Hi please can I get some help on Question 1 & 2
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) QUESTION 2 [22] Consider the data and the results obtained in Question 1. (2.1) Calculate the mean absolute deviation. (6) (2.2) Calculate the mean squared residuals. ( 9 ) (2.3) Calculate the coefficient of determination, R2. (6) (2.4) Calculate the adjusted coefficient of determination, Radj. (4) QUESTION 3 [16] The following model (M) was proposed for testing whether there was a significant interaction be- tween two predictor variables X1 and X2. y = Pot Bixit B2x2 + B3x2 + BAXIxzTE. (M) The regression ANOVA table for the model without interaction is the following: df SS MS F Significance F Regression 3 7474.7333 2491.5778 846.1803 2.8653 x 10-8 Residual 17.6667 2.945 Total 7492.4 The regression ANOVA table for the full model is the following: dif SS MS F Significance F Regression 7487.7803 1871.9451 2026.1339 3.3025 x 10-8 Residual 4.6197 0.9239 Total CO 7492.4 (3.1) Do the data provide sufficient evidence to support the model without interaction instead of the full model? Use a = 0.05. Show all necessary calculations before explaining your answer. (10) (3.2) Repeat the appropriate steps in part (3.1) using a = 0.01. (4) (3.3) Do we obtain the same conclusions in parts (3.1) and (3.2)? Explain your answer. (2) 3
