• Regression analysis is a statistical method used in market and marketing research to analyze the relationship between a dependent variable and one or more independent variables.
• Regression analysis helps businesses to understand the nature of the relationship between variables and make predictions or forecasts.
• Regression analysis is a powerful tool for market and marketing research, allowing businesses to gain insights into the relationship between variables and make predictions based on historical data.
• However, it is important to recognize its limitations and to use it in conjunction with other research methods for a complete picture of the market.

#### Example data set:

To illustrate regression analysis, let’s consider a hypothetical data set that includes the number of hours worked and the number of sales made by a group of sales representatives:

• Hours worked: 8, 7, 6, 5, 4, 3, 2, 1
• Sales made: 100, 90, 80, 70, 60, 50, 40, 30

Types of regression:

There are two main types of regression used in market and marketing research:

1. Simple linear regression: This type of regression involves analyzing the relationship between two variables – a dependent variable and an independent variable.
2. Multiple linear regression: This type of regression involves analyzing the relationship between a dependent variable and two or more independent variables.

#### Main features of regression analysis:

1. Line of best fit: Regression analysis produces a line of best fit that represents the relationship between the variables. This line can be used to make predictions or forecasts.
2. Coefficient of determination (R-squared): This is a statistical measure that indicates how well the line of best fit represents the data. An R-squared value of 1 indicates a perfect fit, while a value of 0 indicates no relationship.

Calculation:

For our example data set, the line of best fit for simple linear regression would be:

Sales made = -10 * Hours worked + 110

The R-squared value for this line of best fit would be 0.97, indicating a strong relationship between hours worked and sales made.

• Predictability: Regression analysis can help businesses predict future outcomes based on historical data.
• Identifying key variables: Regression analysis can help businesses identify which variables have the greatest impact on their dependent variable, allowing them to prioritize those variables in their decision-making.
• Flexibility: Regression analysis can be used with both quantitative and qualitative data, making it a versatile tool for market and marketing research.

#### Limitations of Linear Regression

• Causality: Regression analysis can show a correlation between variables, but it cannot prove causation.
• Outliers: Regression analysis can be affected by outliers or data points that do not fit the general pattern of the data set, potentially skewing the results.
• Assumptions: Regression analysis relies on several assumptions, including that the relationship between the variables is linear and that the errors in the data are normally distributed. If these assumptions are not met, the results of the analysis may be inaccurate. 