Structurally deficient highway bridges. Refer to the data on structurally deficient highway bridges compiled by the Federal Highway Administration (FHWA), Exercise. Recall that for future planning and budgeting, the FHWA wants to estimate the total area of structurally deficient bridges in a state based on the number of deficient bridges. Use the results of the simple linear regression relating total area (y) to number of structurally deficient bridges (x) to find a 95% prediction interval for y when x = 350 bridges. Interpret the result.
Exercise
Structurally deficient highway bridges. Data on structurally deficient 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 deficient bridges and the total area (thousands of square feet) of the deficient bridges. The data for the 50 states (plus the District of Columbia and Puerto Rico) are saved in the FHWABRIDGE file. (The first five and last five observations are listed in the table.) For future planning and budgeting, the FHWA wants to estimate the total area of structurally deficient bridges in a state based on the number of deficient bridges.
(a) Write the equation of a straight-line model relating total area (y) to number of structurally deficient bridges (x).
(b) The model, part a, was fit to the data using Minitab as shown in the accompanying printout. 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 find 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 |
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.
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| Washington |
400 |
502 |
| West Virginia |
1058 |
331.5 |
| Wisconsin |
1302 |
399.8 |
| Wyoming |
389 |
143.4 |
| Puerto Rico |
241 |
195.4 |
