T1_ Linear Equation

Linear Regression Analysis

Purpose

To determine the relationship between click-through rating (CTR) and weekly sales, which allows businesses to understand how effectively their advertising campaigns impacts sales performance. By establishing a clear relationship, companies can make informed decisions on future marketing strategies and budget allocations.

Building the Linear Equation

The general format for a linear equation is given as:y = mx + b

• y: The dependent variable, which in this case represents weekly sales.

• m: The slope of the line, also known as the coefficient of the independent variable (CTR). This indicates how much sales are expected to increase (or decrease) for each unit increase in the CTR.

• x: The independent variable, which is the click-through rating (CTR) expressed as a decimal.

• b: The y-intercept of the linear equation. This value represents the predicted sales when the CTR is zero, providing a baseline for comparison.

Replacing Variables in the Equation

During the analysis, coefficient results are obtained which can be plugged into the linear equation as follows:

• Replace m with the calculated coefficient of click-through rating obtained from regression analysis.

• Replace b with the intercept coefficient derived from the analysis.Once these values are substituted, the resulting linear equation articulately expresses the relationship between CTR and weekly sales, making it easier to interpret and apply the results.

Application of the Linear Equation

The established linear equation facilitates various predictive analytics, including estimating weekly sales for a given CTR. This predictive capability can inform marketing strategy by visualizing the potential revenue outcome of adjustments to advertising efforts.

Example Calculation

For instance, to predict weekly sales when the CTR is 62%:

1. Convert CTR to Decimal: 62% is converted to decimal form as 0.62.

2. Plug into Equation: Using the derived linear equation, for example, let’s say the slope is 26.62 and the intercept is 34.84:

   • Calculate Sales = 26.62 * 0.62 = 1,650.56.

3. Add Intercept: Finally, add the intercept value:

   • Total Expected Sales = 1,650.56 + 34.84 = 5,081.40.

4. Conclusion: This analysis predicts that when the click-through rating is 62%, weekly sales are expected to be approximately $5,081.40. This expected sales figure can serve as a target for marketing teams when planning campaigns.