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. One application of regression analysis is in sales forecasting.

Example data set: To illustrate regression analysis, let’s consider a hypothetical data set that includes the number of hours worked and the amount 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

#### Features of regression analysis:

• 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.
• 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.
• Types of regression: There are two main types of regression used in market and marketing research: simple linear regression and multiple linear regression.
$\Large R^2 = \frac{\sum_{i=1}^{n}(\hat{y}i – \bar{y})^2}{\sum{i=1}^{n}(y_i – \bar{y})^2}$

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.

• Regression analysis can help businesses to make accurate sales forecasts based on historical data and other factors.
• It can also help businesses to identify which factors have the greatest impact on sales, allowing them to focus their efforts on those areas.
• Regression analysis is a flexible method that can be used with various types of data, including time series data and cross-sectional data.
• It can also be used to identify outliers and other anomalies in the data, which can provide valuable insights into market trends and consumer behaviour. 