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In Exercises 1-4, find a least-squares solution of Ax = b by (a) constructing the normal equations for
4. A =
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EBK LINEAR ALGEBRA AND ITS APPLICATIONS
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- A professor wants to investigate the relationship between the grades students obtain in their midterm exam (X) and the grades they obtain (Y,) in the final exam. The professor collects data from 65 randomly chosen students. The estimated OLS regression is. ŷ = 45 + 0 .85X, where Y, denotes the predicted value of the grades obtained in the final exam by the " individual and X, denotes the grades obtained in the midterm exam. From the sample data he makes the following calculations: 65 E (X-X)² = 230-48, j= 1 65 04 2^2 = 425.23, j= 1 ^2 where u, is the square of the residual for the " observation. 01 He wants to test whether the grades obtained in the midterm exam have any effect on the grades obtained in the final exam or not. Which of the following are the null and the alternative hypotheses of the test the professor wishes to conduct? O A. Ho B1 0.85 vs. H, B1 = 0.85. %3D Click to select your answer(s). (DOLL P. 響arrow_forwardQ^(2) The Quadratic equation 2x^(2)+6x+7=0 has roots \alpha and B. Calculate the value of (1)/(\alpha )+(1)/(\beta )arrow_forwardChapter 4, Section 4.4, Question 007 Let C(9) represent the cost, R(g) the revenue, and T(g) the total profit, in dollars, of producing 4 items. (a) If C (50) = 76 R (50) = 86 , approximately how much profit is earned by the 51-* and item? The profit earned from the 51 item will be approximately (b) If C (90) = 70 R'(90) = 64 , approximately how much profit is earned by the 91-t and item? The profit earned from the 91st item will be approximately (c) If T9) is a maximum when 9 = 78 , how do C'(78) R'(78) compare? you think and C'(78) R'(78)arrow_forward
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- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning