Question

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

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