SAT scores 510 510 370 590 610 630 620 470 520 470 620 500 490 520 590 540 480 5

Question

SAT scores

510
510
370
590
610
630
620
470
520
470
620
500
490
520
590
540
480
540
640
360
530
550
610
510
490
640
500
440
510
660
470
440
600
450
440
500
450
650
560
600
730
490
650
610
640
410
490
620
510
660
580
470

ACT scores

23
25
14
29
26
32
30
24
28
22
30
21
23
25
23
25
23
24
27
16
16
26
26
31
25
28
22
20
24
29
20
16
27
20
23
21
20
27
22
31
32
25
25
27
27
21
28
21
21
29
28
23

The variables for this question are test scores on the SAT (Y) and ACT (X) examinations

for 52 college applicants. Graph the data to convince yourself that correlation and regression

are appropriate. Use SPSS for as much of the work as possible.

1. A student has an ACT score of 25, which we write as x = 25

(i) What SAT score do we predict this student is most likely to achieve?

(ii) Using the approximate procedures reviewed in the course notes in Sec. 9, p. 52.,

what is the probability this student will score above SAT of 600?

(iii) In this conditional distribution, what SAT score is at the 90th percentile?

Explanation / Answer

Part i

Regression equation = SAT score = 1.846803 * ACT score + 45.75964 = 1.846803 * 25 + 45.75964 = 91.96

Part ii

Part iii

SUMMARY OUTPUT Regression Statistics Multiple R 0.740519 R Square 0.548369 Adjusted R Square 0.539336 Standard Error 55.67512 Observations 52 ANOVA df SS MS F Significance F Regression 1 188183.3 188183.3 60.70979 3.5E-10 Residual 50 154985.9 3099.719 Total 51 343169.2 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 187.5148 45.79564 4.094598 0.000154 95.5315 279.498 95.5315 279.498 ACT scores 14.38964 1.846803 7.791649 3.5E-10 10.68023 18.09905 10.68023 18.09905

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