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.
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.
1 answer
1 answer