Question
In: Statistics and Probability
The table below shows the data of the new type of virus disease (COVID-19) from 11...
The table below shows the data of the new type of virus disease (COVID-19) from 11 March 2020, the day when the first case occurred in our country, until 21 April 2020, when the virus peaked. In response to these data, the number of patients recovering within the same time frame is given. Find a 2nd order polynomial equation (Ŷ = a0 + a1 x + a2 x2) that fits these data. Then calculate the correlation coefficient. Using the parabola equation, find a regression curve for the number of patients recovering based on the number of cases. Also, estimate when the number of cases will end according to these data.
| DAILY CASE NUMBER(Y) | DAILY HEALING PATIENTS(x) | x^2 | |
| 11-Mar | 0 | 1 | 1 |
| 12-Mar | 0 | 0 | 0 |
| 13-Mar | 0 | 4 | 16 |
| 14-Mar | 0 | 1 | 1 |
| 15-Mar | 1 | 12 | 144 |
| 16-Mar | 1 | 29 | 841 |
| 17-Mar | 2 | 41 | 1681 |
| 18-Mar | 3 | 93 | 8649 |
| 19-Mar | 4 | 168 | 28224 |
| 20-Mar | 9 | 311 | 96721 |
| 21-Mar | 21 | 277 | 76729 |
| 22-Mar | 30 | 289 | 83521 |
| 23-Mar | 37 | 293 | 85849 |
| 24-Mar | 44 | 343 | 117649 |
| 25-Mar | 59 | 561 | 314721 |
| 26-Mar | 75 | 1196 | 1430416 |
| 27-Mar | 92 | 2069 | 4280761 |
| 28-Mar | 108 | 1704 | 2903616 |
| 29-Mar | 131 | 1815 | 3294225 |
| 30-Mar | 168 | 1610 | 2592100 |
| 31-Mar | 214 | 2704 | 7311616 |
| 1-Apr | 277 | 2148 | 4613904 |
| 2-Apr | 356 | 2456 | 6031936 |
| 3-Apr | 425 | 2786 | 7761796 |
| 4-Apr | 501 | 3013 | 9078169 |
| 5-Apr | 574 | 3135 | 9828225 |
| 6-Apr | 649 | 3148 | 9909904 |
| 7-Apr | 725 | 3892 | 15147664 |
| 8-Apr | 812 | 4117 | 16949689 |
| 9-Apr | 908 | 4056 | 16451136 |
| 10-Apr | 1006 | 4747 | 22534009 |
| 11-Apr | 1101 | 5138 | 26399044 |
| 12-Apr | 1198 | 4789 | 22934521 |
| 13-Apr | 1296 | 4093 | 16752649 |
| 14-Apr | 1403 | 4062 | 16499844 |
| 15-Apr | 1518 | 4281 | 18326961 |
| 16-Apr | 1643 | 4801 | 23049601 |
| 17-Apr | 1769 | 4353 | 18948609 |
| 18-Apr | 1890 | 3783 | 14311089 |
| 19-Apr | 2017 | 3977 | 15816529 |
| 20-Apr | 2140 | 4674 | 21846276 |
| 21-Apr | 2259 | 4611 | 21261321 |
i konw how to do it with excel so pls dont do it with excel!
Solutions
Expert Solution
The following matrix and vector are defined in order to conduct the matrix calculation required to compute the estimated multiple regression coefficients:
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