Q 619. R-squared (R-sq) is the most sought after number after doing Regression. While potentially R-sq can range from 0% to 100%, could there be a situation where it is 100%? Provide examples to support your answer.

 

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R squared determines goodness of fit or in other words is a coefficient of determination.
Here we need to understand if R2 is 100% meaning it holds a value of 1, then what is inferred.
This can be explained with the help of below diagram

Chart 1 would show us that how closely the values in orange variable Y are dependent on blue variable X meaning a high score of R2

 

 

On the other hand, Chart 2 would show us that how near or far the values in orange variable Y are dependent on blue variable X meaning a slightly lower score of R2 
 

Let us observe in Chart 2 where X is 6 . That is the difference between X and Y meaning that the observed values are deviated from the regression line/data set. 
 

If it was same as a value of 6 for both and all other data points holding same value corresponding to X in Y, then it means there is no variation between X and Y and these are closely tied. In reality, it would be highly impossible that the two correspond to each other and equate an R2 value of 1.

Examples of such an industry would obviously not be from pathological labs but can be where data sets are whole numbers. For example X hit Z because Y asked to do it and so on. Typically high R2 would not denote a very good sign for anything as more is relied upon value of p.
 

Few of the answers to this question could not be approved as they either failed in AI generated content or in plagiarism. From the published answers, unfortunately none of them provide the correct answer, hence there is no winner to this question.

 

R-sq or R-sq (adj) value of 1 is practically impossible to get as there will always be some variation in the observed data points while there will be no such variation in the predicted value (calculated from the equation).

This is an interesting question. R-squared should ideally reflect the % of the dependent variable that can be explained via the independent factors. 

Now think what happens when the independent variable is the factor used to calculate using the dependent variable?

 

Example: Poverty as a function of Income, or Cost as a function of time.