TwoRegressionLines

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Unformatted text preview: TwoRegressionLines.xls This workbook drives home the point that the linear relationship between two variables (call them X and Y) is summarized by two different regression lines, depending on whether we are predicting Y conditional on the value or predicting the value of X conditional on the value of Y. The SATData worksheet contains a sample data set. PivotTables displays two graphs of averages for the relationship between Math and Verbal SAT scores TwoLines displays the regression lines superimposed on the scatter plots and graphs of averages. SDLine contrasts the single SD line with the two regression lines. e of X or SAT data on applicants to a small, liberal arts college Verbal Math 510 690 Univariate Summary Statistics 470 630 Average Verbal 512 SD Verbal 89 470 560 Average Math 595 SD Math 87 440 710 The univariate statistics say nothing about the relationship between Verba 660 730 The scatter diagram helps. 600 650 How can the relationship between Verbal and Math be summarized? 450 510 r = 0.55 500 420 r measures association but says nothing more. 580 610 The regression line shows how, on average, y changes as x changes. 400 500 The point of this workbook is that there are two regression lines. 490 650 Go to the PivotTables sheet to see where the two lines come from. 490 570 340 460 320 380 560 550 400 470 450 610 510 710 730 680 510 560 570 690 690 770 510 620 480 560 590 660 500 650 660 660 360 460 470 640 540 560 560 640 440 480 620 610 560 700 590 740 450 500 400 540 470 550 400 560 500 650 490 530 560 650 540 610 650 520 520 680 450 500 590 640 650 760 500 600 370 610 520 670 200 300 400 500 600 700 800 200 300 400 500 600 700 800 Scatter Plot Verbal Math 750 f(x) = 0.54x + 318.94 Comparing the Regression and SD Lines 480 640 640 720 560 460 450 460 540 640 400 550 480 560 700 710 490 540 420 440 580 730 500 530 610 700 420 580 Slope Intercept 460 620 Reg Line 0.54 318.94 500 570 SD Line 0.98 94.6 470 620 580 740 Reg Line SD Line 380 560 690 540 350 508 437 440 420 450 562 535 600 650 550 616 632 660 640 650 670 730 490 600 750 724 828 560 590 460 750 The Reg and SD lines both go through the point of avera 620 690 Reg Line SD Line 590 640 550 560 511.75 595 595 490 640 520 650 450 490 620 730 620 690 490 610 400 500 590 640 420 460 540 500 300 610 600 710 360 490 440 460 370 370 440 680 480 490 490 460 400 550 540 640 440 570 500 600 Verbal SAT Pred Math SAT Pred Math SAT Verbal SAT Pred Math SAT Pred Math SAT 200 300 400 500 600 700 8 250 350 450 550 650 500 740 480 580 470 690 460 500 580 570 510 560 540 630 540 500 440 540 540 560 500 710 480 660 530 550 500 620 360 740 560 570 490 560 510 730 430 510 650 680 680 720 480 570 480 620 510 530 390 450 360 520 660 780 650 700 580 610 660 750 630 600 490 630 440 560 430 600 480 610 580 720 530 700 630 650 520 570 470 500 570 690 410 570 400 530 480 560 430 500 440 590 600 690 390 470 570 450 460 520 500 580 420 560 640 660 440 620 520 720 460 480 510 560 490 550 350 510 630 650 400 560...
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This note was uploaded on 01/30/2011 for the course ECON 253 taught by Professor Byun during the Spring '10 term at Wabash.

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TwoRegressionLines - TwoRegressionLines.xls This workbook...

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