3.2 Montgomery, Peck, and Vining (2012) present data on the number of pounds of steam used per month at a plant. Steam usage is thought to be related to the average monthly ambient temperature. The past year's usages and temperatures are shown in Table E3.2. TABLE E3.2 Monthly Steam Usage and Average Ambient Temperature Month Temperature (F) Temperature Usage/1000 Month (F) Usage/1000 January 21 185.79 July 68 621.55 February 24 214.47 August 74 675.06 March 32 288.03 September 62 562.03 April 47 424.84 October 50 452.93 May 50 454.68 November 41 369.95 June 59 539.03 December 30 273.98 a. Fit a simple linear regression model to the data. b. Test for significance of regression. c. Analyze the residuals from this model. d. Plant management believes that an increase in average ambient temperature of one degree will increase average monthly steam consumption by 10,000 lb. Do the data support this statement? e. Construct a 99% prediction interval on steam usage in a month with average ambient temperature of 58F.