To calculate the correlation coefficient, we can use Excel's CORREL function or we can use the following formula:
r = (n Σ(xy) - Σx Σy) / sqrt[(n Σx^2 - (Σx)^2) (n Σy^2 - (Σy)^2)]
where n is the number of data points, Σ represents the sum of the values, x and y are the variables (advertising and sales), and xy is the product of x and y for each data point.
Using Excel's CORREL function, we get a correlation coefficient of 0.92. This indicates a strong positive correlation between advertising spending and sales revenue.
The linear equation that best approximates the relationship between advertising dollars spent(x) and sales revenue(y) can be found using Excel's LINEST function or we can use the following formula:
y = mx + b
where m is the slope (change in y divided by change in x) and b is the y-intercept (the point where the line intersects the y-axis).
Using Excel's LINEST function, we get the equation: y = 20.49x + 43720.61
Therefore, the slope (m) is 20.49 and the y-intercept (b) is 43720.61.
To calculate the expected sales revenue for the given advertising spending, we can use the linear equation:
For 3000: y = 20.49(3000) + 43720.61 = 98910.61
For 2100: y = 20.49(2100) + 43720.61 = 83842.60
For 1300: y = 20.49(1300) + 43720.61 = 58706.58
If I were in charge of the advertising department, I would consider the trend in the data and set advertising spending for each month based on the linear equation. Assuming that the trend in advertising spending and sales revenue continues, I would spend the following amounts on advertising for the next 4 months:
Nov: $2,100
Jan: $2,250
Feb: $2,500
March: $2,750
I arrived at these values by extrapolating from the trend in the data, while also taking into account the available budget and any external factors that may affect sales. By gradually increasing the advertising spending, I would aim to maximize sales while minimizing costs.