Time Series Analysis 745 Q.10.26 (a) Fit a straight line to the following data, also determine the trend values as well: Years 1997 1998 1999 2090 2001 2002 Values 12 10 11 18 15 24 (b ) Compute trend values by fitting a straight line. Years 1990 1991 1992 1993 1994 1995 1996 Values 81 84 88 104 134 148 170 Q.10.27 (a) Determine the trend line by the least squares method from the following data. Plot the actual values and the linear trend on same graph. Years 1995 1996 1997 1998 1999 2000 2001 2002 2003 Price in Rs. 3 6 2 10 7 9 14 12 18 ( b ) Use the method of least squares to determine the linear trend line for the following data. Also compute the trend values and make an estimate of the number of bags of fertilizer sold in the Ist and 2nd quarters of 1999. Years Quarters I II III IV 1995 72 98 79 106 1996 79 122 101 143 1997 94 141 128 160 1998 125 143 135 187 Q.10.28 (a) Fit a quadratic parabola to the following series of observations taking the years as independent variable. Years 1924 1927 1930 1933 1936 1939 1942 Index of coal prices 187 142 133 129 136 169 279 Use your results to estimate the value of the index for 1935. ( b ) Fit a second degree parabola to the following results, for the years 1955-1965 (both inclusive). EX= 0, EY= 410, EXY = 601 EX?Y = 4587, EX? = 110, EX' = 0, EX4 = 1958 Find out the trend values as well. Q.10.29 (a) If the second degree parabola fitted to the data for 1970 to 1979 (both inclusive) with origin at the middle of 1974 and 1975 is Y = 100.356 + 11.333X + 1.006X2 the unit of X being half year, find the trend values corresponding to the years 1970-1979. to the