12. ANOVA for Verbal SAT as a Predictor of GPAHow well does a student’s Verbal SAT score (on an 800-point scale) predict future college grade point average (on a four-point scale)? Computer output for this regression analysis is shown below, using the data in StudentSurvey. The regression equation is GPA=2.03+0.00189VerbalSAT Analysis of Variance Source DF SS MS F P Regression 1 6.8029 6.8029 48.84 0.000 Residual Error 343 47.7760 0.1393 Total 344 54.5788 VerbalSAT GPA 540 3.13 520 2.5 550 2.55 490 3.1 720 2.7 600 3.2 640 2.77 660 3.3 550 2.8 670 3.7 500 2.09 580 530 2.9 650 3.08 700 590 3.86 600 3 700 3 610 3.35 550 3.3 550 3.4 560 2.9 560 3.5 550 3 550 3.3 700 3.7 610 3.48 570 3.4 550 2.5 500 3.3 610 3.5 610 3.79 500 3.3 640 2.9 490 2.68 560 3.28 560 3.51 470 2.6 680 3.85 570 2.4 630 3.4 580 2.4 550 3 490 3.1 590 2.94 620 3.31 560 3.3 630 2.9 600 3.4 550 3.16 590 640 3.84 650 3.6 420 2.36 500 2.9 620 3 600 3.3 580 3.7 490 2.9 630 3.6 600 3.56 590 3.7 550 4 600 3.4 500 600 3.3 600 3.1 650 2.5 650 3.2 560 3.1 540 3.5 640 3 690 3.25 600 2.4 610 3.22 610 600 580 3.64 560 3.5 620 2.5 620 3.4 630 430 3.25 640 3.7 490 2.1 550 2.8 690 3.49 550 3.83 600 530 2.7 520 2.8 660 3.13 800 3.62 560 2 610 3.6 660 4 650 3.1 680 2.6 550 3.7 660 3.57 650 2.9 620 3.15 530 3.88 670 3.5 640 2.8 680 670 2.9 730 3.21 580 3.5 610 3.33 580 3 620 3.5 680 3.95 570 2.1 500 3 800 3 610 3.75 550 2.5 600 3.4 660 3.4 640 3.14 560 2.6 600 3.4 480 2.7 650 3.15 520 2.2 640 3.5 610 2.9 450 2.5 700 3.5 540 3.6 550 3.1 640 3 560 3 530 3.8 620 3.15 550 2.75 520 2.8 660 3 470 3.1 570 2.27 560 2.8 520 3.02 560 2.93 600 3.2 400 3 540 3 400 2.7 530 3.2 530 2.9 517 3 620 2.72 590 3.3 590 620 2.22 540 3.26 490 3.5 540 3.1 640 3.3 620 3.29 680 800 3.69 510 2.65 620 3.25 670 2.8 560 3.36 630 2.97 590 3.31 630 3.05 470 2.2 550 3.3 690 3.45 660 3.83 600 3 700 3.35 660 2.4 540 3.1 520 3.4 550 2.82 600 2.9 600 3.4 520 3.2 490 3.2 600 3.8 620 3.57 530 3.33 550 2.9 600 3.2 610 3.1 550 3.25 560 3.4 670 3.8 610 3.38 660 3.88 630 2.75 520 2.9 670 3.6 550 2.8 560 2.2 390 600 3.3 560 2.85 610 3.37 710 3.5 710 3.55 560 3.2 600 2.47 540 2.72 600 3.4 600 550 3.4 550 3.1 620 3.1 550 2.94 570 3 530 570 3.6 620 3.6 520 3.5 620 3.4 520 3.5 680 3 630 2.75 730 3.56 440 2.7 