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QUESTION 1 [32] Describe the usefulness of following statistics and indicate how they are calculated: (1.1) The variance ination factor. (4) {1.2) The adjusted coefficient of determination. (4) (1.3} The C-statistic. (4) (1.4) The table below describes the sales {)5} of a certain product in two consecutive years. As- sume that the simple linear regression model y, = n + m: + at provides the trend of the data. year month time {I} sales 0,) 1 1 200 1 2 21 1 1 3 203 1 4 247 1 5 239 1 6 269 1 7 31 1 1 3 262 1 9 260 1 10 256 1 1 1 261 1 12 283 2 13 296 2 14 276 2 15 305 2 16 303 2 17 356 2 13 393 2 19 363 2 20 336 2 21 443 2 22 303 2 23 365 2 24 391 (a) Calculate the point estimates 3}] and :31 of g and ,6], respectively. Then write down the fitted model. Do not use Excel buih-in routines for regression. but you can use Excel as a calculation spreadsheet. (8} STA2604IO1 1l3f2021 (it) Use the results in part (a) to calculate the tted values 3a} of the data. Insert the tted values in the table after rounding them to the nearest integer. (4) (c) Calculate the residuals n = y; - 33}. (4) (d) Plot the residuals rt versus times t. Use Excel for the plot. (2) (e) Do the plot of residuals indicate first order autocorrelation in the data? If so, which type of autocorrelation is displayed? Explain your answer without using a formal test for autocorrelation. (2)