Eli
In the real business case, the regression model can be deployed to predict how the work/productivity level of an employee increases (changes) with time (e.g. days) according to a set benchmark. HRM can then draw correctly significant factors that affect productivity. This will help the department to adjust itself, motivate factors that increase employee performance and even predict the productivity level of new or future employees more precisely. The result will be increased quality of employees, motivation and high efficiency (rate of delivery) and hence more production. This is one of scenario where we can see the regression analysis in action.
What is regression?
Regression is a means of estimating the relationship between variables. Regression is a frequently used model for prediction and forecasting, it helps us to understand how the change in one variable affects the change in the other variable(s). There are two types of linear regression models, namely simple linear regression, and multiple linear regression.
Simple linear regression is a statistical method that allows us to study and establish the relationships between two continuous (quantitative) variables, usually between the independent variable, also called predictor or explanatory, and the dependent variable also called the response or outcome.
The multiple linear regression is used to explain the relationship between one continuous dependent variable and two or more independent variables. The independent variables can be categorical or continuous. This regression analysis is more realistic because, ideally, many outcomes depend on more than one factor.
Categorical variables represent types of data which may be divided into groups. Examples of categorical variables are race, sex, age group, and educational level.
Continuous variable/data is quantitative and can be measured. It has an infinite number of possible values within a given range, for example, a selected temperature range. This is opposed to discrete data, which is also quantitative but can be counted and has a finite number of possible values, for example, days of the week.
Linear regression employs the least squares technique which reduces the distance between a line/curve and its data points. One of these approaches is called the Ordinary Least Square (OLS). OLS targets to find the parameters that minimize the sum of the squared errors, which is the distance between the predicted values (values on the curve/line) and the actual values (data points or values that we have at hand). The result is the difference known as the error term. We can thus fit the regression line with a set of observations by using the least squares method.
The approach begins with the equation of the straight line
\begin{equation}
y = mx + c
\end{equation}
where \( y \) is dependent variable, \( m \) is the slope/gradient, \( x \) is the independent variable, and \( c \) is the \( y \) intercept. The intention is then to minimize the functional \( F \) such that
\begin{equation}
F = \sum_{i =1 }^{N} \Big( y_{i} - \hat{y} \Big)^{2}
\end{equation}
where \(y_{i}\) is the actual value and \(\hat{y} \) is the predicted value.
Let's now use excel to demonstrate how an HRM can use the regression analysis to find out if there is any correlation which indicates that an increase in salary motivates employee performance. We will use a Google spreadsheet in this example. We assume that the HRM has drawn values from the employees' raw performance data and presents the scores alongside their salary increment as shown in the spreadsheet below:
Steps:
1. First, select the data by simply clicking on it; the selected data range will be A1:B13. In most cases, data selection will be picked automatically.
2. Go to Insert -> Chart, then choose a Chart type to "Scatter Chart", tick the "Aggregate" and "Use row 1 as headers" boxes, do all these under Chart editor -> Setup. See the dialog box as shown below that will open on the right-hand side of the spreadsheet,
and populate the below scatter chart.
3. Right-click the scatter plot and choose "Chart style" or switch to customize under Chart editor. Click on Chart and axis titles and customize, similarly, click on Legend, Horizontal axis, Vertical axis, and Gridlines and customize as appropriate.
4. Add the regression line by clicking "Series" and tick "Trendline"; below Type, choose "Linear", and below Label, choose "Use Equation". You can add error bars by ticking "Error bars". Finally, tick "Show \(R^2\)" to calculate the correlation coefficient. See screenshots below:
The final plot will look as below:
- Performance score vs salary increment_2.png (15.82 KiB) Viewed 4420 times
- Performance score vs salary increment_2.png (15.82 KiB) Viewed 4420 times
You can now apply the regression analysis with excel to your real organization data to help you make various decisions and choices.
NB: To delete or download chart from the Google spreadsheet, follow these steps:
Step 1: Click on the object to select it.
Step 2: Click the three dots at the top right of the chart or graph, then choose the Delete/Download chart option.