670 3.68 500 3.5 630 3.5 680 3.4 530 2.6 630 3.25 600 3.3 700 3.2 590 2.9 670 3.85 780 3.4 660 3.4 600 510 2.7 800 3.81 740 3.4 780 3.23 440 3.1 700 2.89 660 2.81 520 3 600 3.77 760 3.3 680 3 520 2.9 510 3.5 600 3.6 650 3.7 700 3.2 650 2.87 520 3.3 580 3.3 600 3.45 520 3.1 750 3.71 650 3.3 550 3.3 650 640 3.73 660 3.13 640 3.89 530 3.05 690 3.2 630 3.25 600 2.9 560 3 720 3.5 610 3.5 720 3.6 590 3.4 620 3.25 550 2.7 800 3.78 670 4 550 3 620 3.3 520 2.8 440 2.5 720 3.5 390 2.8 560 3.4 570 3 660 3.27 620 3.5 660 3 630 3.6 610 3.25 540 3 570 2.75 600 2.9 600 3 530 3 560 2.9 560 3.36 500 3.25 560 3.5 500 2.76 640 660 2.75 550 3.25 630 3 700 2.8 560 3.4 580 3.25 800 3.5 460 3.05 700 3.18 660 3 500 2.23 600 3.4 650 3.3 640 3.43 620 3.88 570 3.45 540 3 670 3 620 3.18 650 2.2 560 3.29 480 3.5 460 2.8 500 2.9 680 3.5 550 2.5 630 3.25 620 2.9 560 3.66 590 3.01 530 2.25 690 3.2 550 3.35 600 3 610 3 600 3.48 750 2.88 470 2.6 550 2.75 540 3.3 530 3.25 540 3.3 680 3.2 510 2.6 500 3 680 3.25 500 3.3 570 3.25 540 2.83 550 3.3 680 3.6 630 3.7 650 2.83 680 3.3 550 3.44 600 3 540 3.27 550 2.3 500 2.6 (a) What is the predicted grade point average of a student who receives a 510 on the verbal SAT exam?Round your answer to two decimal places. (b) Use the information in the ANOVA table to determine the number of students included in the dataset. (c) Use the information in the ANOVA table to compute R2.Round your answer to one decimal place.
12. ANOVA for Verbal SAT as a Predictor of GPAHow well does a student’s Verbal SAT score (on an 800-point scale) predict future college grade point average (on a four-point scale)? Computer output for this regression analysis is shown below, using the data in StudentSurvey. The regression equation is GPA=2.03+0.00189VerbalSAT Analysis of Variance Source DF SS MS F P Regression 1 6.8029 6.8029 48.84 0.000 Residual Error 343 47.7760 0.1393 Total 344 54.5788 VerbalSAT GPA 540 3.13 520 2.5 550 2.55 490 3.1 720 2.7 600 3.2 640 2.77 660 3.3 550 2.8 670 3.7 500 2.09 580 530 2.9 650 3.08 700 590 3.86 600 3 700 3 610 3.35 550 3.3 550 3.4 560 2.9 560 3.5 550 3 550 3.3 700 3.7 610 3.48 570 3.4 550 2.5 500 3.3 610 3.5 610 3.79 500 3.3 640 2.9 490 2.68 560 3.28 560 3.51 470 2.6 680 3.85 570 2.4 630 3.4 580 2.4 