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#4: A graduate student in educational psychology was interested in the relationship between the amount of...

#4: A graduate student in educational psychology was interested in the relationship between the amount of money a high school student’s parents spend on SAT preparation and the number of points that the students SAT Verbal score improves. Her results for 8 students are listed below (X = amount of money spent on test preparation, Y = amount of increase in Verbal SAT score.)

STUDENT                                         X                                             Y

A                                                         100                                         20

B                                                         600                                        70

C                                                          150                                          40

D                                                         300                                         80

E                                                          400                                         30

F                                                          800                                         110

G                                                         200                                         10

H                                                         700                                         90

According to this data, what will a student’s SAT verbal score if his or her parents spend 900.00 on test preparation? What will the score be if he or she spends 500.00? What if they spend no money at all on test preparation?

Math   Statistics-And-Probability   
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Answer #1

The obtained regression equation is given below:

y = 0.1142x + 9.873

Let's estimate the value of Y at x = 500

y = 0.1142x + 9.873

= 0.1142(900) + 9.873

= 112.653

Let's estimate the value of Y at x = 500

y = 0.1142x + 9.873

= 0.1142(500) + 9.873

= 66.973

Now, what is the money spent is equal to 0,

If the amount is zero then the increase in the SAT score will be equal to 9.873 as it is the value of Y-intercept.

y = 0.1142x + 9.873

= 0.1142(0) + 9.873

= 0 + 9.873

= 9873

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