Question

Table 2 presents the quarterly energy bills for a school system. The energy bills are the combined gas, oil, and electrie bills for the school system and are expressed in units of $100. Table 2: Quarterly v Bills for the School Svstem ( × $100 ter3 (Qa ter4 (Q ear er 1344.39 246.63y2131.53 y) 288.87 313.45 246.84 277.01 365.10 267.00 467.06 336.56 440.00 10 434.66 ( 189.76 209.00 197.98 207.51 230.28 306.03 196.67 315.04 179.10 1.21 50.68 4.63 230.32 253.23 152.15 216.42 221.10 133.89 218.08 214.09 126.41 279.46 319.67 339.78 9 399.66 (y) 330.80 ( 539.78に a.) Plot the energy bills versus time and explain what kind of trend appear to exist? b.) From the plot in part (a), what type of seasonal variation appear to exist? Is a transfor- mation needed to obtain a series that display constant variation? c) Use R to fit the regression model (include your code and output summary) 1.) Do all independent variables in the model seem important? Justify your answer statistically 2.) Write the prediction equation for this model, and use it to calculate u and ý2 3) Find and report point forecasts and 95% prediction intervals for the energy bills in period 41, 42, 43, and 44 .) Test for positive autocorrelation by using the Durbin-Watson statistic and setting 0.05 d.) Use R to fit the regression model where tt-ф14-1 + at L) Identify the value for 여. Is it statistically different from 0? 2.) Do all independent variables in the model seem important? Justify your answer statistically 3.) Write the prediction equation for this model, and use it to calculate and 4) Find and report point forecasts and 95% prediction intervals for the energy bills in period 41, 42, 43, and 44

Answer 1