The table provided presents the data related to the level of personal consumption expenditures of the Puerto Rican population for the period from 2001 to 2017, real data. We are interested in identifying which is the best statistical relationship between the level of personal consumption expenditures with the level of the inflation rate and total employment.

Personal consumption expenses Total Employment Rate of inflation

Y X W

2001 37,590.30 1,144 2.70

2002 38,844.90 1,152 -1.00

2003 40,973.40 1,188 1.90

2004 43,396.00 1,206 0.90

2005 47,065.15 1,213 4.15

2006 50,148.83 1,254 6.56

2007 52,086.58 1,263 4.22

2008 54,553.80 1,203 4.50

2009 55,122.10 1,144 2.80

2010 56,783.80 1,075 2.00

2011 58,154.80 1,043 1.80

2012 60,897.00 1,024 2.60

2013 62,477.60 1,012 0.90

2014 61,899.40 988 0.90

2015 61,640.50 979 -0.30

2016 61,496.60 992 -0.20

2017 61,562.70 989 0.60

With the variables of Personal Consumption Expenditure and Total Employment; find and analyze each of the points:

a. Linear scatter diagram

b. Correlation coefficient

c. Perform null hypothesis test that linear correlation coefficients in the universe are not significantly different from zero. Present the six learned steps, with a significance level of 0.025, for the t & F test.

d. Linear Regression Equation for Y and Error range