find the regression equation for the linear association between the percent of l

Question

find the regression equation for the linear association between the percent of low-income working families and the percent of 18-64 yr-olds with no high school diploma. Provide this equation and write a brief interpretation of its slope

State -- working poor% --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%

Louisana 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 Virgina 36.1%, 12.9%

Wisconsin 28.7% , 8.5%

Wyoming 28.1% , 8%

Explanation / Answer

Independent variable (x): No HS diploma %

Dependent variable (y): working poor%

Following is the output of regression analysis generated by excel:

The required regression equation is

y' = 15.50 + 1.40x

The slope is: 1.40

It shows for each unit increase in independent variable (No HS diploma%) the dependent variable (working poor%) increased by 1.40 units.

SUMMARY OUTPUT Regression Statistics Multiple R 0.700452272 R Square 0.490633385 Adjusted R Square 0.480238148 Standard Error 4.49431858 Observations 51 ANOVA df SS MS F Significance F Regression 1 953.3456894 953.3456894 47.19790252 1.0545E-08 Residual 49 989.7460753 20.1988995 Total 50 1943.091765 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 15.50097143 2.380941794 6.510436951 3.80515E-08 10.71628985 20.28565302 No HS diploma 1.39970504 0.203739472 6.870072963 1.0545E-08 0.990275249 1.80913483

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