Question

A statistical program is recommended.

A certain company produces and sells frozen pizzas to public schools throughout the eastern United States. Using a very aggressive marketing strategy, they have been able to increase their annual revenue by approximately $10 million over the past 10 years. But increased competition has slowed their growth rate in the past few years. The annual revenue, in millions of dollars, for the previous 10 years is shown.

Year	Revenue
1	8.53
2	10.94
3	12.88
4	14.11
5	16.41
6	17.21
7	18.27
8	18.55
9	18.50
10	18.33

(b)

Using Minitab or Excel, develop a quadratic trend equation that can be used to forecast revenue (in millions of dollars). (Round your numerical values to three decimal places.)

T_t =

  

(c)

Using the trend equation developed in part (b), forecast revenue (in millions of dollars) in year 11. (Round your answer to two decimal places.)

$  million

Answer 1

Trend line using MINITAB:

(b) Regression Analysis: Revenue(Y) versus Years (X), X^2

The regression equation is
Revenue(Y) = 5.70 + 2.90 Years (X) - 0.163 X^2

Predictor Coef SE Coef T P
Constant 5.6972 0.3228 17.65 0.000
Years (X) 2.8997 0.1348 21.51 0.000
X^2 -0.16292 0.01195 -13.64 0.000

S = 0.274482 R-Sq = 99.5% R-Sq(adj) = 99.4%

Years

Obs (X) Revenue(Y) Fit SE Fit Residual St Resid
4 4.0 14.1100 14.6891 0.1213 -0.5791 -2.35R

R denotes an observation with a large standardized residual.

(c) FOR X=11
Y= 5.70+2.90 *11-0.163* 11^2
Y= 17.877

Revenue for 11 years = 17.88

STEPS OF MINITAB FOR QUADRATIC LINE:

1. Add an x² column.
   • Name Column C3 by clicking the blank column label and typing "x^2"
   • Select "Calc --> Calculator."
   • Fill out the resulting dialog box as follows:

     Input Type	Label	Value
     	Store result in variable:	'x^2'
     	Expression:	'x'**2

   • Click "OK."
2. Compute a quadratic fit and display summary information.
   • Select "Stat --> Regression --> Regression."
   • Fill out the resulting dialog box as follows:

     Input Type	Label	Value
     	Response:	y
     	Predictors:	x 'x^2'

   • Before closing the dialog box, click "Results."
   • In the dialog box that follows, click the radio button next to the label, "In addition, the full table of fits and residuals.
   • Click "OK" to close the "Results" dialog box.
   • Click "OK" in the "Regression" dialog box.