550 3 490 3.1 590 2.94 620 3.31 560 3.3 630 2.9 600 3.4 550 3.16 590 640 3.84 650 3.6 420 2.36 500 2.9 620 3 600 3.3 580 3.7 490 2.9 630 3.6 600 3.56 590 3.7 550 4 600 3.4 500 600 3.3 600 3.1 650 2.5 650 3.2 560 3.1 540 3.5 640 3 690 3.25 600 2.4 610 3.22 610 600 580 3.64 560 3.5 620 2.5 620 3.4 630 430 3.25 640 3.7 490 2.1 550 2.8 690 3.49 550 3.83 600 530 2.7 520 2.8 660 3.13 800 3.62 560 2 610 3.6 660 4 650 3.1 680 2.6 550 3.7 660 3.57 650 2.9 620 3.15 530 3.88 670 3.5 640 2.8 680 670 2.9 730 3.21 580 3.5 610 3.33 580 3 620 3.5 680 3.95 570 2.1 500 3 800 3 610 3.75 550 2.5 600 3.4 660 3.4 640 3.14 560 2.6 600 3.4 480 2.7 650 3.15 520 2.2 640 3.5 610 2.9 450 2.5 700 3.5 540 3.6 550 3.1 640 3 560 3 530 3.8 620 3.15 550 2.75 520 2.8 660 3 470 3.1 570 2.27 560 2.8 520 3.02 560 2.93 600 3.2 400 3 540 3 400 2.7 530 3.2 530 2.9 517 3 620 2.72 590 3.3 590 620 2.22 540 3.26 490 3.5 540 3.1 640 3.3 620 3.29 680 800 3.69 510 2.65 620 3.25 670 2.8 560 3.36 630 2.97 590 3.31 630 3.05 470 2.2 550 3.3 690 3.45 660 3.83 600 3 700 3.35 660 2.4 540 3.1 520 3.4 550 2.82 600 2.9 600 3.4 520 3.2 490 3.2 600 3.8 620 3.57 530 3.33 550 2.9 600 3.2 610 3.1 550 3.25 560 3.4 670 3.8 610 3.38 660 3.88 630 2.75 520 2.9 670 3.6 550 2.8 560 2.2 390 600 3.3 560 2.85 610 3.37 710 3.5 710 3.55 560 3.2 600 2.47 540 2.72 600 3.4 600 550 3.4 550 3.1 620 3.1 550 2.94 570 3 530 570 3.6 620 3.6 520 3.5 620 3.4 520 3.5 680 3 630 2.75 730 3.56 440 2.7 670 3.68 500 3.5 630 3.5 680 3.4 530 2.6 630 3.25 600 3.3 700 3.2 590 2.9 670 3.85 780 3.4 660 3.4 600 510 2.7 800 3.81 740 3.4 780 3.23 440 3.1 700 2.89 660 2.81 520 3 600 3.77 760 3.3 680 3 520 2.9 510 3.5 600 3.6 650 3.7 700 3.2 650 2.87 520 3.3 580 3.3 600 3.45 520 3.1 750 3.71 650 3.3 550 3.3 650 640 3.73 660 3.13 640 3.89 530 3.05 690 3.2 630 3.25 600 2.9 560 3 720 3.5 610 3.5 720 3.6 590 3.4 620 3.25 550 2.7 800 3.78 670 4 550 3 620 3.3 520 2.8 440 2.5 720 3.5 390 2.8 560 3.4 570 3 660 3.27 620 3.5 660 3 630 3.6 610 3.25 540 3 570 2.75 600 2.9 600 3 530 3 560 2.9 560 3.36 500 3.25 560 3.5 500 2.76 640 660 2.75 550 3.25 630 3 700 2.8 560 3.4 580 3.25 800 3.5 460 3.05 700 3.18 660 3 500 2.23 600 3.4 650 3.3 640 3.43 620 3.88 570 3.45 540 3 670 3 620 3.18 650 2.2 560 3.29 480 3.5 460 2.8 500 