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Poverty Levels in the United States

Regression questions

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15.26 An education task force looking at poverty levels in the United States has collected data for each state and the District of Columbia on the total number of people below the poverty level and the number of adults over the age of 25 who did not graduate from high school for the year 1993. The data are shown in the table below:

Number Number of Adults Number Number of Adults
(1000) Below Over 25 not (1000)Below Over 25 not
State Poverty Level HS Graduates State Poverty Level HS Graduate
Alabama 725 843,638 District of Columbia 158 109,866
Alaska 52 43,244 Florida 2507 2,271,074
Arizona 615 491,080 Georgia 919 1,169,815
Arkansas 484 503,481 Hawaii 91 141,506
California 5803 4,450,528 Idaho 150 121,787
Colorado 354 328,056 Illinois 1600 1,735,789
Connecticut 277 457,208 Indiana 704 850,014
Delaware 73 96,472 Iowa 290 353,800
Kansas 327 293,272 North Dakota 70 92,427
Kentucky 763 825,857 Ohio 1461 1,684,888
Louisiana 1119 803,872 Oklahoma 662 506,961
Maine 196 168,460 Oregon 363 343,609
Maryland 479 673,932 Pennsylvania 1598 1,994,278
Massachusetts 641 792,657 Rhode Island 108 184,344
Michigan 1475 1,356,759 South Carolina 678 687,260
Minnesota 506 488,765 South Dakota 102 98,720
Mississippi 639 549,685 Tennessee 998 1,033,914
Missouri 832 858,368 Texas 3177 2,872,559
Montana 127 96,469 Utah 203 133,315
Nebraska 169 181,072 Vermont 59 68,637
Nevada 141 167,628 Virginia 627 987,203
New Hampshire 112 127,423 Washington 634 505,783
New Jersey 866 1,205,206 West Virginia 400 398,527
New Mexico 282 229,974 Wisconsin 636 662,072
New York 2981 2,977,604 Wyoming 64 47,113
North Carolina 966 1,277,747

(a) The task force would like to find a model that will predict the number of people living below the poverty level from the number of adults who are not high school graduates. Which is the dependent variable and which is the independent variable?

(b) Create a scatter plot of the data. Do you think that a linear relationship exists between the two variables?

(c) Find the linear regression model for the data.

(d) Interpret the meaning of the slope and the y intercept of the model. Do you think that?
the Y intercept makes sense for these data?

(e) Use the model to predict the number of people who are below the poverty level for the states of Wyoming, Connecticut and North Carolina. What are the residuals for these three observations?

(f) At the 0.05 level of significance, is the model significant?

15.27 The Commerce Department also has data available on number of shopping centers and retail sales for the South Central states. The data are given below:

Number of Retail Sales
State Shopping Centers ($ billion)
Kentucky 593 11.7
Tennessee 1137 19.1
Alabama 601 13.2
Mississippi 418 7.2
Arkansas 339 6.4
Louisiana 676 15.6
Oklahoma 556 11.4
Texas 2824 72.7

Source: Statistical Abstract of the United States 1995.

(a) Find the linear regression model for the South Central states.

(b) How does the equation for the South Central states compare to the one you found for the North Central states?

(c) Would you have expected them to be exactly the same? Why or why not?

(d) What similarities would you expect them to have? What differences?

(e) Combine the data from the North Central and South Central states and find the linear regression model for the combined data.

(f) Do you think that the individual models are better or worse than the combined model? On what criteria do you base your conclusion?

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