The following table shows the inflation rate and unemployment rate, both in percent, for the years 1981-2008. We will investigate some methods for predicting unemployment. x (L1) y (L2) Year Inflation Unemployment 1985 3.8 7.2 1986 1.1 7 1987 4.4 6.2 1988 4.4 5.5 1989 4.6 5.3 1990 3.1 6.8 1991 4.1 7.5 1992 1.9 5.5 1993 2.7 6.9 1994 2.7 6.1 1995 3.5 5.6 1996 3.3 5.4 1997 1.7 4.9 1998 1.6 4.5 1999 2.7 4.2 2000 3.4 4 2001 3.6 5.7 2002 2.4 5.8 2003 1.9 6 2004 3.3 5.5 2005 3.4 5.12004 3.3 5.5 2005 3.4 5.1 2006 2.5 4.6 2007 4.1 4.6 2008 0.1 5.8 2009 2.7 9.3 2010 1.5 9.6 2011 3.0 8.9 2012 1.7 8.1 Enter inflation data into LI and unemployment data into L2. Be sure to check that the last entries match up correctly. You should have 28 matched entries in LI and L2: L1 LZ L3 3 L1 LZ L3 2 ASS SHW DowinN N 6. 12(28)=8. 1 1. Construct a scatterplot of unemployment (y) versus inflation (x). (Hint.. .use Excel)1. Construct a scatterplot of unemployment (y) versus inflation (x). (Hint.. .use Excel) 2. Do you detect any strong linearity?3. Compute the least-squares line for predicting unemployment from inflation. 4. Use your equation to predict the unemployment in a year when inflation is 3.5%. (Note: Data is in percent form) 5. Compute the correlation coefficient ( r ) between inflation and unemployment. Does this support your answer in #2? Explain. You have seen that the relationship between inflation and unemployment is not very strong. If we are interested in predicting unemployment, we would probably want to predict next year's unemployment from this year's inflation. To do this quickly in your calculator lists: a) Delete the first entry in L2 (7.2), then 7 becomes the first entry in L2; finally, delete the last entry in LI (1.7) so that 3 becomes the last entry in LI. b) Both lists should now be the same length (27 entries in each). a) b)You have seen that the relationship between inflation and unemployment is not very strong. If we are interested in predicting unemployment, we would probably want to predict next year's unemployment from this year's inflation. To do this quickly in your calculator lists: a) Delete the first entry in L2 (7.2), then 7 becomes the first entry in L2; finally, delete the last entry in LI (1.7) so that 3 becomes the last entry in LI. b) Both lists should now be the same length (27 entries in each). a) b) L1 LZ IL3 2 L1 LZ L3 WOSSSHW -- 12()=7 L1(28) = 6. Compute the least squares line for predicting next year's unemployment from this year's inflation. 7. Predict next year's unemployment if this year's inflation is 5.2%. (Note: Data is in percent form) 8. Compute the correlation coefficient between this year's inflation and next year's unemployment.9. Look at the scatterplot of this year's ination verses next year's unemployment. Do you detect a stronger linearity? If we are going to use data from this year to predict unemployment next year, why not use this year's unemployment to predict next year's unemployment? To do this quickly in your calculator lists: a) Insert 7.2 to the rst entry in L2, then copy L2 into Ll by moving the cursor onto the L1 label, then 2"\" - 2 - ENTER so that 1.2 is copied into L1. h) Finally, we want to go back to L2 and delete the rst entry (7.2) so that the rst entry becomes 7 and then back to L1 and delete the last entry (8.1) so that the last entry in L1 is 8.9. c) Both lists should now he the same length (27 entries in each) 8) h) 6) L1 L2 L3 2 Its ILE Hi 5.: u I L u a .. 3 llIlllltlltllllllltllllltlllllll 1 b) 6) L3 L1 L3 L1 2 ______ P2 ______ In! P 5.2 In: 5.2 5.5 5.3 5.5 5.3 5.3 5.3 5.5 5.5 5.5 5.I as 5.3 as ...... L2m=? Latin): 10. Compute the least squares line for predicting next year's unemployment from this year's unemployment. ll. Predict next year's unemployment if this year's unemployment is 3.7%. (Note: Data is in percent form) 12. Compute the correlation coefcient between this year's unemployment and next year's unemployment. 13. Based on you: correlation coefcient, do you suspect an even stronger linear relationship between this year's unemployment and next year's unemployment than in the last two models? Why or wh not? 10. Compute the least squares line for predicting next year's unemployment from this year's unemployment. 11. Predict next year's unemployment if this year's unemployment is 3.7%. (Note: Data is in percent form) 12. Compute the correlation coefficient between this year's unemployment and next year's unemployment. 13. Based on your correlation coefcient, do you suspect an even stronger linear relationship between this year's unemployment and next year's unemployment than in the last two models? Why or why not? Check your understanding by looking at the scatterplot of this year's and next year's unemployment. 14. Which of the models do you think provides the best linear prediction of unemployment? Explain
