1. Suppose a fire insurance company wants to relate the amount of fire damage in major residential fires to the distance between the burning house and the nearest fire station. The study is to be conducted in a large suburb of a major city; a sample of 15 recent fires in this suburb is selected. The amount of damage (thousands of dollars), y, and the distance between the fire and the nearest fire station (miles), z, are recorded for each fire. The results are given below. ## ## 1 ## 2 ## 3 ## 4 ## 5 ## 6 ## 7 ## 8 ## 9 ## 10 ## 11 ## 12 ## 13 ## 14 ## 15 Distance Damage 3.4 26.2 1.8 17.8 4.6 2.3 3.1 5.5 y = 26.4133 0.7 3.0 2.6 4.3 31.3 23.1 27.5 36.0 14.1 22.3 19.6 31.3 2.1 24.0 1.1 17.3 6.1 43.2 4.8 3.8 36.4 26.1 Summary statistics are provided below. = 3.28, Σ(;)2 = 196.16 Σ(2)² = 34.784 Σ(yg)²=911.5173 Σ(x-2)(y₁ - y) = 171.114 Σ(x-2)(y) = 171.114 Σ(x)(y) = 1470.65 1 (a). Estimate the least-squares regression line. Provide equation explicitly. 1 (b). Test the hypothesis that 3 = 0 at the 0.05 level of significance against the alter- native that 30. 1 (c). Suppose the insurance company wants to predict the fire damage if a major resi- dential fire were to occur 3.5 miles from the nearest fire station. Find a 95% prediction interval. Provide Lower Prediction Limit and Upper Prediction Limit explicitly. As- sume that SSE == 69.751
1. Suppose a fire insurance company wants to relate the amount of fire damage in major residential fires to the distance between the burning house and the nearest fire station. The study is to be conducted in a large suburb of a major city; a sample of 15 recent fires in this suburb is selected. The amount of damage (thousands of dollars), y, and the distance between the fire and the nearest fire station (miles), z, are recorded for each fire. The results are given below. ## ## 1 ## 2 ## 3 ## 4 ## 5 ## 6 ## 7 ## 8 ## 9 ## 10 ## 11 ## 12 ## 13 ## 14 ## 15 Distance Damage 3.4 26.2 1.8 17.8 4.6 2.3 3.1 5.5 y = 26.4133 0.7 3.0 2.6 4.3 31.3 23.1 27.5 36.0 14.1 22.3 19.6 31.3 2.1 24.0 1.1 17.3 6.1 43.2 4.8 3.8 36.4 26.1 Summary statistics are provided below. = 3.28, Σ(;)2 = 196.16 Σ(2)² = 34.784 Σ(yg)²=911.5173 Σ(x-2)(y₁ - y) = 171.114 Σ(x-2)(y) = 171.114 Σ(x)(y) = 1470.65 1 (a). Estimate the least-squares regression line. Provide equation explicitly. 1 (b). Test the hypothesis that 3 = 0 at the 0.05 level of significance against the alter- native that 30. 1 (c). Suppose the insurance company wants to predict the fire damage if a major resi- dential fire were to occur 3.5 miles from the nearest fire station. Find a 95% prediction interval. Provide Lower Prediction Limit and Upper Prediction Limit explicitly. As- sume that SSE == 69.751
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Suppose a fire insurance company wants to relate the amount of fire damage in major
residential fires to the distance between the burning house and the nearest fire station.
The study is to be conducted in a large suburb of a major city; a sample of 15 recent
fires in this suburb is selected. The amount of damage (thousands of dollars), y, and the
distance between the fire and the nearest fire station (miles), r, are recorded for each fire.
The results are given below.
##
## 1
## 2
## 3
## 4
## 5
## 6
## 7
## 8
## 9
## 10
## 11
## 12
## 13
## 14
## 15
Distance Damage
3.4
26.2
1.8
17.8
4.6
31.3
2.3
23.1
3.1 27.5
5.5
36.0
0.7
14.1
3.0
22.3
2.6
19.6
4.3
31.3
2.1
24.0
1.1
6.1
17.3
43.2
4.8
36.4
3.8 26.1
y = 26.4133
Summary statistics are provided below.
* = 3.28,
Σ(x;)2 = 196.16
Σ(x - 2)² = 34.784
(-y)² = 911.5173
Σ(x₁ - x)(y₁ - y) = 171.114
Σ(x-2)(y) = 171.114
Σ(x) (y) = 1470.65
1 (a). Estimate the least-squares regression line. Provide equation explicitly.
1 (b). Test the hypothesis that = 0 at the 0.05 level of significance against the alter-
native that 30.
1 (c). Suppose the insurance company wants to predict the fire damage if a major resi-
dential fire were to occur 3.5 miles from the nearest fire station. Find a 95% prediction
interval. Provide Lower Prediction Limit and Upper Prediction Limit explicitly. As-
sume that SSE == 69.751
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