3.CS: Case Study (Forecasting Future Sales)
- Page ID
- 22080
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The Situation
Lightning Wholesale needs to predict dollar sales for each month in 2014. A variety of techniques are used in business to forecast sales. One technique examines year-to-year change in sales. Thus, the management at Lightning Wholesale has decided to perform a historical three-year analysis on both average monthly sales and average yearly sales to grasp how these figures have changed. Once the change is understood, the averages will be used to project the sales for each month in 2014.
The Data
| Month | 2011 Sales | 2012 Sales | 2013 Sales |
|---|---|---|---|
| January | $1,337 | $1,928 | $1,798 |
| February | $2,198 | $2,122 | $2,407 |
| March | $2,098 | $2,503 | $2,568 |
| April | $2,540 | $2,843 | $2,985 |
| May | $2,751 | $2,765 | $3,114 |
| June | $2,885 | $3,152 | $3,242 |
| July | $2,513 | $3,128 | $3,306 |
| August | $3,784 | $3,513 | $3,852 |
| September | $4,200 | $4,700 | $4,815 |
| October | $6,079 | $6,888 | $7,222 |
| November | $10,878 | $11,120 | $12,839 |
| December | $8,136 | $10,226 | $9,630 |
(All figures are in thousands of dollars)
Your Tasks
- Calculate the average monthly sales for each year.
- Calculate the year-over-year percent changes in average monthly sales.
- Determine the percent changes from year to year using your answers to question 1.
- Using your answers to question 2(a), calculate the annual rate of change.
- Establish monthly average ratios to determine how each month compares to the yearly average.
- For each month, calculate the average sales across all three years. Also average the yearly averages calculated in question 1. Round your answers to whole numbers.
- For each month, establish a ratio between the average sales in the month (from question 3(a)) and the average of the yearly sales (also from question 3(a)). Express the ratio so that the average yearly sales is a term of one. Round your answers to two decimals.
- Project sales into the future to forecast monthly sales in 2014 along with total yearly sales.
- Project the average monthly dollar volume sales for 2014 using the annual rate of change from question 2(b). Round your answer to a whole number.
- Convert the projection from question 4(a) into a monthly projection for 2014 using the monthly ratio established in question 3(b). Total the projected sales for 2014. Round all of your answers to whole numbers.