Do the following problems using R. you need to print both codes and results. 1. Spreading rate of spilled liquid. A contract engineer at DuPont Corp. studied the rate at which a spilled volatile liquid will spread across a surface (Chemical engineering Progress, January 2005). Assume 50 gallons of methanol spills onto a level surface outdoors The engineer used derived empirical formulas (assuming a state of turbulent free convection) to calculate the mass (in pounds) of the spill after a period of time ranging from 0 to 60 minutes. The data are saved in LIQUIDSPILL file Consider a straight-line model relating mass of the spill (v) to elapsed time of the spill(x) a. Draw a scatter plot of the data. Is straight-line model a good model for this data? b. Do the data indicate that the mass of the spill tends to diminish as time increases? If so, how much will the mass diminish each minute? Hint: ind ^1 and interpret it. c. Is there sufficient evidence (at 0.05) to indicate that the spill mass (y) tends to diminish linearly as time (x) increases? d. Find a 90% confidence interval for the mean mass of all spills with an elapsed time of 15 minutes. Interpret the result e. Find a 90% prediction interval for the mass of a single spill with an elapsed time of 15 minutes. Interpret the result f. Find a 95% confidence interval for A. Interpret your results g. Find the coefficient of determination for the linear model you constructed in part b. Interpret your result S444744855954 0778047620 63049495174186319631000 M666544333222-1110000000 02468024680505050