Regression

Description

Regression analysis helps determine if there is a relationship between two or more variables; it is concerned with the problem of describing or estimating the value of the dependent variable on the basis of one or more variables.

Benefits

• Creates a mathematical model capable of predicting the response of the dependant variable to a change in the input (independent or predictor variable)
• Easily done with appropriate software application
• Applies to variable and attribute data
• Applicable to many problems in the service industry (finance, sales, marketing, etc.)

How to Use

• Step 1.  Collect data.
• Step 2.  Structure the data for analysis (most applications require that the data be in columns).
• Step 3.  Run the regression analysis.
• Step 4.  Draw your conclusion based on the graph, mathematical model, correlation index, and hypothesis testing results.
• Further possible steps: Validate the model by re-running the process at known/fixed settings to predict the response. Check the results.

Relevant Definitions

Input, predictor or independent variable: A variable or factor that you control and can change (for example, time spent studying).

Output, response, or dependent variable: A variable that responds to changes in the input (for example, exam results).

Correlation: Interdependence between variables, or how one can or cannot influence the other. If the output varies proportionally to the input, it is said that they are strongly correlated (for example, force applied to the brake pedal and braking distance).

Example

A large retail store is considering a major expansion in many different towns and is preparing a hiring plan. The human resources manager wants to know what strategy to take considering that the corporation requires that the new stores become profitable within a few months after opening.

Based on past experience and tribal knowledge, management wants to hire sales people experienced with similar merchandise rather than young people without experience. Hiring experienced people will require more screening, research, and recruitment time and will increase the payroll.

The management team seeks to learn if the level of sales really depends on employee experience or not. The entire recruiting strategy depends on this information.

All available data are pulled from the accounting system to determine if there is a direct relationship between the predictor (years of experience) and the response (value of sales) using regression analysis.

Below is a summary of the data showing average sales (in \$100.00) based on years of experience in retail sales. The average number of years of experience comes from more than 1,000 employees working the floor at various locations.

The regression analysis (fitted line plot graph) shows that there is a very strong correlation between the years of experience and the level of sales. But it also indicates that beyond14 years, the level of sales does not increase much. It tends to stay flat from that point on. The mathematical model (quadratic equation) can be used to predict the level of sales based on a future employee’s experience level.

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