Structurally de?cient highway bridges. Data on structurally de?cient highway bridges is compiled by the Federal Highway Administration (FHWA) and reported in the National Bridge Inventory (NBI). For each state, the NBI lists the number of structurally de?cient bridges and the total area (thousands of square feet) of the de?cient bridges. The data for the 50 states (plus the District of Columbia and Puerto Rico) are saved in the FHWABRIDGE ?le. (The ?rst ?ve and last ?ve observations are listed in the table.) For future planning and budgeting, the FHWA wants to estimate the total area of structurally de?cient bridges in a state based on the number of de?cient bridges.
(a) Write the equation of a straight-line model relating total area (y) to number of structurally de?cient bridges (x).
(b) The model, part a, was ?t to the data using Minitab as shown in the accompanying print- out. Find the least squares prediction equation on the printout.
(c) List the assumptions required for the regression analysis.
(d) Locate the estimated standard error of the regression model, s, on the printout.
(e) Use the value of s to ?nd a range where most (about 95%) of the errors of prediction will fall.
STATE NUMBER AREA(thousands of sq. ft.)
|
Alabama
|
1899
|
432.7
|
|
Alaska
|
155
|
60.9
|
|
Arizona
|
181
|
110.5
|
|
Arkansas
|
997
|
347.3
|
|
California
...
|
3140
|
5177.9
|
|
Washington
|
400
|
502.0
|
|
West Virginia
|
1058
|
331.5
|
|
Wisconsin
|
1302
|
399.8
|
|
Wyoming
|
389
|
143.4
|
|
Puerto Rico
|
241
|
195.4
|