2.9 680 3.5 550 2.5 630 3.25 620 2.9 560 3.66 590 3.01 530 2.25 690 3.2 550 3.35 600 3 610 3 600 3.48 750 2.88 470 2.6 550 2.75 540 3.3 530 3.25 540 3.3 680 3.2 510 2.6 500 3 680 3.25 500 3.3 570 3.25 540 2.83 550 3.3 680 3.6 630 3.7 650 2.83 680 3.3 550 3.44 600 3 540 3.27 550 2.3 500 2.6 (a) What is the predicted grade point average of a student who receives a 510 on the verbal SAT exam?Round your answer to two decimal places. (b) Use the information in the ANOVA table to determine the number of students included in the dataset. (c) Use the information in the ANOVA table to compute R2.Round your answer to one decimal place.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.6: Regression And Median-fit Lines
Problem 4GP
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Question
12. ANOVA for Verbal SAT as a Predictor of GPA
How well does a student’s Verbal SAT score (on an 800-point scale) predict future college grade point average (on a four-point scale)? Computer output for this
| The regression equation is GPA=2.03+0.00189VerbalSAT | |||||
| Analysis of Variance | |||||
| Source | DF | SS | MS | F | P |
|---|---|---|---|---|---|
| Regression | 1 | 6.8029 | 6.8029 | 48.84 | 0.000 |
|
Residual Error |
343 | 47.7760 | 0.1393 | ||
| Total | 344 | 54.5788 |
| VerbalSAT | GPA |
| 540 | 3.13 |
| 520 | 2.5 |
| 550 | 2.55 |
| 490 | 3.1 |
| 720 | 2.7 |
| 600 | 3.2 |
| 640 | 2.77 |
| 660 | 3.3 |
| 550 | 2.8 |
| 670 | 3.7 |
| 500 | 2.09 |
| 580 | |
| 530 | 2.9 |
| 650 | 3.08 |
| 700 | |
| 590 | 3.86 |
| 600 | 3 |
| 700 | 3 |
| 610 | 3.35 |
| 550 | 3.3 |
| 550 | 3.4 |
| 560 | 2.9 |
| 560 | 3.5 |
| 550 | 3 |
| 550 | 3.3 |
| 700 | 3.7 |
| 610 | 3.48 |
| 570 | 3.4 |
| 550 | 2.5 |
| 500 | 3.3 |
| 610 | 3.5 |
| 610 | 3.79 |
| 500 | 3.3 |
| 640 | 2.9 |
| 490 | 2.68 |
| 560 | 3.28 |
| 560 | 3.51 |
| 470 | 2.6 |
| 680 | 3.85 |
| 570 | 2.4 |
| 630 | 3.4 |
| 580 | 2.4 |
| 550 | 3 |
| 490 | 3.1 |
| 590 | 2.94 |
| 620 | 3.31 |
| 560 | 3.3 |
| 630 | 2.9 |
| 600 | 3.4 |
| 550 | 3.16 |
| 590 | |
| 640 | 3.84 |
| 650 | 3.6 |
| 420 | 2.36 |
| 500 | 2.9 |
| 620 | 3 |
| 600 | 3.3 |
| 580 | 3.7 |
| 490 | 2.9 |
| 630 | 3.6 |
| 600 | 3.56 |
| 590 | 3.7 |
| 550 | 4 |
| 600 | 3.4 |
| 500 | |
| 600 | 3.3 |
| 600 | 3.1 |
| 650 | 2.5 |
