Keerthi vasan

Yes, although it's rare but it is possible for the value to be zero- it means the independent variables don't explain any variability in the dependent variable. Some reasons are below:

1. Selection of incorrect controllable variables
2. Non linearity relationship between variables

Examples

1. Selection of incorrect independent variables
 
     Modelling company top line as dependent variable and employee birthday as independent variable. Since both the variables are completely unrelated, the results would be skewed.

2. Non linearity
 
     Creating a model using delivery time as output variable and inventory level as input variable (this is because of impact of other parameters like traffic, breakdown etc.). This can be solved by using polynomial or non linear regression model.

Correlation shows the direction (positive or negative) and strength (strong, weak or null) of relationship between two variables. It is represented using correlation coefficient. Its value lies between -1 to +1; higher the magnitude, stronger the relationship between variables. Types of correlation coefficient are as follows:
 

 
There can be cases wherein the correlation coefficient is zero for a known cause and effect relationship - this is because of the following reasons:
 
1. Non linear relationship between variables 
    One assumption while working with Correlation coefficient and regression is that there is a linear relationship between variables. If this assumption is violated, the correlation coefficient values can vary significantly.
 
2. Interaction effect
    Interaction between the variables in consideration and other external variables can cause the correlation coefficient to be zero.
 
(Example) In ecommerce, customer satisfaction is poor for slow deliveries. As delivery time improves, the customer satisfaction improves significantly at first. Beyond a certain point any improvement in delivery time will not impact the customer satisfaction - satisfaction will be affected by other variables like quality, customer support, pricing etc. thereby dropping the coefficient value close to zero despite a known cause and effect relationship

The concept of control limits in statistical process control says that control limits are not arbitrarily determined but are instead based on data and statistical analysis. These limits are initially set to reflect the process's historical performance, and they represent the typical variation in the process under stable conditions. Control limits can be influenced or adjusted when process improvements or changes occur. This practice ensures that control charts remain relevant and effective in monitoring the process's ongoing performance and aligning with the principles of continuous improvement.
 
Example

In a roulette game in Casino, the control limits can be set by management based on roulette wheel design. In case the Casino notices an unusual pattern, they can influence the control limits by recalibration / changing to a new wheel. This proves that control limits are not rigid but can be adjusted to maintain the integrity of the game

Attribute Agreement Analysis (AAA) is a statistical method used to assess the level of agreement among different individuals. It is used in cases wherein measurement value has finite number of categories (discrete data). 
 
Parameter used to evaluate level of agreement
 
Fleiss Kappa 

    - Used for nominal data
    - Higher the value of Kappa, stronger the association
    - Absolute agreement between ratings
    - Ranges from 0 to 1 (although negative values is also possible)
 
Kendall's coefficient

    - Used for ordinal data
    - Higher the value, stronger the association
    - Association between ratings
    - Ranges from -1 to +1
 
Cohen's Kappa 

    - Similar to Fleiss Kappa except that there are only two individuals / evaluators
 
Meaning of caution
 
A caution results when Kappa value is greater than 0.7 but less than 0.9. It indicates a moderate level of inconsistency / disagreement among individuals in evaluation. It suggests there can be some issues with reliability of evaluation process. 
 
Steps to improve consistency
 
1. Source of disagreement
    Need to understand why there is a moderate level of inconsistency. If all evaluators have moderate scores, there might be a need to change the measurement system.
 
2. Evaluate training
    Review the training and instructions provided to evaluators. If only few evaluators have moderate scores, they can be trained. In case of poor between evaluators score, all evaluators can be trained. 
 
3. Addition of more evaluators
    Try adding more evaluators to improve the reliability. Rerun AAA to check if the change brings in improvement.