Mark Price, the new productions manager for Speakers and Company, needs to find

Question

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 their 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
($000)

1998

390

275

650

1999

690

216

834

2000

890

211

1,102

2001

1,290

210

1,410

2002

1,145

216

1,210

2003

1,190

190

1,290

2004

890

225

885

2005

1,102

199

1,102

2006

985

223

699

2007

1,235

211

885

2008

885

227

699

2009

801

244

699

a. Perform a regression analysis based on these data using Excel. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)

b. Predict average yearly speaker sales for Speakers and Company based on the regression results if the price was $290 per unit and the amount spent on advertising (in thousands) was $890. (Enter your answer in thousands. Do not round intermediate calculations. Round your answer to the nearest whole number.)

YEAR

SALES/UNIT
(THOUSANDS)

PRICE $/UNIT

ADVERTISING
($000)

1998

390

275

650

1999

690

216

834

2000

890

211

1,102

2001

1,290

210

1,410

2002

1,145

216

1,210

2003

1,190

190

1,290

2004

890

225

885

2005

1,102

199

1,102

2006

985

223

699

2007

1,235

211

885

2008

885

227

699

2009

801

244

699

Explanation / Answer

A.

On the basis of regression analysis,

Sales (in thousands) = 2255.1235 – 7.12*Price + .2859*advertising ($000)

Working note:

Regression analysis output via Excel is as follows:

B.

Price = $290 per unit

Advertising ($000) = $890

Then,

Sales = 2255.1235 - 7.12*290 + .2859*890

Sales = 444.77 or 445 (in thousands)

Regression Statistics Multiple R 0.837189921 R Square 0.700886965 Adjusted R Square 0.634417401 Standard Error 155.8549919 Observations 12 ANOVA df SS MS F Significance F Regression 2 512267.2434 256133.6217 10.54448 0.004378 Residual 9 218617.0066 24290.77851 Total 11 730884.25 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 2255.12352 866.6679041 2.602061885 0.028641 294.5845 4215.663 294.5845 4215.663 Price $ / Unit -7.120024762 3.047955869 -2.335999951 0.04431 -14.015 -0.22507 -14.015 -0.22507 Advertising ($000) 0.285933127 0.258037198 1.108108169 0.296548 -0.29779 0.869654 -0.29779 0.869654

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