Linear Regression Model for Predictions of COVID-19 New Cases and New Deaths Based on May/June Data in Ethiopia

Introduction: On the 15 th of June 2020, we have 7,984,067 total COVID-19 cases, globally and 435,181 deaths. Ethiopia was ranked 2 nd and 15 th in the table by 176 new cases and by 3,521 total new cases from African countries. Then, this study aimed to predict COVID-19 new cases and new deaths based on May/June data in Ethiopia using a linear regression model. Methods: In this study, I used Pearson’s correlation analysis and the linear regression model to predict COVID-19 new cases and new deaths based on the available data from 12 th May to 10 th June 2020 in Ethiopia. Results: There was a significant positive correlation between COVID-19 new cases and new deaths with different related variables. In the multiple linear regression model, variables such as the number of days, the number of new laboratory tests, and the number of new cases from AA city significantly predicted the COVID-19 new cases. In this model, the number of days and new recoveries significantly predicted new deaths of COVID-19. Conclusions: The number of days, daily laboratory tests, and new cases from Addis Ababa city significantly predicted new COVID-19 cases, and the number of days and new recoveries significantly predicted new deaths from COVID-19. According to this analysis, if strong preventions and action are not taken in the country, the predicted values of COVID-19 new cases and new deaths will be 590 and 12 after two months (after 9 th of August) from now, respectively. The researcher recommended that the Ethiopia government, Ministry of Health and Addis Ababa city administrative should give more awareness and protections for societies, and they should also open more COVID-19 laboratory testing centres. Generally, the obtained results of this study may help Ethiopian decision-makers put short-term future plans to face this epidemic. the by using a comparison of linear regression and nonlinear regression models.

(COVID-19 new cases from 12th of May to 10th of June, 2020) and independent variables.
Each univariate analysis in the linear regression model is used to show how much each independent variable will be predicted by the dependent variable. Multivariate analysis was also used to determine the most predicator variables for th total number of COVID-19 new cases from 12th May to 10th June 2020 in Ethiopia.
Where is the total number of COVID-19 new cases and 1 , 2 ,..., and are p-independent. 0 , 1 , 2 , … , are the intercept and coefficients of the variables, respectively. is the error term in the model. times greater from 12 th May to 10 th June than from 14 March to 11 May in Ethiopia, 2020. New deaths peaked at 7 deaths on June 7 th in 2020.

Recovery rate:
The recovery rates were 16% (401) and 13% (294) from 14 March to 10 June and from 12 May to 10 June, respectively. In addition, 73.3% of the total recovered cases were reported from 12th May to 10th June in Ethiopia, 2020.  respectively. All these histories of the cases were considered from May 12 th to June 2 nd , 2020.  per day with its min (1,775) and max (6,187) in the given duration.  The fitted models for new deaths due to COVID-19:̂=̂+̂, = , , , … , .
➢ New deaths will be increased by 12 after 100 days.
➢ New deaths will be increased by 100 if 100,000 laboratory tests are conducted.
➢ New deaths will be raised by 16 when the new cases increase to 1000.
➢ New deaths will be increased by 104 if 1,000 cases are recovered. This may be due to other corresponding reasons.
➢ New deaths will be raised by 30 as the new cases of males increase by 1,000.
➢ New deaths will be raised to 40 when the new cases of females increase by 1,000.
• Comparing the deaths by sex groups, the female group will count more deaths.
➢ New deaths will be increased to 200 for 10,000 new cases from Addis Ababa city.
➢ New deaths will decline to 1 when the minimum age of the case is increased by 10.
➢ New deaths will be raised to 0.4 when the maximum age of the case is increased by 10.

Multiple Linear Regression (MLR) Model for COVID-19 New Cases
In this model, COVID-19 new cases were predicted significantly by the number of days, daily laboratory tests and new cases from Addis Ababa city at the 5%, 10% and 1% levels of significance, respectively.  (Figure 1, R-software output).

