2. (35 points) The manager of a car plant wishes to investigate how the plant's electricity usage depends upon the amount of plant's production. The data set for plant's production and electrical usage for each month ofthe previous year is provided. The electrical usage (dependent variable), Y, is in units of million kWh, and production is measured as the value in million dollar units ofthe cars produced in that month. The followings are the results from the data set: 12 12 12 12 12 2x,- = 58.62, 2y, = 34.15, 2x3 = 291.231, 231,2 = 98.69676, 2 x,- y,- = 169.2583 i=1 i=1 i=1 i=1 i=1 a. (12 points) Find estimate of the slope and intercept parameters. b. {12 points) Find a 1-01 =95% prediction interval for a future response at x*= . c. (11 points) Find the sample correlation coefficient and test whether this is equal to "O\