Question

**#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?**

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

Student
1
2
3
4
5
6
7
Score on first SAT
530
410
380
600
480
440
380
Score on second SAT
560
460
400
620
500
520
430
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