During its manufacture, a product is subjected to four different ...

[charchew]

Question 1

True or False.

It is safe to conduct t-tests on the individual β parameters in a first-order linear model in order to determine which independent variables are useful for predicting y and which are not.
◦ True
◦ False

Question 2

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

Suppose the 95% confidence interval for β₃ is (.15, .47). Which of the following statements is incorrect?
◦ We are 95% confident that the estimated slope for the Test4-Test3 line falls between .15 and .47 holding Test1 and Test2 fixed.
◦ At α = .05, there is insufficient evidence to reject H₀: β₃ = 0 in favor of H_a: β₃ ≠ 0.
◦ We are 95% confident that the increase in Test4 score for every 1-point increase in Test3 score falls between .15 and .47, holding Test1 and Test2 fixed.
◦ We are 95% confident that the Test3 is a useful linear predictor of Test4 score, holding Test1 and Test2 fixed.

[mceravolo]

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