Answer to Question #281073 in Macroeconomics for Asmita dixit

Question

Forecast the demand for the rice for a country for the year 2021 on the basis of 7-year moving average and least square method, data given in table:

Year 2014 2015 2016 2017 2018 2019 2020

Population (millions) 10 12 15 20 25 30 40

Rice consumed (million tonnes) 40 50 60 70 80 90 100

Answer 1

Mean of x values:

$=(10+12+15+20+25+30+40)/7=21.7$

Mean of y values:

$=(40+50+60+70+80+90+100)/7=70$

The normal equations are:

$y=an+b\Sigma x$

$xy=a\Sigma x +b\Sigma x^2$

Subst. into the normal equations:

$7a+152b=490$

$152a+3994b=12000$

$1064a+23104b-(1064a+27958b)=74480-84000$

$b=2.$

$7a=490-152(2)$

$a=26.57$

$y=a+bx$

$y=26.57+2x$