Retail Price Data For $n = 60$ Hard Disk Drives Were Recently Reported in a Computer Magazine

question 125

Multiple Choice

Retail price data for $n = 60$ hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive:
$y =$ Retail PRICE (measured in dollars)
$x _ { 1 } =$ Microprocessor SPEED (measured in megahertz)
(Values in sample range from 10 to 40 )
$x _ { 2 } = \mathrm { CHIP }$ size (measured in computer processing units)
(Values in sample range from 286 to 486 )

A first-order regression model was fit to the data. Part of the printout follows:

$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$ Parameter Estimates
$\quad$$\quad$$\quad$ PARAMETER STANDARD $\quad$ $\quad$ T FOR 0:
VARIABLE DF ESTIMATE ERROR PARAMETER $= 0$ PROB $> | T |$

$\begin{array} { l l l l l l } \text { INTERCEPT } &1 & - 373.526392 & 1258.1243396 & - 0.297 & 0.7676 \\\text { SPEED } & 1 & 104.838940 & 22.36298195 & 4.688 & 0.0001 \\\text { CHIP } & 1 & 3.571850 & 3.89422935 & 0.917 & 0.3629\end{array}$


Identify and interpret the estimate for the SPEED $\beta$ -coefficient, $\hat { \beta } _ { 1 }$ .

• A) \(\hat { \beta } _ { 1 } = 3.57\); For every 1-megahertz increase in SPEED, we estimate PRICE to increase \(\$ 3,57\), holding CHIP fixed.
• B) \(\hat { \beta } _ { 1 } = 105\); For every 1-megahertz increase in SPEED, we estimate PRICE (y) to increase \(\$ 105\), holding CHIP fixed.
• C) \(\hat { \beta } _ { 1 } = 105\); For every \(\$ 1\) increase in PRICE, we estimate SPEED to increase 105 megahertz, holding CHIP fixed.
• D) \(\hat { \beta } _ { 1 } = 3.57\); For every \(\$ 1\) increase in PRICE, we estimate SPPED to increase by about 4 megahertz, holding CHIP fixed.

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