The following output (from MATLAB) is for the least-squares fit of model ln y =

Question

The following output (from MATLAB) is for the least-squares fit of 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 in. (A scatterplot 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

a. Equation of the least-square line is as follows

ln y=-0.4442+0.70833 ln x

b. Predicted ln y= -0.4442 +0.70833 *ln(2500)= 5.0978    

Hence , Y=exp(5.0978)=163.6625213

c. From given output end, Predicted ln y=5.4457

Hence Y=exp(5.4457) =231.7594546

d. From given output 95% prediction interval of ln Y=(3.9738 , 6.9176)

So, 95% predictor interval for Y=(exp(3.9738) , exp(6.9176)) =( 53               1010)

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