3.   In order to help estimate the peak power demand of a generating plant, data was collected to see if there was a linear relationship between the forecast high temperature for a day and the peak load demand for that day.  A random sample of 10 days was collected. Computer analysis of the data gave the following (abbreviated) results:

Variable        N       Mean       Std Dev           

temp           10      91.400      6.687         

load            10     195.000     45.225

                         Analysis of Variance

                           Sum of          Mean

Source           DF       Squares        Square   F Value   Pr > F

Regression      1         16735         16735     80.01   <.0001

Residual           8          1673           209   

Total                 9         18408

                       Parameter Estimates

                     Parameter       Standard

Variable     DF       Estimate          Error    

Intercept     1     -394.42097       66.05542

temp            1        6.44881        0.72097

(a)     Write the equation of the regression line of y on x for these data (use the “printout”, no computation required).

Regression line:

(b)    Does the “printout” indicate that the line is useful for prediction? Motivate your answer

(c)     Suppose the forecast high for tomorrow is 94. Provide the formula for the prediction interval in this case. Give a point estimate and 95% prediction interval for tomorrow’s peak demand load.