HW 10 Chap 12 Exemplar

HW 10 Chap 12 Exemplar - Exemplar for the Regression...

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Exemplar for the Regression Problems Required for Homework #10 12.13. For n = 7 sampled tax payers, given data for their total adjusted gross income and amount of itemized deductions, both in thousands of dollars. Let x denote the independent variable of total adjusted gross income and let y denote the amount of itemized deductions, both in thousands of dollars. x y 22 9.6 27 9.6 32 10.1 48 11.1 65 13.5 85 17.7 120 25.5 a. Graph of the n = 7 sample data. There appears to be an increasing linear relationship between total adjusted gross income and the amount of itemized deductions. HW #10 regression exemplar 1 © 2010 Harvey Singer 0.0 5.0 10.0 15.0 20.0 25.0 30.0 0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 x y

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The trend is increasing, meaning that y generally increases as x increases. Therefore, anticipate that the slope b 1 of the line will be positive. b. Calculations: Calcs x y x^2 xy y^2 22 9.6 484 211.200 92.160 27 9.6 729 259.200 92.160 32 10.1 1024 323.200 102.010 48 11.1 2304 532.800 123.210 65 13.5 4225 877.500 182.250 85 17.7 7225 1504.500 313.290 120 25.5 14400 3060.000 650.250 Sums 399.000 97.100 30391.000 6768.400 1555.330 Means 57.000 13.871 The summations needed to compute the slope and the y -intercept are: xbar = 57.000 ybar = 13.871 Σ x 2 = 30391.000 Σ y 2 = 6768.400 Σ xy = 1555.330
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