.00540 | 3.828244 |
| Oakwood High School | Oakwood | 31.40098 | 6.625893 |
| Oakwood High School | Oakwood | 36.01010 | 6.426547 |
| Oakwood High School | Oakwood | 24.41876 | 1.736647 |
| Oakwood High School | Oakwood | 38.60989 | 9.087638 |
| Oakwood High School | Oakwood | 37.99014 | 9.597266 |
| Oakwood High School | Oakwood | 39.07729 | 7.896098 |
| Oakwood High School | Oakwood | 43.98547 | 11.253760 |
| St Mary’s Church of England School | St Mary’s | 42.94447 | 6.799156 |
| St Mary’s Church of England School | St Mary’s | 34.92019 | 4.874427 |
| St Mary’s Church of England School | St Mary’s | 49.85766 | 10.277724 |
| St Mary’s Church of England School | St Mary’s | 44.38598 | 6.545091 |
| St Mary’s Church of England School | St Mary’s | 60.11943 | 13.311574 |
| St Mary’s Church of England School | St Mary’s | 46.89865 | 7.684932 |
| St Mary’s Church of England School | St Mary’s | 50.23389 | 10.946214 |
| St Mary’s Church of England School | St Mary’s | 49.43679 | 9.945046 |
| St Mary’s Church of England School | St Mary’s | 40.07521 | 6.627753 |
| St Mary’s Church of England School | St Mary’s | 60.94646 | 13.706453 |
| St Mary’s Church of England School | St Mary’s | 57.77003 | 10.907968 |
| St Mary’s Church of England School | St Mary’s | 48.67736 | 9.248552 |
| St Mary’s Church of England School | St Mary’s | 51.15944 | 9.808922 |
| St Mary’s Church of England School | St Mary’s | 51.22429 | 11.017137 |
| St Mary’s Church of England School | St Mary’s | 46.55865 | 9.248769 |
| St Mary’s Church of England School | St Mary’s | 23.99421 | 0.000000 |
| St Mary’s Church of England School | St Mary’s | 54.27720 | 9.833919 |
| St Mary’s Church of England School | St Mary’s | 48.37929 | 7.877566 |
| Hillcrest High School | Hillcrest | 45.30004 | 9.534962 |
| Hillcrest High School | Hillcrest | 57.01957 | 10.724741 |
| Hillcrest High School | Hillcrest | 56.86480 | 13.178481 |
| Hillcrest High School | Hillcrest | 46.07672 | 6.797394 |
| Hillcrest High School | Hillcrest | 55.57510 | 12.886898 |
| Hillcrest High School | Hillcrest | 47.07002 | 9.986815 |
| Hillcrest High School | Hillcrest | 49.22528 | 12.094788 |
| Hillcrest High School | Hillcrest | 52.23690 | 11.741456 |
| Hillcrest High School | Hillcrest | 47.77480 | 11.141905 |
| Hillcrest High School | Hillcrest | 45.58995 | 5.849913 |
| Hillcrest High School | Hillcrest | 52.34357 | 8.708711 |
| Hillcrest High School | Hillcrest | 47.91817 | 10.849825 |
| Hillcrest High School | Hillcrest | 43.12712 | 6.118700 |
| Hillcrest High School | Hillcrest | 46.96063 | 7.350784 |
| Hillcrest High School | Hillcrest | 47.81392 | 10.722260 |
| Hillcrest High School | Hillcrest | 50.39072 | 11.283807 |
| Hillcrest High School | Hillcrest | 53.06295 | 10.370573 |
| Hillcrest High School | Hillcrest | 48.49496 | 6.321941 |
| Hillcrest High School | Hillcrest | 45.96745 | 5.679928 |
| Hillcrest High School | Hillcrest | 48.66620 | 13.517391 |
| Oakwood High School | Oakwood | 41.34408 | 9.753035 |
| Oakwood High School | Oakwood | 43.68350 | 9.244591 |
| Oakwood High School | Oakwood | 41.67275 | 8.616581 |
| Oakwood High School | Oakwood | 32.22012 | 5.396284 |
| Oakwood High School | Oakwood | 35.53073 | 10.815261 |
| Oakwood High School | Oakwood | 38.83860 | 8.327851 |
| Oakwood High School | Oakwood | 40.58326 | 8.431000 |
| Oakwood High School | Oakwood | 45.69603 | 11.779309 |
| Oakwood High School | Oakwood | 45.36142 | 11.444590 |
