tanaka-geek / JPN-covid19-stats

Japan covid-19 correlation matrix analysis

Stage 1

The dataset is obtained from kaggle

This is a covid-19 dataset in Japan. The dataset include the following.

• Total number of cases in Japan
• The number of cases at prefecture level
• Metadata of each prefecture

There are attributes for respective dataset. The variables are the following.

• Date : YYYY-MM-DD
• Prefecture : char
• Positive : int
• Tested : int
• Discharged : int
• Fatal : int
• Hosp_required : int
• Hosp_severe : int

Additionally, I have added one variable Active_Case to track the actual positive cases. Active_Case = Positive - Discharged

There is no other missing data or errors (NA etc) in this dataset.

Basic Distribution Graph

Stage 2

Compute Central Tendency and Variability Measures

In our dataset, the variable Positive of the latest date is picked. As per boxplots/hisogram of this variable, the following factors are discovered.

• Mode : It is extremely higher (5.2k)and derivative scalar in the graph. This is due to the fact that Tokyo has so much higher infection rate and population.

• Median : This was (161) in Hyogo Prefecture.

• Mean : The average positive cases is (434.4) among 47 prefectures. This is higher than Median value '161'. It can be inferred that there are scalar values Positive with significant higher values which gives a skew to this Mean and Median values in comparison.

Central tendency

Stage 3

Compute correlation matrix.

Correlation Analysis

Correlated variables are the following

• Fatal and Hosp_require
• Positive and Population

Fatal and Hosp_require are correlated since the more people are in severe infected condition, the fatality cases are likely to increase.

Positive and Population are also correlated because the more population means higher probablity of infection.

However, it is observable that Hosp_severe is only correlated with Fatal and shares lower correlation rate with other variables.

Presumably, Severe cases on covid-19 is due to the fact that although many population can be infected, only minority number of the infected experience severe cases because of variant factors such as their age, pre-medical condition and limited treatment in the hospital in country-side area.

Therefore, We can conclude that Hosp_severe is indepent variable except with Fatal.

We also conclude for dependent variable in this dataset is Positive and the rest are more or less dependent variables except Hosp_severe

Stage 5

After multiple linear regression analysis, Positive is defined as dependent variable.

However, straight regression line is not able to calculate the patterns which in the dataset is underfitting. In order to resolve this issue, the complexity of the model must be increased which the original features of the model are converted into the higher order polynomial terms. This operation is possible with the help of scikit-learn module.

The model is trained with 70-30 ratio.

According to the different types of regression models used for the analysis, the R-squared gets the value around 0.80~. This almost represents a model that explains all of the variation in the response variable around its mean.

Various analysis are conducted by using Linear and Polynomial Regression Models. The x variable is Positive and Date (Dataframe Date's Index Values) Caution for the Date, it is converted into the number of days passed. (Integer)

X = pd.DataFrame(np.c_[df.Positive], columns=['Infect Toll'])
Y = df.index.values

Linear Regression coefficient was calculated as 0.00162564

RMSE, R2's value and MAPE are calculated respectively.

Root Mean Square Error is higher in Linear Model since there's considerable deviation in predicted values. Mean Absolute Percentage Error is significantly lower in the Polynomial Model because of the dataset with 80% pf R-squared percentage.

The Linear Model's performance for training:

• RMSE : 35.755953979357685
• R2 : 0.8491951960374975

The Linear Model's performance for testing:

• RMSE : 31.36388399092678
• R2 : 0.8816123287196085
• MAPE: 39.87470903917527

The graph analysis

The Polynomial Model's performance for training:

• RMSE : 21.040343639302094
• R2 : 0.9477815358294585

The Polynomial Model's performatnce for testing:

• RMSE :17.514006809561216
• R2 :0.9630837287177351
• MAPE: : 18.110589685632135

Redisual Plot

Residuals in regression models are basically the difference between the observed value of the target variable Positive and the predicted value Date in this case.

The Linear Model's Performance on Redisual Compulation

The Polynomial Model's Performance on Redisual Compulation

Deviation between Training and Testing in Residuals Plot