During Its Manufacture, a Product Is Subjected to Four Different $$E ( y ) = \beta _ { 1 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 }$$

question 131

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 (x1) , Test 2 score (x2) , and Test3 score (x3) . [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. A 95% prediction interval for Test4 score of a product with Test1 = 590, Test2 = 750, and Test3 = 710 is (583, 793) . Interpret this result.

• A) We are 95% confident that a product's Test4 score will fall between 583 and 793 points when the first three scores are 590, 750, and 710, respectively.
• B) We are 95% confident that a product's Test4 score increases by an amount between 583 and 793 points for every 1 point increase in Test1 score, holding Test 2 and Test 3 score constant.
• C) Since 0 is outside the interval, there is evidence of a linear relationship between Test4 score and any of the other test scores.
• D) We are 95% confident that the mean Test4 score of all manufactured products falls between 583 and 793 points.

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Definitions:

Classified Balance Sheet

A balance sheet that organizes assets and liabilities into subcategories like current and long-term.

Unclassified Balance Sheet

A balance sheet that presents assets and liabilities without categorizing them into long-term or short-term classifications.

Current Ratio

A company's short-term financial health, specifically its ability to settle obligations due within a year, is gauged by this ratio, which is the quotient of current assets and current liabilities.

Broad Categories

General classifications or groups into which items or concepts can be divided based on common characteristics.