| Oakwood High School | Oakwood | 49.60593 | 13.155619 |
| Oakwood High School | Oakwood | 35.91185 | 7.550749 |
| Oakwood High School | Oakwood | 47.79057 | 10.930316 |
| Oakwood High School | Oakwood | 49.71638 | 13.152602 |
| Oakwood High School | Oakwood | 29.56580 | 5.646904 |
| Oakwood High School | Oakwood | 38.93851 | 6.396892 |
| Oakwood High School | Oakwood | 36.78149 | 5.584054 |
| Oakwood High School | Oakwood | 33.67548 | 4.601628 |
| Oakwood High School | Oakwood | 35.45055 | 9.219218 |
| Oakwood High School | Oakwood | 42.16985 | 10.938883 |
| Oakwood High School | Oakwood | 49.07087 | 12.582166 |
| Oakwood High School | Oakwood | 46.35821 | 12.113523 |
| Oakwood High School | Oakwood | 34.98333 | 5.969644 |
| Oakwood High School | Oakwood | 58.42821 | 14.524716 |
| St Mary’s Church of England School | St Mary’s | 39.48171 | 6.978950 |
| St Mary’s Church of England School | St Mary’s | 42.54783 | 9.295812 |
| St Mary’s Church of England School | St Mary’s | 44.95859 | 7.712503 |
| St Mary’s Church of England School | St Mary’s | 44.77387 | 8.612220 |
| St Mary’s Church of England School | St Mary’s | 50.96967 | 9.543849 |
| St Mary’s Church of England School | St Mary’s | 46.57311 | 9.336753 |
| St Mary’s Church of England School | St Mary’s | 54.34814 | 8.903993 |
| St Mary’s Church of England School | St Mary’s | 48.53935 | 9.303488 |
| St Mary’s Church of England School | St Mary’s | 42.13689 | 7.522964 |
| St Mary’s Church of England School | St Mary’s | 42.90107 | 7.466619 |
| St Mary’s Church of England School | St Mary’s | 35.57561 | 3.995973 |
| St Mary’s Church of England School | St Mary’s | 44.78883 | 7.832269 |
| St Mary’s Church of England School | St Mary’s | 38.44711 | 7.441319 |
| St Mary’s Church of England School | St Mary’s | 72.24097 | 17.084943 |
| St Mary’s Church of England School | St Mary’s | 37.95949 | 4.892922 |
| St Mary’s Church of England School | St Mary’s | 49.29009 | 9.391039 |
| St Mary’s Church of England School | St Mary’s | 36.70040 | 4.498395 |
| St Mary’s Church of England School | St Mary’s | 34.26447 | 4.567963 |
| Hillcrest High School | Hillcrest | 49.05039 | 9.353377 |
| Hillcrest High School | Hillcrest | 46.63433 | 5.989353 |
| Hillcrest High School | Hillcrest | 51.74739 | 8.973802 |
| Hillcrest High School | Hillcrest | 43.49421 | 7.694494 |
| Hillcrest High School | Hillcrest | 46.46544 | 7.138255 |
| Hillcrest High School | Hillcrest | 41.27340 | 2.905237 |
| Hillcrest High School | Hillcrest | 42.08927 | 5.305026 |
| Hillcrest High School | Hillcrest | 46.31831 | 9.517820 |
| Hillcrest High School | Hillcrest | 48.92636 | 10.682132 |
| Hillcrest High School | Hillcrest | 48.76119 | 7.500638 |
| Hillcrest High School | Hillcrest | 47.52638 | 8.979459 |
| Hillcrest High School | Hillcrest | 50.46286 | 12.347939 |
| Hillcrest High School | Hillcrest | 54.44885 | 13.298837 |
| Hillcrest High School | Hillcrest | 41.11537 | 5.687929 |
| Hillcrest High School | Hillcrest | 51.49040 | 8.627312 |
| Hillcrest High School | Hillcrest | 51.64673 | 12.583766 |
| Hillcrest High School | Hillcrest | 47.65148 | 7.570081 |
| Hillcrest High School | Hillcrest | 48.73925 | 8.821862 |
| Hillcrest High School | Hillcrest | 48.46442 | 8.720948 |
| Hillcrest High School | Hillcrest | 51.00763 | 6.316233 |
| Oakwood High School | Oakwood | 34.81445 | 7.645218 |
| Oakwood High School | Oakwood | 43.21828 | 8.890936 |
