SLOPE

Fits a straight line to data using linear regression and returns its slope.

Syntax:

SLOPE(yvalues, xvalues)

yvalues and xvalues are single row or column ranges specifying points in a set of data. yvalues and xvalues must be the same size.

SLOPE fits a straight line through these data points, using the linear regression method (least squares). It then returns the slope of that line.

The equation of a straight line may be given as y = a + bx. The linear regression method calculates:

$b=\frac{\sum (x_i-\overline{x})(y_i-\overline{y})}{\sum (x_i-\overline{x}{)}^2}$

and

$a=\overline{y}-b\overline{x}$

b is the slope, returned by this function.

Example:

SLOPE(B2:B6, A2:A6)

where the x values in A2:A6 are 1, 2, 3, 4, 5 and the y values in B2:B6 are 2, 4, 6, 8, 11 returns 2.2. The equation of the straight line found is very nearly y = 2x - thus the slope is very nearly (but not quite) 2.

The company wants to find out the rate of change in sales for every email sent. In other words, they want to calculate the slope of the linear relationship between these two variables.

Using the SLOPE function

To find the slope, the company can use the SLOPE function. The syntax for the function is:

SLOPE(data_y, data_x)

• data_y is the range of cells containing the dependent variable (Sales Generated).
• data_x is the range of cells containing the independent variable (Emails Sent).

The company would use the following formula:

SLOPE(B1:B5, A1:A5)

Result: The result of this calculation would be 0.11.

Interpretation of the Result

The slope of 0.11 means that, on average, for every additional email sent, the company can expect to generate about 0.11 more sales.

This information is valuable for a number of reasons:

• Predictive Analysis: The company can use this slope to forecast future sales. For example, if they plan to send a new campaign of 10,000 emails, they could predict the number of sales to be approximately 10,000×0.11=1100.
• Budgeting and ROI: By knowing the cost of sending each email, the company can determine if their email marketing campaigns are profitable. A low slope might indicate a need to revise their strategy, such as improving the email content or targeting a different audience.
• Performance Monitoring: The company can track the slope over time for different campaigns to see which ones are the most effective. A campaign with a steeper slope (a higher number) would be considered more successful as it generates more sales per email sent.