How are prices set for computer processor chips? At one time, the frequency was a good indicator of the processing speed; however, more recently manufacturers have developed alternative ways to deliver computing power because a high frequency tends to lead to overconsumption of power. Consider the multiple regression analysis in Table 12.5.2 to explain the price of eight chips from the two major manufacturers Intel (i3, i5, i7, i8) and AMD (Athlon and Phenom) based on their performance (as measured by the WorldBench score, where higher numbers are better), their frequency (gigahertz, or billions of cycles per second), and their power consumption (when idling, in watts).34
a. Approximately how much of the variation in price from one processor to another can be explained by the frequency, the power consumption, and the benchmark score?
b. Have frequency, power, and benchmark score taken together explained a significant proportion of the variability in price? How do you know?
c. Which, if any, of frequency, power, and benchmark score has a significant effect on price while controlling for the two others?
d. Find the predicted value of price and the residual value for the Phenom II X4 945 processor, given that its price is $140, its frequency is 3 gigahertz, its power is 98.1 watts, and its WorldBench score is 110.
e. What exactly do the regression coefficient 22.80 for the WorldBench benchmark test and its confidence interval tell you?
f. Approximately how accurately does the regression equation match the actual prices of these eight processor chips?
g. Write a paragraph summarizing what you can learn about the pricing structure of computer processors from this multiple regression analysis.
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TABLE 12.5.2 Multiple Regression Results for Computer Processor Chip Prices The regression equation is Price--1,873 22341 Frequency) + 237 (Power + 22.80 WorldBench S 99.827 R-94.3% F 22.04 P 0.00598 Hypothesis Test Effect on Price Coeff -1,873 StdErr of Coeff 95% Confidence interval From -3441 t Statistic p Value Variable Constant Frequency Power WorldBench Significant? StdErr -305 565 3.317 -0.831 0.618 6.713 0.029 0.453 0.570 0.003 es -223.41 2.37 22.80 969.59 -8.29 13.37 522.76 13.04 32.23 No No Yes 268.75 3.84 3.40