| Oakwood High School | Oakwood | 37.57005 | 7.737664 |
| Oakwood High School | Oakwood | 44.13324 | 12.319428 |
| Oakwood High School | Oakwood | 36.86629 | 7.536292 |
| Oakwood High School | Oakwood | 39.59984 | 7.679763 |
| Oakwood High School | Oakwood | 42.86316 | 11.069858 |
| Oakwood High School | Oakwood | 31.30408 | 5.810165 |
| Oakwood High School | Oakwood | 40.17264 | 8.857175 |
| Oakwood High School | Oakwood | 33.61506 | 4.324636 |
| Oakwood High School | Oakwood | 46.74118 | 12.480779 |
| Oakwood High School | Oakwood | 34.15559 | 8.158333 |
| Oakwood High School | Oakwood | 33.23144 | 7.575734 |
| Oakwood High School | Oakwood | 30.22384 | 5.264513 |
| Oakwood High School | Oakwood | 38.33064 | 8.955984 |
| Oakwood High School | Oakwood | 35.09257 | 6.578424 |
| Oakwood High School | Oakwood | 38.76908 | 7.378793 |
| Oakwood High School | Oakwood | 46.38074 | 12.842296 |
| Oakwood High School | Oakwood | 35.56375 | 8.452693 |
| Oakwood High School | Oakwood | 35.34916 | 5.763923 |
| Oakwood High School | Oakwood | 41.76415 | 9.468891 |
| Oakwood High School | Oakwood | 41.25415 | 7.891055 |
| Oakwood High School | Oakwood | 38.45118 | 10.749311 |
| St Mary’s Church of England School | St Mary’s | 61.09157 | 13.276536 |
| St Mary’s Church of England School | St Mary’s | 43.06366 | 6.001193 |
| St Mary’s Church of England School | St Mary’s | 54.20218 | 10.343221 |
| St Mary’s Church of England School | St Mary’s | 46.20423 | 9.233964 |
| St Mary’s Church of England School | St Mary’s | 58.19549 | 11.665967 |
| St Mary’s Church of England School | St Mary’s | 43.25403 | 8.289936 |
| St Mary’s Church of England School | St Mary’s | 54.10719 | 11.489128 |
| St Mary’s Church of England School | St Mary’s | 35.79491 | 3.744103 |
| St Mary’s Church of England School | St Mary’s | 62.27251 | 14.047647 |
| St Mary’s Church of England School | St Mary’s | 58.20645 | 11.573604 |
| St Mary’s Church of England School | St Mary’s | 45.70714 | 8.526942 |
| St Mary’s Church of England School | St Mary’s | 30.16766 | 4.632249 |
| St Mary’s Church of England School | St Mary’s | 51.17844 | 10.908296 |
| St Mary’s Church of England School | St Mary’s | 49.02100 | 10.428852 |
| St Mary’s Church of England School | St Mary’s | 46.42774 | 8.960203 |
| St Mary’s Church of England School | St Mary’s | 48.29198 | 9.433638 |
| St Mary’s Church of England School | St Mary’s | 42.22076 | 7.226943 |
| St Mary’s Church of England School | St Mary’s | 50.52733 | 10.085690 |
| test_score | study_time | |
|---|---|---|
| Min. :23.99 | Min. : 0.000 | |
| 1st Qu.:38.89 | 1st Qu.: 7.190 | |
| Median :45.97 | Median : 8.891 | |
| Mean :44.77 | Mean : 8.899 | |
| 3rd Qu.:49.37 | 3rd Qu.:10.898 | |
| Max. :72.24 | Max. :17.085 |
The test_score plotted results as the
following.
After looking at the isolated variable, we do now a linear
correlation between the two variables: 0.7493898
Such a correlation does in fact show a
strong positive linear correlation, ince it is very close to 1,
meaning that a longer study time is correlated with the fact that
students who study longer achieve a higher test score on average.
Now we want to look at the relationship between how many hours
students studied (x-axis) and the scores they achieved on a test
(y-axis). For such, we compute the following
scatterplot.
We can notice how the two variables are linearly
correlated to each other.