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
Ha:
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.
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