Question

Instructions: Analyze the residuals in from the simulated data. Your submission should include:

o Part 1: Distribution of Residuals
- a histogram
- A comparison of the measures of center
- A discussion of the spread (standard deviation is sufficient for this project)
- a brief explanation of what you learned from the analysis about the distribution of residuals. Be sure to discuss shape, symmetry, and/or skew of the distribution.   What does the shape of the distribution reveal about the distribution of residuals? Did you learn anything interesting? Unexpected? Note-worthy?

o Part 2: Unusual Residuals
- Illustrate 2 methods for detecting “unusual” residuals.
• 1.5 IQR Rule for detecting outliers
• Z-scores greater than +/- 2
- Were you able to detect any unusual residuals? If so, which classrooms? In which schools were the classrooms located? Do you think that you uncovered a “pattern” of unusual residuals?

o Part 3: Read the 2009 AJC article about the APS cheating scandal. How does our project work mimic the analysis utilized by the AJC investigators? Write a narrative (about 500 words) that explains the parallels. Your narrative should include quotes from the AJC article. The focus of the narrative should be on the statistical analysis. What techniques were employed by the AJC/you? What standards were employed by the AJC/you?
Bonus: Deduce the regression equation that the AJC analysts used. Interpret the slope and the y-intercept of their equation. How does it compare the your project equation?

School 2008 2009
Monroe 690 716
Jackson 667 712
Monroe 648 632
Monroe 742 714
Harrison 723 727
Adams 697 708
Van Buren 688 745
Madison 759 753
Madison 738 745
Madison 781 789
Washington 692 754
Van Buren 770 810
Van Buren 648 674
Jackson 724 711
Jefferson 646 675
Jackson 681 680
Harrison 600 637
Adams 684 690
Adams 728 745
Washington 624 672
Washington 678 720
Washington 731 774
Madison 657 702
Jackson 694 706
Van Buren 700 712
jackson 659 671
Harrison 703 695
Washington 589 643
Monroe 704 729
Harrison 677 677
Jefferson 681 709
Madison 703 715
Jackson 681 711
Adams 707 713
Jefferson 620 596
Jefferson 649 700
Van Buren 698 680
Monroe 788 804
Jefferson 674 700
Jackson 773 738
Van Buren 670 673
Washington 710 738
Jefferson 677 680
Washington 803 867
Jefferson 607 638
Van Buren 609 622
Harrison 635 660
Monroe 748 770
Van Buren 722 710
Harrison 621 631
Van Buren 678 653
Washington 711 790
Monroe 742 731
Monroe 699 757
Washington 717 738
Jefferson 714 742
Van Buren 672 709
Monroe 732 765
Jefferson 652 673
Madison 648 670
Washington 718 786
Harrison 619 650
Adams 778 782
Washington 689 701
Harrison 625 651
jackson 714 743
Madison 639 618
Washington 648 690
Monroe 642 642
Van Buren 704 744
Jackson 755 761
Jackson 754 760
Monroe 613 631
Washington 740 771
Monroe 716 733
Adams 670 661
Harrison 747 810
Jefferson 651 635
Adams 690 685
Van Buren 682 730
Jefferson 697 719
Jackson 706 712
Jackson 801 820
Harrison 689 669
Madison 709 694
Jackson 663 679
Washington 651 710
Madison 691 695
Van Buren 735 727
Van Buren 660 693
Adams 719 756
Harrison 713 690
Harrison 643 687
Jefferson 665 694
Adams 706 755
Jackson 631 690
Jefferson 705 727
Monroe 702 738
Monroe 753 771
Monroe 754 780

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Part 1:
The residuals are taken as a percentage change in the scores between two years. This calculation is more appropriate than simply taking a difference of two values because the change in the same points at schools with high score and schools with low score will have a different interpretation in the improvement/worsening of students’ learning outcome. Because students in the same school are expected to perform similarity between two years, the percentage change will have a correct interpretation to analyze the score data and the discussion in Part 3 of this project. I also refer to the residuals as improvement rate to make the discussion of data analysis sound more practical....

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