Question
In: Math
The table below provides several temperature values taken at various altitudes Altitude(in the thousands of feet)...
The table below provides several temperature values taken at various altitudes
Altitude(in the thousands of feet) 3 10 14 22 28 31 33
Temperature 57 37 24 -5 -30 -41 -54
Determine if there is linear correlation between altitude and temperature. Give the appropriate r-value(do not calculate this value by hand) and what values you used to determine if there was or was not correlation. Conduct a hypothesis test at the 0.05 level of significance and List the equation of best fit(found via technology) and use this equation to find the predicted temperature at 6327 feet(show the calculation).
Show ALL WORK in a sample step to step process please
Solutions
Expert Solution
data
| altitude | temperature |
| 3 | 57 |
| 10 | 37 |
| 14 | 24 |
| 22 | -5 |
| 28 | -30 |
| 31 | -41 |
| 33 | -54 |
we use excel for regression
data -> data analysis -> regression
result
| SUMMARY OUTPUT | |||||||
| Regression Statistics | |||||||
| Multiple R | 0.996776806 | ||||||
| R Square | 0.993564001 | ||||||
| Adjusted R Square | 0.992276801 | ||||||
| Standard Error | 3.710411471 | ||||||
| Observations | 7 | ||||||
| ANOVA | |||||||
| df | SS | MS | F | Significance F | |||
| Regression | 1 | 10626.59 | 10626.59281 | 771.8802 | 1.13E-06 | ||
| Residual | 5 | 68.83577 | 13.76715328 | ||||
| Total | 6 | 10695.43 | |||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | |
| Intercept | 72.49817518 | 3.016935 | 24.03040629 | 2.33E-06 | 64.7429 | 80.25345 | 64.7429 |
| altitude | -3.684306569 | 0.132611 | -27.78273175 | 1.13E-06 | -4.02519 | -3.34342 | -4.02519 |
r = -0.996776
TS = -27.7827
p-value = 0.00000113 < 0.05
hence we reject the null hypothesis
y^ = 72.4981 -3.6843 *x
y^ = 72.4981 -3.6843 *6.327 = 49.18753
milcah answered 2 hours agoRelated Solutions
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
temperatures (degree Fahrenheit).
Altitude
3
10
14
22
28
31
33
Temperature
57
37
24
-5
-30
-41
-54
a. Construct a scatterplot.
b. Find the value of the linear correlation coefficient r.
c. Find the regression equation and draw the regression line on
the scatterplot in a).
d. Find the critical values from Table A-6 using α = .05 and
draw the graph.
e. Determine whether there is sufficient...
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...
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
3 60
10 40
13 22...
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...
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
from New Orleans to Atlanta. Construct a scatterplot, and find the
value of the linear correlation coefficient Also find the -value or
the critical values of from Table A-6 (page 732) using Is there
sufficient evidence to support a claim that there is a linear
correlation between altitude and outside air temperature? Altitude
3 10 14 22 28 31 33 Temp 57...
The payoff table below provides the profits (in thousands of dollars) for each of four alternatives...
The payoff table below provides the profits (in thousands of
dollars) for each of four alternatives in each of three
supplies.
Supplies
Alternative
S1
S2
S3
A1
112
67
-26
A2
82
85
101
A3
85
72
80
A4
-50
90
110
Suppose that the probabilities for the supplies above are
P(S1) = 0.6,
P(S2) = 0.2, and
P(S3) = 0.1.
Which alternative should be selected under Bayes’ Rule?
What is the expected value of perfect information for this
decision?
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