Question

# Given are five observations for two variables, x and y. xi 1 2 3 4 5...

Given are five observations for two variables, x and y.

 xi 1 2 3 4 5 yi 4 6 6 11 15

1. Which of the following scatter diagrams accurately represents the data?

1.

2.

3.

• What does the scatter diagram indicate about the relationship between the two variables?

1. Develop the estimated regression equation by computing the the slope and the y intercept of the estimated regression line (to 1 decimal).
ŷ = + x
2. Use the estimated regression equation to predict the value of y when x = 3 (to 1 decimal).
ŷ =

#### Homework Answers

Answer #1
 X Y X * Y X2 Y2 1 4 4 1 16 2 6 12 4 36 3 6 18 9 36 4 11 44 16 121 5 15 75 25 225 Total 15 42 153 55 434

Part a)

Scatter diagram indicate there is positive and strong relationship between variables.

Part b)

Equation of regression line is Ŷ = a + bX

b = 2.7
a =( Σ Y - ( b * Σ X) ) / n
a =( 42 - ( 2.7 * 15 ) ) / 5
a = 0.3
Equation of regression line becomes Ŷ = 0.3 + 2.7 X

Part c)

When X = 3
Ŷ = 0.3 + 2.7 X
Ŷ = 0.3 + ( 2.7 * 3 )
Ŷ = 8.4

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