Please help The following output (from MINITAB) is for the least-squares fit of

Question

Please help The following output (from MINITAB) is for the least-squares fit of the model ln y = beta_0 + beta_1 ln x + epsilon, when represents the monthly production of a gas well and x represents the volume of fracture fluid pumped in. (A scatterp of these data is presented in Figure 7.22.) a. What is the equation of the least-squares line for predicting ln y from ln x? b. Predict the production of a well into which 2500 gal/ft of fluid have been pumped. c. Predict the production of a well into which 1600 gal/ft of fluid have been pumped. d. Find a 95% prediction interval for the production of a well into which 1600 gal/ft of fluid have been pump.

Explanation / Answer

Part-a

Equation of the least-square line for predicting ln y from lnx is

Ln PROD=-0.444+0.708 LN FLUID

Or ln Y= -0.444+0.798 LN X

Part-b

We have Fluid=2500

So, Ln PROD=-0.444+0.708 LN(2500)= 5.0954

Hence Production of well= exp(5.0954)= 163.27

Part-C

We have Fluid=1600

So, Ln PROD=-0.444+0.708 LN(1600)= 4.7795

Hence Production of well= exp(4.7795)= 119.04

Part-d

From output we have

95% prediction interval for ln PROD when ln FLUID=ln1600=7.3778 is (3.9738, 6.9176)

So, 95% prediction interval for PRODUCTION= (exp(3.9738), exp(6.9176)) =(53.19               1009.89)

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