A chemical power plant suspects that the number of pounds of steam used per month by the plant is related to the average ambient temperature for that month. The past year's steam usage (in thousand pounds) and temperatures (in °F) are in the following table Month Temp. Usage Month Temp. Usage Jan 21 185.79 July 68 621.55 Feb 24 214.47 Aug 74 675.06 Mar 32 288.03 Sept 62 562.03 Apr 47 424.84 Oct 50 452.93 May 50 454.58 Nov 41 369.95 June 59 539.03 Dec 30 273.98 In this section present the methods and analytical results. Be sure to include the work for any calculations you do. As part of your answer, specifically include these tasks. a) Provide a scatterplot. Does a simple linear regression model seem to be appropriate to describe the relationship between the steam usage per month (y) and the average monthly temperature (x)? b) Fit a simple linear regression model and graph the regression line in the scatterplot in a). c) Compute 95% confidence intervals (CIs) for the two regression coefficients. d) What is the estimate of expected steam usage when the monthly average temperature is 55°F? Provide a 95% CI for the expected steam usage when x=55. e) Construct a 95% prediction interval for the steam usage when x=55. f) Estimate the variance σ². g) Test the significance of regression. h) Produce residual plots and comment on model adequacy. i) Compute the R² value and explain what it means. The power plant suspects that the steam usage is related to the average temperature. Did the data support that? Explain why?