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Find trend values using least square method 2010 2011 2012 2013 2014 2015 2016 year sales: (1000) 37 47 67 87 92 98 99?
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Find trend values using least square method 2010 2011 2012 2013 2014 2...
Calculating Trend Values using Least Square Method
Step 1: Calculate the sum of the x-values (years) and the sum of the y-values (sales)
- Σx = 2010 + 2011 + 2012 + 2013 + 2014 + 2015 + 2016 = 140
- Σy = 37 + 47 + 67 + 87 + 92 + 98 + 99 = 527
Step 2: Calculate the sum of the x-values squared and the sum of the product of x and y
- Σx^2 = 2010^2 + 2011^2 + 2012^2 + 2013^2 + 2014^2 + 2015^2 + 2016^2 = 1974570
- Σxy = (2010*37) + (2011*47) + (2012*67) + (2013*87) + (2014*92) + (2015*98) + (2016*99) = 146970
Step 3: Calculate the slope (b) of the trend line
- b = (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2)
- b = (7*146970 - 140*527) / (7*1974570 - 140^2)
- b = 7.42
Step 4: Calculate the y-intercept (a) of the trend line
- a = (Σy - bΣx) / n
- a = (527 - 7.42*140) / 7
- a = -994.57
Step 5: Form the equation of the trend line
- y = a + bx
- y = -994.57 + 7.42x
Step 6: Use the equation to find the trend values for the given years
- For 2010: y = -994.57 + 7.42*2010 = 37.8
- For 2011: y = -994.57 + 7.42*2011 = 45.2
- For 2012: y = -994.57 + 7.42*2012 = 52.6
- For 2013: y = -994.57 + 7.42*2013 = 60
- For 2014: y = -994.57 + 7.42*2014 = 67.4
- For 2015: y = -994.57 + 7.42*2015 = 74.8
- For 2016: y = -994.57 + 7.42*2016 = 82.2
These trend values represent the expected sales for each year based on the calculated trend line.
Step 1: Calculate the sum of the x-values (years) and the sum of the y-values (sales)
- Σx = 2010 + 2011 + 2012 + 2013 + 2014 + 2015 + 2016 = 140
- Σy = 37 + 47 + 67 + 87 + 92 + 98 + 99 = 527
Step 2: Calculate the sum of the x-values squared and the sum of the product of x and y
- Σx^2 = 2010^2 + 2011^2 + 2012^2 + 2013^2 + 2014^2 + 2015^2 + 2016^2 = 1974570
- Σxy = (2010*37) + (2011*47) + (2012*67) + (2013*87) + (2014*92) + (2015*98) + (2016*99) = 146970
Step 3: Calculate the slope (b) of the trend line
- b = (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2)
- b = (7*146970 - 140*527) / (7*1974570 - 140^2)
- b = 7.42
Step 4: Calculate the y-intercept (a) of the trend line
- a = (Σy - bΣx) / n
- a = (527 - 7.42*140) / 7
- a = -994.57
Step 5: Form the equation of the trend line
- y = a + bx
- y = -994.57 + 7.42x
Step 6: Use the equation to find the trend values for the given years
- For 2010: y = -994.57 + 7.42*2010 = 37.8
- For 2011: y = -994.57 + 7.42*2011 = 45.2
- For 2012: y = -994.57 + 7.42*2012 = 52.6
- For 2013: y = -994.57 + 7.42*2013 = 60
- For 2014: y = -994.57 + 7.42*2014 = 67.4
- For 2015: y = -994.57 + 7.42*2015 = 74.8
- For 2016: y = -994.57 + 7.42*2016 = 82.2
These trend values represent the expected sales for each year based on the calculated trend line.
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Find trend values using least square method 2010 2011 2012 2013 2014 2015 2016 year sales: (1000) 37 47 67 87 92 98 99?
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Find trend values using least square method 2010 2011 2012 2013 2014 2015 2016 year sales: (1000) 37 47 67 87 92 98 99? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find trend values using least square method 2010 2011 2012 2013 2014 2015 2016 year sales: (1000) 37 47 67 87 92 98 99? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find trend values using least square method 2010 2011 2012 2013 2014 2015 2016 year sales: (1000) 37 47 67 87 92 98 99?.
Find trend values using least square method 2010 2011 2012 2013 2014 2015 2016 year sales: (1000) 37 47 67 87 92 98 99? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find trend values using least square method 2010 2011 2012 2013 2014 2015 2016 year sales: (1000) 37 47 67 87 92 98 99? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find trend values using least square method 2010 2011 2012 2013 2014 2015 2016 year sales: (1000) 37 47 67 87 92 98 99?.
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