HW_Week7.docx - UMUC STAT-200 Homework Assignments Dr Brian...

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UMUC STAT-200 Homework Assignments Week #7 Dr. Brian Killough Textbook #1: Lane et al . Introduction to Statistics, David M. Lane et al., 2013. ( http://onlinestatbook.com/Online_Statistics_Education.pdf ) Textbook #2: Illowsky et al . Introductory Statistics, Barbara Illowsky et al., 2013. ( http://openstaxcollege.org/files/textbook_version/hi_res_pdf/15/col11562-op.pdf ) See the file named “UMUC_STAT200_EXCEL_Tips” at the “Course Materials” menu link to find functions for calculating Linear Regression and Chi Square Distribution statistics. For problems Lane #14 and Illowsky #102, you can use the following online tool to evaluate the Chi- Square statistic, degrees of freedom and probability values: http://vassarstats.net/newcs.html Lane - Chapter 14: (2,6) 2. The formula for a regression equation is Y’ = 2X + 9, where Y’ is the predicted score. a. What would be the predicted score for a person scoring 6 on X? Y’ = 2(6) +9 = 21 b. If someone’s predicted score was 14, what was this person’s score on X? 14 = 2x + 9 5 = 2x 5/2 = x X = 2.5 6. For the given (X,Y) data points, compute: (4,6), (3,7), (5,12), (11,17), (10,9), (14,21) a. The correlation (r) and determine if it is significantly different from a hypothesized slope of 0 (null hypothesis). HINT: Use the significance test for correlation on Page-482 and assume a 95% confidence. 2 4 6 8 10 12 14 16 0 10 20 30 f(x) = 1.13x + 3.12 R² = 0.72 y y Linear (y) Linear (y) X Y x x^2 y y^2 4 6 -3.83 14.67 -6 36 3 7 -4.83 23.33 -5 25 5 12 -2.83 8.01 0 0 11 17 3.17 10.05 5 25 10 9 2.17 4.71 -3 9 14 21 6.17 38.07 9 81 Sum 47 72 0.02 98.84(ssx) 0 176 (ssy)
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Using excel: Correlation = 0.849199964 Sest = standard error of the estimate Sest = √(1-r^2)(ssy)/(n-2) = √(1-0.8492)(176)/(4) = 1.29 Sb (estimated standard error of b) = Sest/√SSX Sb = 1.29/√98.84 = 0.13 t= slope/sb t= 1.13/0.13 = 8.69 df = 6-2 = 4 p = 0.000965323 p<α, therefore p is
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