During Its Manufacture, a Product Is Subjected to Four Different $\left( x _ { 1 } \right)$

question 10

Multiple Choice

During its manufacture, a product is subjected to four different tests in sequential order. An efficiency expert claims that the fourth (and last) test is unnecessary since its results can be predicted based on the first three tests. To test this claim, multiple regression will be used to model Test4 score (y) , as a function of Test1 score $\left( x _ { 1 } \right)$ , Test 2 score $\left( x _ { 2 } \right)$ , and Test3 score ( $\left. x _ { 3 } \right)$ ) . [Note: All test scores range from 200 to 800 , with higher scores indicative of a higher quality product.] Consider the model:
$$E ( y ) = \beta _ { 1 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 }$$
The first-order model was fit to the data for each of 12 units sampled from the production line. The results are summarized in the printout.
$\begin{array}{lrrrrr}\hline & & & & & \\\text { SOURCE } & \text { DF } & \text { SS } & \text { MS } & \text { F VALUE } & \text { PROB }>\text { F } \\\text { MODEL } & 3 & 151417 & 50472 & 18.16 & .0075 \\\text { ERROR } & 8 & 22231 & 2779 & & \\\text { TOTAL } & 12 & 173648 & & &\end{array}$

$\begin{array}{llll}\text { ROOT MSE } & 52.72 & \text { R-SQUARE } & 0.872 \\\text { DEP MEAN } & 645.8 & \text { ADJ R-SQ } & 0.824\end{array}$

$\begin{array}{lrrrr} & \text { PARAMETER } & \text { STANDARD } & \text { T FOR 0: } & \\\text { VARIABLE } & \text { ESTIMATE } & \text { ERROR } & \text { PARAMETER }=0 & \text { PROB }>|\mathrm{T}| \\\text { INTERCEPT } & 11.98 & 80.50 & 0.15 & 0.885 \\\text { X1(TEST1) } & 0.2745 & 0.1111 & 2.47 & 0.039 \\\text { X2(TEST2) } & 0.3762 & 0.0986 & 3.82 & 0.005 \\\text { X3(TEST3) } & 0.3265 & 0.0808 & 4.04 & 0.004 \\\hline\end{array}$

Compute a $95 \%$ confidence interval for $\beta _ { 3 }$ .

• A). \(33 \pm 105\)
• B) \(.33 \pm 4.04\)
• C) \(.33 \pm .08\)
• D) \(.33 \pm .19\)

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Definitions:

Normal Distribution

It is a probability distribution that features a symmetric alignment around the mean, emphasizing that data around the mean occur more than data at a distance.

Degrees of Freedom

The count of separate values or amounts that are capable of changing in an analysis while still respecting all limitations.

T-test

A statistical method employed to ascertain whether there's a notable disparity between the averages of two sets.

Interval Data

A type of numerical data that has meaningful intervals between values but no true zero, allowing for the measurement of differences.