19. Consider the following sample data: a. Construct a scatterplot and verify th

Question

19.

Consider the following sample data:

a.

Construct a scatterplot and verify that estimating a simple linear regression is appropriate in this problem.

b.

Calculate b0 and b1. What is the sample regression equation?

c.

Find the predicted value for y if x equals 20, 100, and 200.

19.

Consider the following sample data:

a.

Construct a scatterplot and verify that estimating a simple linear regression is appropriate in this problem.

b.

Calculate b0 and b1. What is the sample regression equation?

c.

Find the predicted value for y if x equals 20, 100, and 200.

22 24 27 21 23 14 14 15 101 139 250 88 87 14 16 20

Explanation / Answer

a.
Mean of X = X / n =    20
Mean of Y = Y / n =   89.375
(Xi - Mean)^2 =   176
(Yi - Mean)^2 =   44283.88
(Xi-Mean)*(Yi-Mean) =   2577
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2    
b1 = 2577 / 176 = 14.642  
bo = Y / n - b1 * X / n  
bo = 89.375 - 14.642*20 = -203.466  
  
Y = bo + b1 X  
  
Y'=-203.466+14.642*X  
c.
when x=20 then y=-203.466+14.642*20=89.374
when x=100 then y= -203.466+14.642*100 =1264.734
when x=200 then y= -203.466+14.642*200=2724.934

Line of Regression Y on X i.e Y = bo + b1 X X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 22 101 4 135.141 23.25 24 139 16 2462.641 198.5 27 250 49 25800.391 1124.375 21 88 1 1.891 -1.375 23 87 9 5.641 -7.125 14 14 36 5681.391 452.25 14 16 36 5383.891 440.25 15 20 25 4812.891 346.875

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