Estimate the price of printers based on the printer’s speed (pages per minute) a

Question

Estimate the price of printers based on the printer’s speed (pages per minute) and whether it can print in color. (Use data file:Printer)

Description of Variables in the data set:

Price = the list price for the printer

Speed = printing speed for text, pages per minute

Color = whether it is able to print in color

a. Use the least squares method to develop the estimated regression equation.

b. At the .10 level of significance, is the model statistically significant?

c. At the .10 level of significance, are the individual slope coefficients statistically significant?

d. Construct the 90 % confidence interval for each of the slope coefficient.

e. Another printer that is not on the list is able to print in color and prints 20 pages per minute, predict the price of this printer using the estimated regression equation.

f. Provide a 90% confidence interval for the printer with the characteristics in part f.

Price Color 549 349 349 299 499 399 599 399 399 799 300 499 349 599 269 649 429 199 199 649 31 Yes 21 Yes 20 Yes 16 Yes 21 Yes 20 Yes 25 Yes 21 Yes 26 Yes 28 Yes 32 No 35 No 30 No 40 No 30 No 40 No 30 No 17 No 24 No 27 No 10 13 14 16 2 17 2 20

Explanation / Answer

a] The regression equation is:   Price = 137 + 11.3 Speed

b] At the .10 level of significance, is the model statistically significancy:

MTB > Name c3 "CLIM1" c4 "CLIM2" c5 "PLIM1" c6 "PLIM2"
MTB > Regress 'Price' 1 'Speed';
SUBC>   Constant;
SUBC>   Predict 20;
SUBC>     Confidence 90;
SUBC>     CLimits 'CLIM1'-'CLIM2';
SUBC>     PLimits 'PLIM1'-'PLIM2';
SUBC>   Brief 1.

Regression Analysis: Price versus Speed

Predictor    Coef     SE Coef     T      P
Constant    137.0    133.3     1.03    0.318
Speed       11.311    4.842 2.34 0.031

S = 146.073   R-Sq = 23.3%   R-Sq(adj) = 19.0%

Analysis of Variance

Source        DF      SS      MS      F      P
Regression     1     116450 116450 5.46 0.031
Residual Error 18     384070   21337
Total            19     500521

Predicted Values for New Observations that is speed = 20 pages per minute

New Obs    Fit     SE Fit      90% CI          90% PI
         1 363.3    46.0 (283.4, 443.1)   (97.7, 628.8)

Here P-value of regression model is 0.031 and level of significant (alpha) = 0.10

P-value < alpha. Hence we reject null hypothesis that is the given model is significnt at 0.10 level of significance.

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