Time- Series Method of Least Square to fit Trend Fita trend line to the following data by the least squares method : Year 1985 1987 1989 1991 1993 Production (in ‘000) 18 a 23 27 16 Estimate the production in 1995 and 1997. The production data of a factory for the past 10 years are given : Year| 1977 | 1978 | 1979 | 1980 | 1981 | 1982 | 1983 | 1984 | 1985 | 1986 Production (intonnes) Fit a straight line trend and tabulate the trend value. What is the expected prodution in 1987 ‘on the basis of the trend? Given below are the figures of production a sugar factory: 75 | 86 | 98 | 90 | 96 | 108 | 124 | 140 |\.450 | 165 Year 1995 1996 1997 1998 (599, | 2000 2001 Production (ino00 tons) | 4° 45 46 42 49 46 Fita straight line trend by method of least squares and eatimate its value for 2004. Fit a straight line trend of the following data using the method of least squares. From the straight line trend, estimate the demand for the year 1995. Year it) 1979 | 1980 | 1981 | 1982 | 1983 | 1984 | 1985 Demand for House Hold Heaters (in thousand) _| L Fit a straight line trend of the following data using the method of least squares. From the straight line trend, estimate the demand for the year 2005, Year (y) 7998_[ 1999 | 2000 | 2001 | 2002 | 2003 | 2004 Demand for(v) productin| oq | 709 | @s0 | 1100 | 1300 | 1600 | 1800 units (in thousand) Fit a straight line showing the trend of the following data 600 | 825 | 970 | 1210 | 1440 | 1790 | 2070 Year 2004 | 2005 2006 | _2007 2008 Production of Rice | reas) 2B 39 2 | 4 56 Fita straight line trend for the following data. Estimate the production for the year 2010. Year 2002 [2003 2004 2005 | 2006 2007 2008 Production | 195 128 133 135 140 a. 143 (units) Calculate the trend values by the method of least square from the data given below and estimate the vear ny 1977 1978 1979 1980 [ Sales of Tv. sales (in'000) 18 20 2 27a The following are the annual profits in thousand in a certain business Year 1971 | 1972 1973 1974 | 1975, 1976 1977 Profit thousands) |_ © R 5 65 | 80 85 95 By the method of least squares fit a straight line. Using that estimate profit for 1981. www.beinggourav.com Scanned with CamScannerTime- Series 10. Fit a straight line by the method of least squares for the data relating to the Indian population census given below. [Year [1901 [1911 [1921 [1931 _| 1941 | 1951 | 1961 | i971 Feat opulation | 238.3 | 2520 | 251.2 | 2739 | 3185 | 3610 | 4391 | sazo (milion) 11. From the data given below fit a straight line trend by the method of least squares: [Year 1975 | 1976 | 1977 | 1978 | 1979 | 1980 | 1981 | 1982 a 67 53 | 43 | 61 s6 | 79 | 58 | 641 12. Below are given figures of production of a sugar factory : Year| 200i [2002 | 2003 | 2004 | 2005 | 2006 [2007 | 2008 Pao 80 90 92 83 94 2 | @ 110 Find the trend to the above data by method of least squares. 13, Using 2005 as the origin, obtain a straight line trend equation by Gres of least squares : Year| 2001 | 2003 2004 2005 2007 2008 value | 140 144 160 152 168 180 Find the trend value of the missing year 2002. 14. Fit a straight line trend method of the least squares to the following data: “Year 3003 | 2008 | 2005 | 2006 | 2007 Production (Rs. In Crores) 7 10 12 14 17 15. Fit a straight line trend method of the least squares to the following indices. Year 2002 2003 2004 2005, 2006 2007 2008 indexNo.| 127 [| 101 | 130 | 132 | 126 | 142 | 137 16. The following table show the number of salesman working a certain concern. ~ Year 2004 2005 2006 2007 [2008 —] number 28 38 46 40 56 Use the method of Least Square o fit a straight line and estimate the number of salesman in 2009. 17. Fit a parabolic trend of the form Y = a + bX +cX’ for the following data x 1 2 3 4 5 y 19 27 29 33 29 18, Fit a parabolictrend of the form ¥ = a + bX +cX° for the following data : Year 2004 2005 2006 2007 2008 Sales fn 10 2 13 10 8 tillion Rs.) Gourav Manjrekar Assistant Professor, Department of Mathematics and Statistics, MuLT.M,, Indore Scanned with CamScanner19, Time- Series Method of Moving Average: Calculate the 3-yearly moving averages of the data given below: 7983 [1984 | 1985 | 1986 | 1987 | 1988 | 1989 20. Years: i980 | 1981 | 1982 ‘Sales(milions| 3 [4 [8 6 | 7 |m [9 a0 [aa [a2 of rupees) Calculate the 3-yearly moving averages of f the data given below: Years: 1953 | 1954 | 1955 1956 | 1957_| 1958 | 1959 _| 1960 Values 36 to | 12 [14 [15 [16 21. Calculate the 4-yearly moving averages of the data given below: Years: 1991 | 1992 | 1993 1994 [1995 | 1996 | 1997 _| 1998 2. ‘Annual Sales( Rs. In Crores) 36 [43 (| 43 34 44 | 54 34 [2a The following table shows the average monthly production of coal in millions of fones for the year 1987-1996. year ‘Average monthly production of year Keil monthly production of coal (in million tones) ® “coal fin million tones) 1987 50.0 19928 38.1, 1988 36.5 1993 32.6 [1989 43.0 1994 47 1990. 44.5 1995, % Alt 1991 8.9 1996 33.8 Determine 4-yearly moving average figures Gourav Manjrekar Assistant Professor, Department of Mathematics and Statistics, M.LT.M., Indore Scanned with CamScanner