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During its manufacture, a product is subjected to four different tests in sequential order. An ...

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

, as a function of Test1 score

, Test 2 score

, and Test3 score

[Note: All test scores range from 200 to 800, with higher scores indicative of a higher quality product.] Consider the model:

E(y) = β₁ + β₁x₁ + β₂x₂ + β₃x₃

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.
_____________________________________________________________________

ROOT MSE 52.72 R-SQUARE 0.872

DEP MEAN 645.8 ADJ R-SQ 0.824

Compute a 95% confidence interval for β₃.

▸ .33 ± 4.04

▸ .33 ± 105

▸ .33 ± .19

▸ .33 ± .08

Textbook

Statistics

Edition: 12^th

Authors: McClave, Sincich, Tamarack

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