Table 7 Summary of ANOVA results for COVID-19 cases per day in states of India: (a) Maharashtra (b) Karnataka and (c) T and P values for Maharashtra and Karnataka.

From: Exploring dependence of COVID-19 on environmental factors and spread prediction in India

Source

DF

 

Seq SS

Adj SS

 

Adj MS

F

P

(a) Maharashtra

 Regression

5

 

28.2979

28.2979

 

5.65958

121.55

<0.001

 Linear

2

 

26.6721

5.7102

 

2.85511

61.32

<0.001

 X1

1

 

0.0002

0.8593

 

0.85933

18.46

<0.001

 X2

1

 

26.6718

5.6886

 

5.68862

122.17

<0.001

 Square

2

 

1.4279

1.2234

 

0.61169

13.14

<0.001

 X1*X1

1

 

0.0405

0.0286

 

0.02863

0.61

0.435

 X2*X2

1

 

1.3874

1.1481

 

1.14813

24.66

<0.001

 Interaction

1

 

0.1979

0.1979

 

0.19794

4.25

0.041

 X1*X2

1

 

0.1979

0.1979

 

0.19794

4.25

0.041

 Residual error

119

 

5.541

5.541

 

0.04656

  

 Total

124

 

33.8389

     

S = 0.215785 PRESS = 6.11034 R-Sq = 83.63% R-Sq(adj) = 82.94%

(b) Karnataka

 Regression

5

 

12.6119

12.6119

 

2.52238

28.09

<0.001

 Linear

2

 

9.4486

2.9548

 

1.47741

16.45

<0.001

 X1

1

 

7.0128

0.612

 

0.61202

6.82

0.01

 X2

1

 

2.4358

1.1516

 

1.15155

12.83

0.001

 Square

2

 

2.8456

1.4256

 

0.71278

7.94

0.001

 X1*X1

1

 

0.8792

0.1598

 

0.15981

1.78

0.185

 X2*X2

1

 

1.9664

1.0323

 

1.03227

11.5

0.001

 Interaction

1

 

0.3177

0.3177

 

0.31771

3.54

0.063

 X1*X2

1

 

0.3177

0.3177

 

0.31771

3.54

0.063

 Residual error

105

 

9.4279

9.4279

 

0.08979

  

 Total

110

 

22.0398

     

S = 0.299649 PRESS = 10.3891 R-Sq = 57.22% R-Sq(adj) = 55.19%

(c) Terms

Maharashtra

Karnataka

Coef

SE Coef

T

P

Coef

SE Coef

T

P

Constant

−0.70846

0.05398

−13.125

<0.001

−0.816

0.08533

−9.563

<0.001

X1

0.43807

0.10197

4.296

<0.001

0.9819

0.37611

2.611

0.01

X2

0.69336

0.06273

11.053

<0.001

1.3233

0.3695

3.581

0.001

X1*X1

0.09904

0.12631

0.784

0.435

0.6901

0.51729

1.334

0.185

X2*X2

0.82839

0.16683

4.966

<0.001

1.3987

0.41251

3.391

0.001

X1*X2

0.5833

0.28291

2.062

0.041

1.6627

0.8839

1.881

0.063

  1. Note: X1: Temperature, (°C); X2: Relative Humidity, %; both in coded units
  2. The Analysis of Variance (ANOVA) helps understand the significance of the input parameters, i.e., Temperature and Relative Humidity on the response variable, i.e., COVID-19 cases per day. DF represents the degree of freedom from each source term in the model, Seq SS represents sequential sum of squares between the input variables (factor) and within the group (error). Adj MS represents Adjusted Mean Square, which is a ratio of SS/DF and F is calculated by dividing factor MS by MS of the residual error. The term Seq. SS, Adj. SS and Adj. MS, explain the model variability explained by each term of the response surface methodlogy (RSM) model.The significance of the each terms in the full quadratic RSM model is interpreted by F, T and P values, where high values of T and F (against a critical values T and F, computed from T and F tables for two-tailed test) and p < 0.05 at 95% confidence interval denotes the significant impact of the variable on the response. The R-sq (regression coefficients) and Adjusted R-sq (within 10% of the R-sq value), explains good model adequacy of the RSM model to map the responses (outputs) against the inputs variable. S represents the how far the actual data fall from the RSM fitted values.
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