3. The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in °F) for that month. The past year's usage and temperatures are in the following table: Month Temp. Usage/1000 Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. 21 24 32 47 50 59 68 74 62 50 41 30 185.79 214.47 288.03 424.84 454.58 539.03 621.55 675.06 562.03 452.93 369.95 273.98 Assuming that a simple linear regression model is appropriate, fit the regression model relating steam usage (y) to the average temperature (x). (a) Find a 99% confidence interval for B₁. (b) Find a 99% confidence interval for B. (c) Find a 95% confidence interval on mean steam usage when the ave is 51°F. (d) Find a 95% prediction interval on steam usage when the temperature is 51°F. perat

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