Given the following data X (consumers of teff) or popn 3 6 8 1 13 13 14 Y ( teff consumption) 8 6 10 12 12 14 20 year 2013 2014 2015 2016 2017 2018 2019 Estimate the regression equation, Y= a+bX, Where Y denotes demand for teff while X is consumers of teff (population) By assuming demand for teff is only affected by its consumers, find the amount demand for teff in the year 2022 if the populations (consumers of teff) are about 18 people?
- Given the following data
|
X (consumers of teff) or popn |
3 |
6 |
8 |
1 |
13 |
13 |
14 |
|
Y ( teff consumption) |
8 |
6 |
10 |
12 |
12 |
14 |
20 |
|
year |
2013 |
2014 |
2015 |
2016 |
2017 |
2018 |
2019 |
- Estimate the regression equation, Y= a+bX, Where Y denotes demand for teff while X is consumers of teff (population)
- By assuming demand for teff is only affected by its consumers, find the amount demand for teff in the year 2022 if the populations (consumers of teff) are about 18 people?
(Hint: use the least square method, parameter a and b can be estimated by solving the two linear equations)
SY= na+ bSX
SXY=aSX +b Where n is number of years.
For example, Estimate the sales for 2012, 2015 and fit a linear regression equation and
draw a trend line.ar X Sales (Y) XY X2
|
year |
X |
Sales (Y) |
XY |
X2 |
|
2002 |
1 |
22734 |
22734 |
1 |
|
2003 |
2 |
24731 |
49462 |
4 |
|
2004 |
3 |
31489 |
94467 |
9 |
|
2005 |
4 |
44685 |
178740 |
16 |
|
2006 |
5 |
55319 |
276595 |
25 |
|
2007 |
6 |
91021 |
546126 |
36 |
|
2008 |
7 |
146234 |
1023638 |
49 |
|
2009 |
8 |
107887 |
863096 |
64 |
|
2010 |
9 |
127483 |
1147347 |
81 |
|
2011 |
10 |
97275 |
972750 |
100 |
|
|
ΣX = 55 |
ΣY= 748858 |
ΣXY= 5174955 |
ΣX2= 385 |
ΣY = na + bΣX ----- (i)
ΣXY = aΣX + bΣX2 ----- (ii)
748858 = 10a + 55b ----- (i)
5174955 = 55a + 385 b ----- (ii)
Equation (i) x 3 5242006 = 70a + 385 b ----- (iii)
Equation (iii) – (ii) 67051 = 15a, 4470.07 = a
Substitute value of ‘a’ in equation (i)
748858 = 44700 + 55 b
55b = 748858 – 44700 Y = 4470.07 + 12802.8 X
b = 12802.8 Sales for 2012 = 4470.07 + 12802.8 (11) = 145300.87
Y = a + b X Sales for 2015 = 4470.07 + 12802.8 (14) = 183709
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