Practice Problem 2: Hours Spent | Math SAT Studying (x)1 Score (y) Is there a re

Question

Practice Problem 2: Hours Spent | Math SAT Studying (x)1 Score (y) Is there a relationship between Math SAT scores and the number of hours spent studying for the test? A study was conducted involving 20 students as they prepared for and took the Math section of the SAT Examination. 390 580 650 730 410 530 600 790 350 400 590 640 450 520 690 690 770 10 14 4 7 12 a. Find the equation of the best-fit line. b. Decide whether the new equation is a "good fit to 5 6 represent this data, and explain why your statistics justify your decision. 16 13 13 10 700 730 640 If a student spent 20 hours studying, what would be the expected Math SAT score? c.

Explanation / Answer

2.

a.

calculation procedure for regression

mean of X = X / n = 9.45

mean of Y = Y / n = 592.5

(Xi - Mean)^2 = 470.95

(Yi - Mean)^2 = 346575

(Xi-Mean)*(Yi-Mean) = 11927.5

b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2

= 11927.5 / 470.95

= 25.3265

bo = Y / n - b1 * X / n

bo = 592.5 - 25.3265*9.45 = 353.1649

value of regression equation is, Y = bo + b1 X

Y'=353.1649+25.3265* X

b. yes,

equation of regression is good for best fit line

c.

student spent 20 hours then expected value is

Y' = 353.1649 +25.3265*20

Y'=859.6949

Line of Regression Y on X i.e Y = bo + b1 X X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 4 390 29.7025 41006.25 1103.625 9 580 0.2025 156.25 5.625 10 650 0.3025 3306.25 31.625 14 730 20.7025 18906.25 625.625 4 410 29.7025 33306.25 994.625 7 530 6.0025 3906.25 153.125 12 600 6.5025 56.25 19.125 22 790 157.5025 39006.25 2478.625 1 350 71.4025 58806.25 2049.125 3 400 41.6025 37056.25 1241.625 8 590 2.1025 6.25 3.625 11 640 2.4025 2256.25 73.625 5 450 19.8025 20306.25 634.125 6 520 11.9025 5256.25 250.125 10 690 0.3025 9506.25 53.625 11 690 2.4025 9506.25 151.125 16 770 42.9025 31506.25 1162.625 13 700 12.6025 11556.25 381.625 13 730 12.6025 18906.25 488.125 10 640 0.3025 2256.25 26.125

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