Question
In: Statistics and Probability
Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a flight....
Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a flight. Find the (a) explained variation, (b) unexplained variation, and (c) indicated prediction interval. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 95% confidence level with the altitude of 6327 ft (or 6.327 thousand feet).
Altitude Temperature
3 60
10 40
13 22
24 -5
28 -25
31 -41
33 -60
a. Find the explained variation.
b. Find the unexplained variation.
c. Use technology to construct the prediction interval.
Solutions
Expert Solution
a)
| explained variation =SSR = 'Σ(Ŷ-Y̅)2 = | 11313.786 (please take care of number of decimals) |
b)
| unexplained variation =SSE =Syy-(Sxy)2/Sxx= | 289.642(please take care of number of decimals) |
c)
| predcited value at X=6.327: | 50.97 | |||
| std error prediction interval= s*√(1+1/n+(x0-x̅)2/Sxx)= | 8.9545 | |||
| for 95 % CI value of t= | 2.571 | |||
| margin of error E=t*std error = | 23.018 | |||
| lower prediction bound=sample mean-margin of error = | 27.947 | |||
| Upper prediction bound=sample mean+margin of error= | 73.984 |
prediction interval =(27.947 , 73.984)
(please take care of number of decimals)
orchestra answered 2 years agoRelated Solutions
Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a flight....
Listed below are altitudes (thousands of feet) and outside air
temperatures (°F) recorded during a flight. Find the (a)
explained variation, (b) unexplained variation, and (c)
indicated prediction interval. There is sufficient evidence to
support a claim of a linear correlation, so it is reasonable to
use the regression equation when making predictions. For the
prediction interval, use a 95% confidence level with the altitude
of 6327 ft (or 6.327 thousand feet).
Altitude
4
6
16
22
27
31
33...
Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a flight....
Listed below are altitudes (thousands of feet) and outside air
temperatures (°F) recorded during a flight. Find the (a)
explained variation, (b) unexplained variation, and (c)
indicated prediction interval. There is sufficient evidence to
support a claim of a linear correlation, so it is reasonable to
use the regression equation when making predictions. For the
prediction interval, use a 95% confidence level with the altitude
of 6327 ft (or 6.327 thousand feet).
Altitude Temperature
2
55
9
33
16
23...
Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a flight....
Listed below are altitudes (thousands of feet) and outside air
temperatures (°F) recorded during a flight. Find the (a)
explained variation, (b) unexplained variation, and(c) indicated
prediction interval. There is sufficient evidence to support a
claim of a linear correlation, so it is reasonable to use the
regression equation when making predictions. For the prediction
interval, use a 95% confidence level with the altitude of 6327 ft
(or 6.327 thousand feet).
Altitude
4
11
15
20
29
31
33
...
Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a flight....
Listed below are altitudes (thousands of feet) and outside air
temperatures (°F) recorded during a flight. Find the (a)
explained variation, (b) unexplained variation, and (c)
indicated prediction interval. There is sufficient evidence to
support a claim of a linear correlation, so it is reasonable to
use the regression equation when making predictions. For the
prediction interval, use a 95% confidence level with the altitude
of 6327 ft (or 6.327 thousand feet).
Altitude 4 12 15 20 28 31 33...
Listed below are altitudes (in thousands of feet) and outside air temperatures (in °F) recorded by...
Listed below are altitudes (in thousands of feet) and outside
air temperatures (in °F) recorded by a curious passenger during
Delta Flight 1053 from New Orleans to Atlanta.
Altitude
3
10
14
22
28
31
33
Temperature
57
37
24
-5
-30
-41
-54
Below is the scatterplot of this data with the best-fit
line.
Correlation coefficient (r) = -0.997
Meanaltitude = 20.14
Meantemperature = -1.71
Standard deviationaltitude (sx) =
11.423
Standard deviationtemperature (sy) = 42.221
Write down the equation...
1. Listed below are altitudes (thousands of feet) and outside air temperatures (°F) recorded during a...
1. Listed below are altitudes (thousands of feet) and outside
air temperatures (°F) recorded during a flight. Find the (a)
explained variation, (b) unexplained variation, and (c)
indicated prediction interval. There is sufficient evidence to
support a claim of a linear correlation, so it is reasonable to
use the regression equation when making predictions. For the
prediction interval, use a 95% confidence level with the altitude
of 6327 ft (or 6.327 thousand feet).
Altitude
4
10
13
22
29
31...
Listed below are altitudes (thousands of feet) and outside air temperatures (degrees Fahrenheit) recorded during Delta...
Listed below are altitudes (thousands of feet) and outside air
temperatures (degrees Fahrenheit) recorded during Delta Flight 1053
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1. Listed below are altitudes (thousands of feet) and air temperatures (degree Fahrenheit). Altitude 3 10...
1. Listed below are altitudes (thousands of feet) and air
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3
10
14
22
28
31
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Temperature
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37
24
-5
-30
-41
-54
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