Multiple Linear Regression
Expert-defined terms from the Professional Certificate in Regression Analysis in Human Resources course at London School of Planning and Management. Free to read, free to share, paired with a globally recognised certification pathway.
Multiple Linear Regression #
Multiple linear regression is a statistical technique used to understand the rel… #
It is an extension of simple linear regression, where only one independent variable is used to predict the dependent variable.
In multiple linear regression, the relationship between the independent variable… #
The model takes the form:
Y = β0 + β1X1 + β2X2 + #
.. + βnXn + ε
Where: #
Where:
- Y is the dependent variable #
- Y is the dependent variable
- X1, X2, #
.., Xn are the independent variables
- β0 is the intercept #
- β0 is the intercept
- β1, β2, #
.., βn are the coefficients for the independent variables
- ε is the error term #
- ε is the error term
The goal of multiple linear regression is to estimate the coefficients (β) that… #
The goal of multiple linear regression is to estimate the coefficients (β) that best fit the data and use them to make predictions about the dependent variable.
Assumptions of Multiple Linear Regression #
1. Linearity #
The relationship between the independent variables and the dependent variable is linear.
2. Independence #
The errors are independent of each other.
3. Homoscedasticity #
The variance of the errors is constant across all values of the independent variables.
4. Normality #
The errors are normally distributed.
5. No multicollinearity #
The independent variables are not highly correlated with each other.
- Simple Linear Regression: A regression analysis that involves only one indepen… #
- Simple Linear Regression: A regression analysis that involves only one independent variable.
- Coefficients: The values that represent the relationship between the independe… #
- Coefficients: The values that represent the relationship between the independent variables and the dependent variable.
- Interactions: The relationship between two or more independent variables that… #
- Interactions: The relationship between two or more independent variables that affect the dependent variable differently when combined.
- Residuals: The differences between the observed values and the values predicte… #
- Residuals: The differences between the observed values and the values predicted by the regression model.
Example #
Suppose a human resources manager wants to predict employee performance based on… #
They can use multiple linear regression to build a model that estimates how these variables are related to employee performance.
In this example, the dependent variable would be employee performance, while the… #
By analyzing the coefficients of these variables, the manager can determine which factors have the most significant impact on employee performance.
Practical Applications #
- Human Resources: Predicting employee turnover, performance, and satisfaction b… #
- Human Resources: Predicting employee turnover, performance, and satisfaction based on various factors such as training, compensation, and work environment.
- Marketing: Forecasting sales based on advertising spending, market size, and c… #
- Marketing: Forecasting sales based on advertising spending, market size, and competitor data.
- Finance: Predicting stock prices based on market trends, interest rates, and c… #
- Finance: Predicting stock prices based on market trends, interest rates, and company performance.
Challenges #
- Overfitting: Including too many independent variables in the model can lead to… #
- Overfitting: Including too many independent variables in the model can lead to overfitting, where the model performs well on the training data but poorly on new data.
- Nonlinearity: If the relationship between the independent variables and the de… #
- Nonlinearity: If the relationship between the independent variables and the dependent variable is not linear, a different regression technique may be more appropriate.