4. (3 points) Data has been collected regarding 88 different computer simulations conducted in designing the...

 

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4. (3 points) Data has been collected regarding 88 different computer simulations conducted in designing the layout for a chemical warehouse. The dependent (Y) variable is CPU time (the operating time required by the computer's central processing unit to run the simulation), the first independent variable (X₁) is the number of trials in the simulation, and the second independent variable (X2) is the number of statements in the computer program. Since it is hypothesized that the effect of the number of statements (X₂) on CPU time (Y) is curvilinear, the model being considered is: Y₁ = Bo + B₁X₁1 + B₂X₁2 + B3X2/12 + Full Model It is desired that we test whether the number-of-statements variables (X₂ and X2) can be dropped from the model. Perform this test. Use a = 0.10. Note: This should be done as a single test, not two separate tests. The partial sum of squares table for the above regression is Component df 1 X1₁ X₂|X₁ X²|X1, X₂ Residuals SS 15,644.2 118.5 1 587.4 84 6574.6 (a) State the hypotheses being tested (that is, write out Ho and H₁). (b) Perform an F test to determine whether the number-of-statements variables (X₂ and X2) can be dropped from the model. Your response should include the formula for the test statistic, the value of the test statistic, and the p-value. (c) At a = 0.05, what is the conclusion of your test? Do you prefer the full model given above or the smaller model: Y₁ = Bo + B₁X₁1 + €? 4. (3 points) Data has been collected regarding 88 different computer simulations conducted in designing the layout for a chemical warehouse. The dependent (Y) variable is CPU time (the operating time required by the computer's central processing unit to run the simulation), the first independent variable (X₁) is the number of trials in the simulation, and the second independent variable (X2) is the number of statements in the computer program. Since it is hypothesized that the effect of the number of statements (X₂) on CPU time (Y) is curvilinear, the model being considered is: Y₁ = Bo + B₁X₁1 + B₂X₁2 + B3X2/12 + Full Model It is desired that we test whether the number-of-statements variables (X₂ and X2) can be dropped from the model. Perform this test. Use a = 0.10. Note: This should be done as a single test, not two separate tests. The partial sum of squares table for the above regression is Component df 1 X1₁ X₂|X₁ X²|X1, X₂ Residuals SS 15,644.2 118.5 1 587.4 84 6574.6 (a) State the hypotheses being tested (that is, write out Ho and H₁). (b) Perform an F test to determine whether the number-of-statements variables (X₂ and X2) can be dropped from the model. Your response should include the formula for the test statistic, the value of the test statistic, and the p-value. (c) At a = 0.05, what is the conclusion of your test? Do you prefer the full model given above or the smaller model: Y₁ = Bo + B₁X₁1 + €?

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a The hypotheses being tested are Ho B2 B3 0 the numberofstatements variables have no effect on the ... View the full answer