The electric power consumed each month by a chemical plant

Chapter 12, Problem 10E

(choose chapter or problem)

The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature  \(\left(x_{1}\right)\) , the number of days in the month \(\left(\mathrm{x}_{2}\right)\) , the average product purity  \(\left(x_{3}\right)\), and the tons of product produced  \(\left(\mathrm{x}_{4}\right)\) . The past year’s historical data are available and are presented in Table E12-2.

Fit a multiple linear regression model to these data. Estimate \(\sigma^{2}\). Compute the standard errors of the regression coefficients. Are all of the model parameters estimated with the same precision?  Why or why not? Predict power consumption for a month in which  \(\mathrm{x}_{1}=75^{\circ} \mathrm{F}, \mathrm{x}_{2}=24\)  days, \(x_{3}=90 \%\)  and  \(\mathrm{x}_{4}=98\) tons.

Equation Transcription:

 

 

   

     

   

   

Text Transcription:

(x1)  

(x2)  

(x3)  

(x4)  

\sigma^{2}

x1=75° F, x2=24    

x3=90%

x4=98