91Ó°ÊÓ

Demand for stereo headphones and MP3 players for joggers has caused Nina Industries to grow almost 50 percent over the past year. The number of joggers continues to expand, so Nina expects demand for headsets to also expand, because, as yet, no safety laws have been passed to prevent joggers from wearing them. Demand for the players for last year was as follows:

Month	Demand (units)
January	4200
February	4300
March	4000
April	4400
May	5000
June	4700
July	5300
August	4900
September	5400
October	5700
November	6300
December	6000

1. Using linear regression analysis, what would you estimate demand to be for each month next year? Using a spreadsheet, follow the general format in Exhibit 18.8. Compare your results to those obtained by using the forecast spreadsheet function.
2. To be reasonably confident of meeting demand, Nina decides to use three standard errors of estimate for safety. How many additional units should be held to meet this level of confidence?

Step by step solution

01

(a) Definition of linear regression analysis

Linear regression analysis could be a tool of statistics accustomed help predict future values from past values. It’s commonly used as a quantitative way to find the underlying trend and when prices are overextended.

Using linear regression analysis, the estimate of demand to be for each month next year is shown as follows:

$$\begin{gathered} \stackrel{¯}{t}=6.5 \\ \stackrel{¯}{y}=5016.667 \\ B=\frac{∑ty-n\stackrel{¯}{t}\stackrel{¯}{y}}{∑t^2-n\stackrel{¯}{t^2}}=192.3077 \\ a=\stackrel{¯}{y}-b\stackrel{¯}{t}=3766.667 \end{gathered}$$

Using Excel, the FORECAST () function comes up with the same answers as this regression model, so it seems obvious that the function uses linear regression as its methodology.

02

(b) Standard error of estimate

The mean is derived from the actual mean of a population; this deviation is known as the standard error of the mean.

The three standard errors of the estimate for safety and additional units held to meet the level of confidence are as follows:

$S_{yt}=\frac{\sqrt{\underset{i=1}{\overset{n}{∑}}{\left(yi-Yi\right)}^2}}{n-2}=\sqrt{\frac{728205.128}{12-2}}=269.85$

Therefore, 3 standard errors of the estimate would be 3(269.85) = 809.55 = 810

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!