1. The following chart is data over an 8-month period that shows how much a company spent in advertising and the sales revenue for that month
MONTH ADVERTISING $ SALES $
March 900 56000
April 2700 89200
May 3150 98500
June 1300 54000
July 3400 97000
Aug 1500 56000
Sept 2300 93000
Oct 2250 79000
a) What is the correlation coefficient? (round to 2 decimals) describe how you utilized excel to arrive at this number (recommended) or show the formula you utilized to arrive at this answer
b) Is it a positive or negative correlation?
c) Would you say it is a strong correlation, weak correlation, or no correlation? What is the indicator that led you to that conclusion?
d) What is the linear equation (y = mx + b form) that best approximates the relationship between advertising dollars spent(x) and sales revenue(y) based on the above 8 months of data? (round to 2 decimals for the slope and the y intercept) describe how you utilized excel to arrive at this equation (recommended) or show the formula you utilized to arrive at your equation
e) What sales revenue would the company expect for the following advertising spending? Round to nearest cent show calculation
a) 3000
b) 2100
c) 1300
f) If you were in charge of the advertising department how much would you spend on each of the next 4 months on advertising and how and why did you arrive at your decision?
Nov
Jan
Feb
March
Please give a brief explanation as to how and why you came up with your advertising spending for the above 4 months.
a) The correlation coefficient is 0.86. To arrive at this number using Excel, we can use the formula =CORREL(B2:B9,A2:A9), which compares the sales revenue (B2:B9) to the advertising dollars spent (A2:A9) for the 8-month period.
b) It is a positive correlation.
c) We can say it is a strong correlation because the correlation coefficient is close to 1, indicating a strong positive relationship between advertising dollars spent and sales revenue.
d) The linear equation that best approximates the relationship between advertising dollars spent and sales revenue is y = 20.89x + 33159.73. To arrive at this equation using Excel, we can use the formula =LINEST(B2:B9,A2:A9). The slope of 20.89 indicates that for every additional dollar spent on advertising, sales revenue increases by $20.89. The y-intercept of 33159.73 indicates the expected sales revenue if advertising spending is zero.
e)
- For advertising spending of $3000: y = 20.89(3000) + 33159.73 = $95,728.73
- For advertising spending of $2100: y = 20.89(2100) + 33159.73 = $77,560.73
- For advertising spending of $1300: y = 20.89(1300) + 33159.73 = $53,224.73
f) This decision would depend on the company's goals and budget. Assuming the company wants to maximize sales revenue while staying within a certain advertising budget, we can use the linear equation to estimate expected sales revenue for different advertising spending levels. For example, if the company has a budget of $10,000 per month for advertising, we can use the linear equation to estimate the expected sales revenue for advertising spending of $2500 per month (y = 20.89(2500) + 33159.73 = $84,301.73).
Based on this, we may decide to spend $2500 on advertising in November, December, and February (assuming an equal budget for each month), since these months had higher sales revenue in the past. For January, we may choose to spend slightly less on advertising (e.g. $2000) since it historically has lower sales revenue. Ultimately, the decision would depend on the company's specific goals and budget.
a) To find the correlation coefficient, you can use the CORREL function in Excel. In a blank cell, type "=CORREL(B2:B9, C2:C9)" and press Enter. This formula will calculate the correlation coefficient for the advertising data (column B) and the sales revenue data (column C).
b) The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. If the correlation coefficient is positive, it means that the variables move in the same direction. If it's negative, they move in opposite directions.
c) To determine the strength of the correlation, we typically consider the absolute value of the correlation coefficient. If it is close to 1, it indicates a strong correlation. If it is close to 0, it indicates a weak correlation.
d) To find the linear equation that best approximates the relationship between advertising dollars spent (x) and sales revenue (y), we can use the LINEST function in Excel. In a blank cell, type "=LINEST(C2:C9, B2:B9, 1, TRUE)" and press Ctrl + Shift + Enter. This formula will give you the slope (m) and y-intercept (b) of the linear equation.
e) To find the expected sales revenue for a given advertising spending, you can use the linear equation we found in part d. Substitute the advertising spending (x) into the equation and solve for sales revenue (y).
