Pricing Dells Navigreat

Dell has experience selling GPS systems built by other firms and plans to introduce a Dell system, the Navigreat. They would like information that will help them set a price. The Navigreat has

• an innovative, highly portable design, weighing only 5 ounces, with a state-of the art display

• a 3.5 screen, neither large, nor small, relative to competitors.

• innovative technology which guarantees precise routing time estimates,

  Dell executives believe that these features, portability, weight, display quality, screen size, and routing time precision, drive the price that customers are willing to pay for a GPS system.

  Recent ratings by Consumer Reports provide data on the retail price of 18 competing brands, as well as

• portability (1 to 5 scale), weight (ounces), and display quality (1 to 5 scale),

• screen size (inches)

• routing time precision (1 to 5 scale),

  These data are in Lab 8 Dell Navigreat.xls. Also in the file, in row 21, are the attributes and expected ratings of the Navigreat.

  Build a multiple regression model of GPS system price, including the characteristics thought by management to be drivers of price.

Regression results. Is the model RSquare significantly greater than 0? Y N Evidence: Significance F=__________

Which of the potential drivers have slopes significantly different from 0?

portability weight display

Slope different from zero Y or N Y or N Y or N Evidence (p-value)

Which of the drivers have slopes of unexpected sign?

portability weight display

Slope sign unexpected Y or N Y or N Y or N

Screen size

Y or N

Screen size

Y or N

Routing time

Y or N

Routing time

Y or N

Confirm suspected multicollinearity. The GPS system physical design determines its screen size, display quality, weight and portability. Run correlations to see if these characteristics are highly correlated.

Lab 8 Model Building with Multiple Regression 231

Highly correlated (rx1,x2>.5) Portability, weight YorN Portability, display YorN Portability, screen size YorN Weight, display YorN Weight, screen size YorN Display, screen size YorN

Choose one of the set of correlated characteristics to represent the set, eliminating the other potentially redundant characteristics, and re-run the regression.

Is this partial model RSquare significantly greater than 0? Y N Evidence: Significance F=_____________

Which of the potential drivers in this reduced model have slopes significantly different from 0? (Cross out characteristics that you excluded in this reduced model.)

portability weight display Screen size Routing time

Slope different from zero Y or N Y or N Y or N Y or N Y or N Evidence (p value)

Which of the drivers have slopes of unexpected sign? (Cross out characteristics that you excluded in this partial model.)

portability weight display Screen size Routing time

Slope sign unexpected Y or N Y or N Y or N Y or N Y or N

Find Partial F to decide whether the partial models explanatory power is significantly lower than in the full model.

Full model RSquare (1)

Partial model RSquare (2)

Change in RSquare (3) =(1)-(2)

Change per g predictors excluded (4) =(3)/g

%variation unexplained by full model (5) =1-(1)

%variation unexplained per residual dfs (6) =(5)/(N-1-k)

Partial F (7) =(4)/(6)

p value with g and (N-1-k) dfs

Conclusion: __________partial model RSquare is significantly lower than full model RSquare,

and potentially redundant variables are jointly significant and cannot be excluded

OR __________partial model RSquare is not significantly lower than full model RSquare, excluded variables are redundant or unimportant, and can remain excluded.

232 8 Building Multiple Regression Models Determine the improvement in predictive accuracy:

Full model Reduced model Improvement in margin (1) (2) of error

Standarderror $ $ (3)=(2)-(1) Approximatemarginof $ $ $ error in 95% predictions

Assess fit. Change the Line Fit chart type to scatterplot, adjust axes, and add chart and axis titles. Does the impact of screen size on price seem to be linear? Y or N

Assess residuals. Produce a residual histogram. Are residuals approximately Normal? Y or N

Predict prices. Copy the coefficients and paste into the Navigreat sheet, then use the regression equation to find expected prices for each of the GPS systems, including the Navigreat. Copy the standard error and paste into the Navigreat sheet.

Find the t value for 95% prediction intervals with your model residual degrees of freedom. Find the lower and upper 95% prediction intervals for each model, including the Navigreat.

Will Dell be able to charge a retail price of $650 for the Navigreat? Y or N

Sensitivity analysis: Identify the most important driver of prices by comparing the differences in expected prices between four hypothetical GPS systems. Add these four hypotheticals at the bottom of the file, then extend expected price, lower and upper 95% prediction bounds to include these.

Screen size

Largest (5) Smallest (3.4) Average (3.8) Average (3.8)

Route time rating

Average (4=Good) Average(4=Good) Best (5=Excellent:) Worst (2=poor)

Expected price

$ $ $ $

Difference due to

Screen size: $__________ Route time rating: $__________

If Dell wants to charge a retail price of $650 for the Navigreat, what product design modification ought to be made?___________________________________