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# [Solved] STA304 Assignment 2 Fall 2019

Joined: 1 year ago
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05/02/2020 10:13 pm

STA304 Applied Statistics Assignment 2 Solution & Discussion Fall 2019

Question

For the following time series, determine the trend by using the method of (i) semi-averages, (ii) 3-year moving averages, and (iii) least-squares for fitting a straight line:

 Year 1968 1969 1970 1971 1972 1973 1974 1975 1976 Values of series 2 4 6 8 7 6 8 10 2

Which of the trend do you prefer, and why?

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Joined: 1 year ago
Posts: 2359
05/02/2020 10:18 pm

STA304 Applied Statistics Assignment 2 Solution & Discussion Fall 2019

Solution Idea:

I) semi –average

 year value Total Average Trend 1968 2 3.8 1969 4 4.6 20 5 1970 6 5.4 1971 8 6.2 1972 7 7.0 1973 6 7.8 1974 8 8.6 36 9 1975 10 9.4 1976 12 10.2

ii) 3 year moving:

 value Total Average 2 -- -- 4 12 4.0 6 18 6.0 8 21 7.0 7 21 7.0 6 21 7.0 8 24 8.0 10 30 10.0 12 -- --

iii) least-squares for fitting a straight line.

 year value X XY Trend value 1968 2 -4 16 -18 3 1969 4 -3 9 -12 4 1970 6 -2 4 -12 5 1971 7 -1 1 -8 6 1972 7 0 0 -40 7 1973 6 1 1 6 8 1974 8 2 4 16 9 1975 10 3 9 30 10 1976 12 4 16 48 11 Total 63 0 60 +100\+60 63

Let the equation of the straight line be

Then the two normal equations reduce to

Substituating the value, we get

Hence the require is with the origin at 1972. The trend values are obtained bu substituating the value of x in the first equation.these values appear in the last column of the above table. We prefer the least square trend as it is the better.