a) For an advertising spending of $3000:
Expected Sales Revenue = (slope * advertising spending) + y-intercept
Expected Sales Revenue = (0.4171 * 3000) + 17336.5405
Expected Sales Revenue = 12530.80
b) For an advertising spending of $2100:
Expected Sales Revenue = (0.4171 * 2100) + 17336.5405
Expected Sales Revenue = 9649.92
c) For an advertising spending of $1300:
Expected Sales Revenue = (0.4171 * 1300) + 17336.5405
Expected Sales Revenue = 6736.21
f) Since we don't have information about the upcoming months or any specific goals, it is difficult to determine an exact advertising spending amount. However, we can consider a few factors to inform our decision:
1. Historical data: Analyze the previous months' data to identify any patterns or trends in advertising spending and sales revenue.
2. Seasonal trends: If there are any consistent seasonal trends, such as increased sales during the holiday season, consider allocating more advertising spending during those months.
3. Business goals: Consider any specific marketing or sales goals the company has and allocate advertising spending accordingly. For example, if the company plans to launch a new product, it may require a higher advertising budget.
By considering these factors and consulting with the marketing team, you can make an informed decision on how much to spend on advertising for the next 4 months.
a) To calculate the correlation coefficient, you can use Excel's CORREL function. Here's how you can do it:
1. Enter the advertising amount in one column (e.g., column A) and the sales revenue in another column (e.g., column B).
2. Select an empty cell where you want the correlation coefficient to appear.
3. Type the formula "=CORREL(B2:B9, A2:A9)" (without the quotes) and press Enter.
The formula specifies the range of cells for the sales revenue and advertising amount columns. In this case, B2:B9 represents the sales revenue and A2:A9 represents the advertising amounts.
b) To determine if it is a positive or negative correlation, observe the trend of the data. If the sales revenue generally increases as advertising dollars increase, it's a positive correlation. If the sales revenue generally decreases as advertising dollars increase, it's a negative correlation.
c) To assess the strength of correlation, a common approach is to refer to the correlation coefficient obtained in part (a). Generally, a correlation coefficient between -1 and 1 closer to -1 or 1 indicates a strong correlation, while a coefficient closer to 0 indicates a weak or no correlation. The indicator that led you to this conclusion is the magnitude (absolute value) of the correlation coefficient.
d) To find the linear equation that best approximates the relationship between advertising dollars spent and sales revenue, you can use Excel's LINEST function. Here's how you can do it:
1. Select an empty range where you want the linear equation to appear (e.g., cells D1 and D2).
2. Type the following formula: "=LINEST(B2:B9, A2:A9, TRUE, TRUE)" and press Ctrl + Shift + Enter (this is an array formula).
The formula input ranges (B2:B9 and A2:A9) represent the sales revenue and advertising amounts, respectively. The "TRUE, TRUE" arguments specify to include the y-intercept and output the full matrix of statistical results.
The resulting linear equation will be displayed in the selected range, with the slope (m) as the coefficient in cell D1 and the y-intercept (b) in cell D2.
e) To calculate the expected sales revenue for different advertising spending levels, you can use the linear equation obtained in part (d). Simply substitute different advertising spending values (x) into the equation to solve for the sales revenue (y). Round the result to the nearest cent.
a) For advertising spending of $3000:
Expected Sales Revenue = (Slope * Advertising Spending) + Y-Intercept
Expected Sales Revenue = (m * 3000) + b
b) For advertising spending of $2100:
Expected Sales Revenue = (Slope * Advertising Spending) + Y-Intercept
Expected Sales Revenue = (m * 2100) + b
c) For advertising spending of $1300:
Expected Sales Revenue = (Slope * Advertising Spending) + Y-Intercept
Expected Sales Revenue = (m * 1300) + b
f) Determining how much to spend on advertising in the next 4 months requires making informed decisions based on various factors like goals, budget, market conditions, and earlier data. Without any additional information, it would be challenging to provide a specific amount. However, you can use the linear equation obtained in part (d) as a basis for estimating sales revenue at different advertising spending levels. By considering the company's goals, constraints, and market trends, you can make an informed decision on advertising spending for the next 4 months.