Question

Consider the following table of data. x 1 1 2 2 10 y 3 2 3...

Consider the following table of data.

x

1

1

2

2

10

y

3

2

3

2

10

a.

Calculate the least squares line and the correlation coefficient.

b.

Repeat part​ (a), but this time delete the last point.

c.

Draw a graph of the​ data, and use it to explain the dramatic difference between the answers to parts​ (a) and​ (b).
Math   Statistics-And-Probability   
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Homework Answers

Answer #1

a.

Sum of X = 16
Sum of Y = 20
Mean X = 3.2
Mean Y = 4
Sum of squares (SSX) = 58.8
Sum of products (SP) = 51

Regression Equation = ŷ = bX + a

b = SP/SSX = 51/58.8 = 0.8674

a = MY - bMX = 4 - (0.87*3.2) = 1.2245

ŷ = 0.8674X + 1.2245

b.

Sum of X = 6
Sum of Y = 10
Mean X = 1.5
Mean Y = 2.5
Sum of squares (SSX) = 1
Sum of products (SP) = 0

Regression Equation = ŷ = bX + a

b = SP/SSX = 0/1 = 0

a = MY - bMX = 2.5 - (0*1.5) = 2.5

ŷ = 0X + 2.5

c. With last point graph is

Without last point graph is

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