RSQ
Returns the square of the Pearson correlation coefficient of two sets of data.
Syntax:
RSQ(x, y)
where x and y are ranges or arrays containing the two sets of data.
Any text or empty entries are ignored.
RSQ calculates the square of the Pearson correlation coefficient (which is conventionally given the letter r, hence "r squared").
RSQ indicates how much of the variance in y is attributable to the variance in x.
Example:
RSQ(A1:A30, B1:B30)
returns the square of the Pearson correlation coefficient for the two sets of data in A1:A30 and B1:B30.
Application:
A company wants to determine if the number of hours an employee spends in professional development training has a significant impact on their annual performance review scores. They collect data for 10 employees, tracking their total training hours for the year and their corresponding performance scores (on a scale of 1-100).
The Data Table:
Employee ID | Training Hours (Independent Variable, X) | Performance Score (Dependent Variable, Y) | ||
|---|---|---|---|---|
A | B | C | ||
1 | 1 | 25 | 78 | |
2 | 2 | 10 | 65 | |
3 | 3 | 40 | 92 | |
4 | 4 | 15 | 70 | |
5 | 5 | 30 | 85 | |
6 | 6 | 5 | 60 | |
7 | 7 | 20 | 75 | |
8 | 8 | 35 | 88 | |
9 | 9 | 50 | 95 | |
10 | 10 | 18 | 72 |
Applying the RSQ Function:
The function takes the known Y-values (Performance Scores) and the known X-values (Training Hours) as its arguments.
The formula would look something like this: RSQ(C1:C10, B1:B10)
- C1:C10 represents the range of Performance Scores (Y-values).
- B1:B10 represents the range of Training Hours (X-values).
Interpretation of the Result:
The calculation yields an RSQ value of 0.975035873.
This result means that 97.5% of the variation in employee performance scores can be explained by the number of training hours they completed.
Context:
- Strong Relationship: A high RSQ value (close to 1) indicates a strong positive relationship between the two variables. In this case, there is a clear trend: as training hours increase, performance scores tend to increase as well.
- Predictive Power: The company can be confident that investing in employee training is a good strategy to improve overall performance.
- The Other 2.5%: The remaining 2.5% of the variance in performance scores is due to other factors not included in the model. These could be things like:
- Years of experience
- Job satisfaction
- Team collaboration
- Management quality
- Personal aptitude
Conclusion:
This RSQ analysis provides the HR department with data-driven evidence to support increasing the training budget and encouraging employee participation in professional development programs. It demonstrates a clear and quantifiable return on investment for the company's training initiatives.
Result for RSQ(C1:C10, B1:B10):
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