Given information:
The below table presents the inflation rate and unemployment rate, both in percent, for the year 1988−2015 .
Year 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Inflation ( x ) 4.4 4.6 6.1 3.1 2.9 2.7 2.7 2.5 3.3 1.7 1.6 2.7 3.4 1.6 2.4 1.9 3.3 3.4 2.5 4.1 0.1 2.7 1.5 3 1.7 1.5 0.8 0.8 Unemployment ( y ) 5.5 5.3 5.6 6.8 7.5 6.9 6.1 5.6 5.4 4.9 4.5 4.2 4 4.7 5.8 6 5.5 5.1 4.6 4.6 5.8 9.3 9.6 8.9 8.1 7.4 6.2 5.3
Concept Used:
The correlation coefficient is given as,
r=1n−1∑( x− x ¯ s x )(y−y¯sy)
The coefficient of variation is denoted by r2 .
Where,
n is the number of observationsx¯ is the average of xy¯ is the average of ysx is the standard deviation of xsy is the standard deviation of y
Calculation:
Here,
x=inflation and y=unemployment
n=28 x¯=2.60714 y¯=6.04286sx=1.27452sy=1.51154
Year 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Inflation ( x ) 4.4 4.6 6.1 3.1 2.9 2.7 2.7 2.5 3.3 1.7 1.6 2.7 3.4 1.6 2.4 1.9 3.3 3.4 2.5 4.1 0.1 2.7 1.5 3 1.7 1.5 0.8 0.8 Unemployment ( y ) 5.5 5.3 5.6 6.8 7.5 6.9 6.1 5.6 5.4 4.9 4.5 4.2 4 4.7 5.8 6 5.5 5.1 4.6 4.6 5.8 9.3 9.6 8.9 8.1 7.4 6.2 5.3 x− x ¯ s x 1.406694 1.563616 2.74053 0.386702 0.229781 0.072859 0.072859 −0.08406 0.543624 −0.71175 −0.79021 0.072859 0.622085 −0.79021 −0.16252 −0.55483 0.543624 0.622085 −0.08406 1.171312 −1.96712 0.072859 −0.86867 0.308242 −0.71175 −0.86867 −1.4179 −1.4179 y− y ¯ s y −0.35914 −0.49146 −0.29299 0.500906 0.96401 0.567064 0.037803 −0.29299 −0.4253 −0.75609 −1.02072 −1.21919 −1.35151 −0.88841 −0.16067 −0.02836 −0.35914 −0.62377 −0.95456 −0.95456 −0.16067 2.154849 2.353322 1.890218 1.360956 0.897853 0.10396 −0.49146 ( x− x ¯ s x )( y− y ¯ s y ) −0.50521 −0.76845 −0.80294 0.193702 0.221511 0.041316 0.002754 0.024629 −0.2312 0.538147 0.806585 −0.08883 −0.84075 0.702028 0.026113 0.015732 −0.19524 −0.38804 0.080243 −1.11809 0.316059 0.157 −2.04427 0.582644 −0.96866 −0.77994 −0.14741 0.696839
r=1n−1∑( x− x ¯ s x )( y− y ¯ s y ) =−4.4737228−1 =−0.16569r2=(−0.16569)2 =0.027454
Calculation:
In regression, the coefficient of determination explains the proportion of variation in the dependent variable.
It was calculated that the coefficient of determination
r2=0.027454
Therefore the proportion of the variation in unemployment is explained by inflation is 0.027454 .