During Its Manufacture, a Product Is Subjected to Four Different $( y )$

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 global $F$ statistic is used to test the null hypothesis, $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0$ . Describe this hypothesis in words.

A) The model is not statistically useful for predicting Test4 score.
B) The first three test scores are poor predictors of Test 4 score.
C) The model is statistically useful for predicting Test4 score.
D) The first three test scores are reliable predictors of Test 4 score.