Question

Test 2, Version 1: Name Show AL grading. L work. If more than one approach is shown, the wrong approach will be used for A study of external disk drives finds the following: 1) Capacity | 80 (in GB) | 120 | 240 | 320 | 1000 | 1500 | 4000 | X SD(x)- 1037.14 1408.38 | 27.95 | 34.00 | 50.50 | 69.95 | 95.00 | 205.00 | 459.00 | y- SD(y) 134.49155.19 Price (in S) The least squares line was found to be: Price 20.94+ 0.109 Capacity with Sc-19.27 and SE(bi)-0.0056. Find the 95% prediction interval for the price of a 1000 GB hard drive. (12)

Answer 1

SE(b1) = Se/√SSxx =

so, SSxx =[ Se/SE(b1) ]² = (19.27/0.0056)² = 11901142.9

X Value=   100  
Confidence Level=   95%  
      
      
Sample Size , n=   7  
Degrees of Freedom,df=n-2 =   5  
critical t Value=tα/2 =   2.571   [excel function: =t.inv.2t(α/2,df) ]
X̅ =    1037.14  

Predicted Y (YHat),Ŷ =   20.94   +   0.11   *x
x=100

Ŷ =   20.94   +   0.11   *100 = 31.886

margin of error,E=t*std error=t*S(ŷ)= = t*Se * √( 1 + 1/n+(X-X̅)²/Sxx)

= 2.571*19.27 * √(1 + 1/7 + (100-1037.14)²/11901142.9) = 54.6492

Prediction Interval Lower Limit=Ŷ -E =   -22.763
Prediction Interval Upper Limit=Ŷ +E =   86.535