Multiple Linear Regression (MLR) Model for New Deaths due to COVID-19
In this model, new deaths due to COVID-19 were predicted significantly by the number of days and new recoveries at the 10% and 1% levels of significance, respectively.  (Figure 2, R-software output).  A study from India used a linear regression analysis to predict the average week 5 and 6 death counts. In the study, there was a strong correlation between weeks 5 and 6 death counts with total cases, active cases, recoveries, and week 4 death counts. Despite this, the week 4 variables (total cases, active cases, and recoveries) were not significantly predicted by weeks 5 and 6 deaths count. However, the week 4 death count significantly predicted the week 5 death count.
Therefore, my study agreed with this study on the correlation analysis but not on the linear regression analysis [10].
Another study from India used simple linear regression analysis of the number of deaths as a function of the number of confirmed cases. In this study, the coefficient of determination (R 2 ) was calculated to be 0.997, which implies a strong linear correlation between confirmed and dead cases [11]. My study also found that there was a moderate linear correlation between new

How does this analysis help?
The study used simple and multiple linear regression models to predict COVID-19 new cases as the number of days (reported date) increased, as the number of daily laboratory tests increased, and as the number of new cases from Addis Ababa city increased. It is also used to predict new deaths as the number of days increases, as the number of new cases increases, and as the maximum and minimum ages of new cases increase. I speculate the need for more urgent interventions (which are being taken again now) to prevent these extreme increments and spread through the country, especially in Addis Ababa city. More recommendations are mentioned below.

Limitations of this analysis
The main limitation of this analysis was that the data were not found together as collectively for all the previous reports and were taken from the face book and telegram pages of Ethiopia Ministry of Health. Second, limiting my analysis was that some data values were missed to report for 8 dates (such as the contact and travel history of the cases).

Strength of the study
Despite all the limitations, the greatest strength of this study was the very high adjusted R 2 found in the predictive model. Three predictors for COVID-19 new cases were found in the multiple linear regression model, and its assumptions were fitted. In addition, there was crossvalidation with two different software programs (R and SPSS).

Conclusions
There were 2,506 total COVID-19 cases and 35 deaths due to COVID-19 with a crude mortality of 1.4% from 14th march to 10 th June in Ethiopia, 2020. However, the total cases and total deaths of COVID-19 were 10 times and 6 times more, respectively, from the 12 th of May to the 10 th of June compared to the 14th of March to the 11 th of May 2020 in Ethiopia.
In the correlation analysis, the Finally, according to this analysis, if strong preventions and action are not taken in the country, the predicted values of COVID-19 new cases and new deaths will be 590 and 12 after two months (after 9 th of August) from now, respectively.

Recommendations
Even if Ethiopia has taken strong measures, including complete lockdown of both its internal and external borders and announced the command posts and keeping social isolation for the last three months, the number of new cases and deaths due to COVID-19 new cases were highly increased day to day. The research has predicted the total number of COVID-19 new cases where it is easy to see how it is likely to progress in the future. The above information should help the government make plans on how to deal with pandemics, especially when dealing with the current situation in Ethiopia.
The prevalence of the disease and its crude mortality from 12th May to 10th June 2020 increased more and more, and Ethiopia might be one of the top countries from Africa by leading this Pandemic for the next months if very strong necessary measures will not be taken into consideration. The government must come up with more isolation beds, more trained health care professionals, and more mass education and campaigns with the aim of ensuring that the public has information about how to stop the spread of the virus. Let us consider that a huge population of the Ethiopia population lives in rural areas, more education as well as infrastructure must be done in the rural area to make preparations in case the COVID-19 finds its way more for the districts and the villages.
Moreover, the Ethiopia government, the Ministry of Health and Regional Governments (especially the AA city administrative and Somali region) should give more awareness and protections collaboratively for societies, and they should also open more COVID-19 laboratory testing health centres in different areas of the country to ensure that those health centres can test