Question

The table provided presents data related to the level of personal consumption expenses of the Puerto Rican population for the period from 2001 to 2017, real data. We are interested in identifying the best statistical relationship between the level of personal consumption expenses 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

(3) With the variables of personal consumption expenditure, total employment and inflation rate; Find and analyze each of the points.

a. Correlation coefficient

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

c. Multiple regression equation for Ye

d. Error range

Answer 1

a. The correlation coefficient between

Y and X is -0. 722

Y and W is -0. 167

X and W is 0.680

b. Using large sample test for correlation coefficient, the test statistic is

t = r*√(n-2) /√(1-r^2), which follow a t distribution with n-2 degrees of freedom, the p-values for testing three correlation coefficients are given below

Y and X 0.001

Y and W 0.523

X andW 0.003

Therefore, correlation between Y and X, and between X and W are significant.

c. Multiple regression equation is given by

Ye = 155316563 - 96.917X + 2656.154W

d. Error range or the residual range is -14024. 45 to 7967.64.