| 650 | 3.2 |
| 560 | 3.1 |
| 540 | 3.5 |
| 640 | 3 |
| 690 | 3.25 |
| 600 | 2.4 |
| 610 | 3.22 |
| 610 | |
| 600 | |
| 580 | 3.64 |
| 560 | 3.5 |
| 620 | 2.5 |
| 620 | 3.4 |
| 630 | |
| 430 | 3.25 |
| 640 | 3.7 |
| 490 | 2.1 |
| 550 | 2.8 |
| 690 | 3.49 |
| 550 | 3.83 |
| 600 | |
| 530 | 2.7 |
| 520 | 2.8 |
| 660 | 3.13 |
| 800 | 3.62 |
| 560 | 2 |
| 610 | 3.6 |
| 660 | 4 |
| 650 | 3.1 |
| 680 | 2.6 |
| 550 | 3.7 |
| 660 | 3.57 |
| 650 | 2.9 |
| 620 | 3.15 |
| 530 | 3.88 |
| 670 | 3.5 |
| 640 | 2.8 |
| 680 | |
| 670 | 2.9 |
| 730 | 3.21 |
| 580 | 3.5 |
| 610 | 3.33 |
| 580 | 3 |
| 620 | 3.5 |
| 680 | 3.95 |
| 570 | 2.1 |
| 500 | 3 |
| 800 | 3 |
| 610 | 3.75 |
| 550 | 2.5 |
| 600 | 3.4 |
| 660 | 3.4 |
| 640 | 3.14 |
| 560 | 2.6 |
| 600 | 3.4 |
| 480 | 2.7 |
| 650 | 3.15 |
| 520 | 2.2 |
| 640 | 3.5 |
| 610 | 2.9 |
| 450 | 2.5 |
| 700 | 3.5 |
| 540 | 3.6 |
| 550 | 3.1 |
| 640 | 3 |
| 560 | 3 |
| 530 | 3.8 |
| 620 | 3.15 |
| 550 | 2.75 |
| 520 | 2.8 |
| 660 | 3 |
| 470 | 3.1 |
| 570 | 2.27 |
| 560 | 2.8 |
| 520 | 3.02 |
| 560 | 2.93 |
| 600 | 3.2 |
| 400 | 3 |
| 540 | 3 |
| 400 | 2.7 |
| 530 | 3.2 |
| 530 | 2.9 |
| 517 | 3 |
| 620 | 2.72 |
| 590 | 3.3 |
| 590 | |
| 620 | 2.22 |
| 540 | 3.26 |
| 490 | 3.5 |
| 540 | 3.1 |
| 640 | 3.3 |
| 620 | 3.29 |
| 680 | |
| 800 | 3.69 |
| 510 | 2.65 |
| 620 | 3.25 |
| 670 | 2.8 |
| 560 | 3.36 |
| 630 | 2.97 |
| 590 | 3.31 |
| 630 | 3.05 |
| 470 | 2.2 |
| 550 | 3.3 |
| 690 | 3.45 |
| 660 | 3.83 |
| 600 | 3 |
| 700 | 3.35 |
| 660 | 2.4 |
| 540 | 3.1 |
| 520 | 3.4 |
| 550 | 2.82 |
| 600 | 2.9 |
| 600 | 3.4 |
| 520 | 3.2 |
| 490 | 3.2 |
| 600 | 3.8 |
| 620 | 3.57 |
| 530 | 3.33 |
| 550 | 2.9 |
| 600 | 3.2 |
| 610 | 3.1 |
| 550 | 3.25 |
| 560 | 3.4 |
| 670 | 3.8 |
| 610 | 3.38 |
| 660 | 3.88 |
| 630 | 2.75 |
| 520 | 2.9 |
| 670 | 3.6 |
| 550 | 2.8 |
| 560 | 2.2 |
| 390 | |
| 600 | 3.3 |
| 560 | 2.85 |
| 610 | 3.37 |
| 710 | 3.5 |
| 710 | 3.55 |
| 560 | 3.2 |
| 600 | 2.47 |
| 540 | 2.72 |
| 600 | 3.4 |
| 600 | |
| 550 | 3.4 |
| 550 | 3.1 |
| 620 | 3.1 |
| 550 | 2.94 |
| 570 | 3 |
| 530 | |
| 570 | 3.6 |
| 620 | 3.6 |
| 520 | 3.5 |
| 620 | 3.4 |
| 520 | 3.5 |
| 680 | 3 |
| 630 | 2.75 |
| 730 | 3.56 |
| 440 | 2.7 |
| 670 | 3.68 |
| 500 | 3.5 |
| 630 | 3.5 |
| 680 | 3.4 |
| 530 | 2.6 |
