Question

It is widely believed that the more education one receives the higher the income earned at the time of first employment and over the course of a career. However, due to varying reasons, many people never complete high school and, thus, never receive their high-school diploma. Although individuals without a high-school diploma are often able to find employment, they experience economic outcomes quite different from those who finish high school before entering the workforce to earn a living. Across the nation, there are millions of individuals with families who are now working but do not possess the credentials of a high-school diploma. Many of these individuals and their families are considered to be a part of the working poor that make up a considerable portion of this nation’s labor force.

1. A student states that a decrease in the percent of 18-64 yr-olds with no high school diploma will no doubt lead to a decrease in the percent of low-income working families. Write at least two concise sentences addressing the key uses and limitations of linear correlation and use these to respond to the student’s statement. In addition, using the R-squared value for the regression equation, provide a statement about its meaning, in general, and, specifically, in the context of this project.

1. Reference(s): The Working Poor Families Project. (2011). Indicators and Data. Retrieved from http://www.workingpoorfamilies.org/indicators/ 2011 Data Jurisdiction Percent of low income working families (<200% poverty level) Percent of 18-64 year olds with no HS diploma Alabama 37.3 15.3 Alaska 25.9 8.6 Arizona 38.9 14.8 Arkansas 41.8 14 California 34.3 17.6 Colorado 27.6 10.1 Connecticut 21.1 9.5 Delaware 27.8 11.9 District of Columbia 23.2 10.8 Florida 37.3 13.1 Georgia 36.6 14.9 Hawaii 25.8 7.2 Idaho 38.6 10.7 Illinois 30.4 11.5 Indiana 31.9 12.2 Iowa 28.8 8.1 Kansas 32 9.7 Kentucky 34.1 13.6 Louisiana 36.3 16.1 Maine 30.4 7.1 Maryland 19.5 9.7 Massachusetts 20.1 9.1 Michigan 31.6 10 Minnesota 24.2 7.3 Mississippi 43.6 17 Missouri 32.7 11.1 Montana 36 7 Nebraska 31.1 8.7 Nevada 37.4 16.6 New Hampshire 19.7 7.3 New Jersey 21.2 10.1 New Mexico 43 16.2 New York 30.2 13 North Carolina 36.2 13.6 North Dakota 27.2 5.9 Ohio 31.8 10.3 Oklahoma 37.4 13.2 Oregon 33.9 10.8 Pennsylvania 26 9.4 Rhode Island 26.9 12 South Carolina 38.3 14.2 South Dakota 31 8.7 Tennessee 36.6 12.7 Texas 38.3 17.8 Utah 32.3 9.9 Vermont 26.2 6.6 Virginia 23.3 10.2 Washington 26.4 10.2 West Virginia 36.1 12.9 Wisconsin 28.7 8.5 Wyoming 28.1 8

Answer 1

since there is positive correlation between  Percent of low income working families (y) and Percent of 18-64 year olds with no HS diploma (x) following information has been generated using ms-excel. that is if x increase and y increases and vice-versa. so decrease in the percent of 18-64 yr-olds with no high school diploma will no doubt lead to a decrease in the percent of low-income working families.

here R²=0.4906, means 49.06 % of variation in in y is explained by x

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.700452
R Square	0.490633
Adjusted R Square	0.480238
Standard Error	4.494319
Observations	51
ANOVA
	df	SS	MS	F	Significance F
Regression	1	953.3457	953.3457	47.1979	1.05E-08
Residual	49	989.7461	20.1989
Total	50	1943.092
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	15.50097	2.380942	6.510437	3.81E-08	10.71629	20.28565	10.71629	20.28565
X Variable 1	1.399705	0.203739	6.870073	1.05E-08	0.990275	1.809135	0.990275	1.809135