18. A random sample of 4 professional athletes produced the following data where

Question

18.

A random sample of 4 professional athletes produced the following data where x is the number of endorsements the player has and y is the amount of money made (in millions of dollars).

X

0

1

2

5

Y

1

2

4

8

(a) Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit.

(b) Based on the equation from part (a), what is the predicted value of y if x = 3? Show all work and justify your answer

X

0

1

2

5

Y

1

2

4

8

Explanation / Answer

We will find an equation of the regression line in 4 steps.

Step 1: Find XY and X2 as it was done in the table below.

Step 2: Find the sum of every column:

X=8 , Y=15 , XY=50 , X2=30

Step 3: Use the following equations to find a and b:

a=YX2-XXY/nX2-(X)2=1530850/430(8)20.893

b=nXYXY/nX2-(X)2=450815430(8)2=1.429

Step 4: Substitute a and b in regression equation formula

y = a + bx

y=0.893+1.429x

for x=3. y= 5.18

X Y XY XX 0 1 0 0 1 2 2 1 2 4 8 4 5 8 40 25

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