| 630 | 3.25 |
| 600 | 3.3 |
| 700 | 3.2 |
| 590 | 2.9 |
| 670 | 3.85 |
| 780 | 3.4 |
| 660 | 3.4 |
| 600 | |
| 510 | 2.7 |
| 800 | 3.81 |
| 740 | 3.4 |
| 780 | 3.23 |
| 440 | 3.1 |
| 700 | 2.89 |
| 660 | 2.81 |
| 520 | 3 |
| 600 | 3.77 |
| 760 | 3.3 |
| 680 | 3 |
| 520 | 2.9 |
| 510 | 3.5 |
| 600 | 3.6 |
| 650 | 3.7 |
| 700 | 3.2 |
| 650 | 2.87 |
| 520 | 3.3 |
| 580 | 3.3 |
| 600 | 3.45 |
| 520 | 3.1 |
| 750 | 3.71 |
| 650 | 3.3 |
| 550 | 3.3 |
| 650 | |
| 640 | 3.73 |
| 660 | 3.13 |
| 640 | 3.89 |
| 530 | 3.05 |
| 690 | 3.2 |
| 630 | 3.25 |
| 600 | 2.9 |
| 560 | 3 |
| 720 | 3.5 |
| 610 | 3.5 |
| 720 | 3.6 |
| 590 | 3.4 |
| 620 | 3.25 |
| 550 | 2.7 |
| 800 | 3.78 |
| 670 | 4 |
| 550 | 3 |
| 620 | 3.3 |
| 520 | 2.8 |
| 440 | 2.5 |
| 720 | 3.5 |
| 390 | 2.8 |
| 560 | 3.4 |
| 570 | 3 |
| 660 | 3.27 |
| 620 | 3.5 |
| 660 | 3 |
| 630 | 3.6 |
| 610 | 3.25 |
| 540 | 3 |
| 570 | 2.75 |
| 600 | 2.9 |
| 600 | 3 |
| 530 | 3 |
| 560 | 2.9 |
| 560 | 3.36 |
| 500 | 3.25 |
| 560 | 3.5 |
| 500 | 2.76 |
| 640 | |
| 660 | 2.75 |
| 550 | 3.25 |
| 630 | 3 |
| 700 | 2.8 |
| 560 | 3.4 |
| 580 | 3.25 |
| 800 | 3.5 |
| 460 | 3.05 |
| 700 | 3.18 |
| 660 | 3 |
| 500 | 2.23 |
| 600 | 3.4 |
| 650 | 3.3 |
| 640 | 3.43 |
| 620 | 3.88 |
| 570 | 3.45 |
| 540 | 3 |
| 670 | 3 |
| 620 | 3.18 |
| 650 | 2.2 |
| 560 | 3.29 |
| 480 | 3.5 |
| 460 | 2.8 |
| 500 | 2.9 |
| 680 | 3.5 |
| 550 | 2.5 |
| 630 | 3.25 |
| 620 | 2.9 |
| 560 | 3.66 |
| 590 | 3.01 |
| 530 | 2.25 |
| 690 | 3.2 |
| 550 | 3.35 |
| 600 | 3 |
| 610 | 3 |
| 600 | 3.48 |
| 750 | 2.88 |
| 470 | 2.6 |
| 550 | 2.75 |
| 540 | 3.3 |
| 530 | 3.25 |
| 540 | 3.3 |
| 680 | 3.2 |
| 510 | 2.6 |
| 500 | 3 |
| 680 | 3.25 |
| 500 | 3.3 |
| 570 | 3.25 |
| 540 | 2.83 |
| 550 | 3.3 |
| 680 | 3.6 |
| 630 | 3.7 |
| 650 | 2.83 |
| 680 | 3.3 |
| 550 | 3.44 |
| 600 | 3 |
| 540 | 3.27 |
| 550 | 2.3 |
| 500 | 2.6 |
(a) What is the predicted grade point average of a student who receives a 510 on the verbal SAT exam?
Round your answer to two decimal places.
(b) Use the information in the ANOVA table to determine the number of students included in the dataset.
(c) Use the information in the ANOVA table to compute R2.
Round your answer to one decimal place.
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