Statistics

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?