What is Linear Regression and How Do You Interpret the R-Squared Value?

Understanding linear regression and the R-squared value is crucial for data-driven professionals seeking to validate relationships between variables, such as identifying key factors that predict employee performance or turnover. The R-squared value quantifies the strength of this relationship, with a value above 0.75 often indicating high statistical significance. This guide explains how to perform the analysis and interpret the results for actionable insights.

What is Linear Regression Analysis?

Linear regression analysis is a foundational statistical method used to model the relationship between a dependent variable and one or more independent variables. In a recruitment context, the dependent variable (or response variable) could be an employee's first-year performance score. The independent variable (or explanatory variable) might be their pre-employment assessment score. The goal is to determine how much of the change in the dependent variable (performance) can be explained by a change in the independent variable (assessment score). It's critical to remember that regression identifies correlation, not necessarily causation. The outcome is a linear equation (y = mx + b) that produces a best-fit line through the data points.

How Do You Interpret the R-Squared Value?

The R-squared value, also known as the coefficient of determination, is a key output of linear regression. It is a statistical measure that represents the proportion of the variance for the dependent variable that's explained by the independent variable(s) in the model. The value ranges from 0 to 1 (or 0% to 100%).

• R-squared = 1 (or 100%): The independent variable perfectly explains all the variance in the dependent variable. In practice, this is extremely rare.
• R-squared = 0.75 (or 75%): This suggests a strong relationship, meaning 75% of the variance in the dependent variable is predictable from the independent variable. Based on our assessment experience, this is often considered a threshold for a meaningful relationship in HR analytics.
• R-squared = 0.50 (or 50%): This indicates a moderate relationship.
• R-squared = 0.25 (or 25%): This suggests a weak relationship.
• R-squared = 0: The independent variable explains none of the variance in the dependent variable.

A higher R-squared value generally indicates a more statistically significant and useful model for prediction.

How to Calculate Linear Regression and R-Squared in Spreadsheets?

You can efficiently perform linear regression using common spreadsheet tools like Microsoft Excel or Google Sheets. Here’s a streamlined process:

1. Prepare Your Data: Organize your data into two columns. For example, place pre-employment assessment scores (independent variable) in column A and subsequent performance ratings (dependent variable) in column B. Ensure each row represents a paired data point for a single candidate or employee.

2. Use Built-in Tools: Both platforms automate the calculation.

• In Microsoft Excel: Use the Data Analysis toolpak (requires activation via File > Options > Add-ins). Select Regression from the list, define your Y (dependent) and X (independent) data ranges, and specify an output location. The results will generate a new sheet with the R-squared value and the regression equation coefficients.
• In Google Sheets: Use the LINEST function. For example, if your performance data is in B2:B100 and assessment data in A2:A100, the formula =LINEST(B2:B100, A2:A100, TRUE, TRUE) will return an array of statistics, including the R-squared value.

3. Locate and Analyze the Key Metrics: After running the analysis, find the R-squared value in the output. In Excel, it's under 'Regression Statistics'. In Sheets, it's typically the middle value in the left column of the LINEST output. Analyze this value in the context of your data. For instance, if you are testing if years of experience predicts salary, a high R-squared would give you confidence in that relationship.

What Should You Check After Getting the Results?

Beyond the R-squared value, a thorough analysis involves checking for residuals—the differences between the observed data points and the values predicted by your regression line. Most spreadsheet tools can generate a residual plot. A healthy model shows residuals randomly scattered above and below the zero line. If residuals display a pattern (e.g., a U-shape), it may indicate your linear model is incomplete, and other variables or a different type of analysis might be needed.

To effectively use linear regression in talent analytics, focus on these steps: clearly define your hypothesis, ensure you have a sufficient sample size, interpret the R-squared value cautiously as it does not prove causation, and always examine residual plots to validate your model's assumptions. This method provides a powerful, objective way to support data-informed hiring and talent management decisions.

Please note that none of the companies, institutions or organisations mentioned in this article are affiliated with ok.com.