91Ó°ÊÓ

Mark Price, the new productions manager for Speakers and Company, needs to Find out which variable most affects the demand for their line of stereo speakers. He is uncertain whether the unit price of the product or the effects of increased marketing are the main drivers in sales and wants to use regression analysis to figure out which factor drives more demand for its particular market. Pertinent information was collected by an extensive marketing project that lasted over the past 10 years and was reduced to the data that follow:

Year	Sales/unit (Thousands)	Price/unit	Advertising
1998	400	280	600
1999	700	215	835
2000	900	211	1100
2001	1300	210	1400
2002	1150	215	1200
2003	1200	200	1300
2004	900	225	900
2005	1100	207	1100
2006	980	220	700
2007	1234	211	900
2008	925	227	700
2009	800	245	690

a. Perform a regression analysis based on these data using Excel. Answer the following questions based on your results.

b. Which variable, price or advertising, has a larger effect on sales and how do you know?

c. Predict average yearly speaker sales for Speakers and Company based on the regression results if the price was \(300 per unit and the amount spent on advertising (in thousands) was \)900

Step by step solution

01

(a) Regression analysis

Regression analysis could be a tool of statistics accustomedto 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.

Where

a = y-intercept

_{${\mathrm{χ}}_1$=} price

b₁= slope of price

${\mathrm{χ}}_2$= advertising

b₂ = slope of advertising

02

(b) Variable that has a larger effect on sales (price/advertising)

Price has a larger effect on sales because its slope value is much higher (-6.9094 versus .3250). Price actually has a negative effect since raising prices decreases sales. (Table shown in step1)

$$\begin{gathered} \text{Price > Advertising} \\ -\text{6.9094 > 0.3250} \end{gathered}$$

03

(c) Average yearly sales

Sales forecasting is regarded as a crucial business practice. Accurate sales forecasts help the business leaders to make smarter decisions about things like goal-setting, budgeting, hiring, and other things that affect cash flow. The following formula is used to find the average annual sales forecast.

$$\begin{gathered} \text{Sales}=\text{Y intercept}-\text{Slope of price}×\left(\text{Price per unit}\right)+\text{Slope of advertising} \\ ×\left(\text{Amount spent on advertising}\right) \end{gathered}$$

$$\begin{gathered} \text{Sales}=\text{2191}.\text{3374}-\text{6}.\text{9}0\text{94}\left(\text{3}00\right)+.\text{325}0\left(\text{9}00\right) \\ \text{Sales}=\text{411}.0\text{4 thousand units} \end{gathered}$$

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