Researchers claim that the surface temperature of the world's oceans mainly changes withchanging latitude. The warmest waters are near the equator and the coldest waters are in theArctic and Antarctic regions. To examine this claim, an experiment has been designed and thefollowing data has been collected from coastal areas in the southern hemisphere for 5consecutive years in the middle of November. The recorded temperatures are all averagesacross the 5 years of data.Coastal oceanSurfaceTemperatureLatitude4442403836343230282624222018161412108614.115.216.217.5182122.123.824.524.224.42626.928.228.528.829.829.831.232.5.Coastal AirTemperature●1617151518.52224.5242526.53031.630.433.5Note: Temperature.xlsx is also attached.a) Convert the latitude numerical variable to a categorical variablewith 4 levels (very low, low, moderate, high), using a statistical software package.Find the overall mean, group means, and group standard deviationsusing the statistical package.33323233.53430Conduct an ANOVA test to find the possible impact of latitude oncoastal ocean surface temperature.Write the assumptions of the model, write out the model in cellmeans/classical/regression form,conduct the analysis in a statistical software package, run theTukey HSD test if needed,and state a conclusion based on the output.b) Plot a scatterplot with coastal ocean surface temperature(horizontal axis) and costal airtemperature (vertical axis). Interpret the output.c) State all possible ways to categorise both latitude and coastal ocean surfacetemperature to design a two-way ANOVA to test their impact on costal airtemperature with the following conditions:Both independent variables must be changed to categories;The design must be balanced;All 20 observations must be used.d) Which one of the designs from part c of this question works?Why? Note: calculate and use the error df(s) to answer this question.e) Run this two-way ANOVA design and state your conclusion.

a) Using a statistical software programme, we can create a new variable based on the latitude values…

Researchers claim that the surface temperature of the world's oceans mainly changes with changing latitude. The warmest waters are near the equator and the coldest waters are in the Arctic and Antarctic regions. To examine this claim, an experiment has been designed and the following data has been collected from coastal areas in the southern hemisphere for 5 consecutive years in the middle of November. The recorded temperatures are all averages across the 5 years of data.

Researchers claim that the surface temperature of the world's oceans mainly changes with changing latitude. The warmest waters are near the equator and the coldest waters are in the Arctic and Antarctic regions. To examine this claim, an experiment has been designed and the following data has been collected from coastal areas in the southern hemisphere for 5 consecutive years in the middle of November. The recorded temperatures are all averages across the 5 years of data.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Researchers claim that the surface temperature of the world's oceans mainly changes with
changing latitude. The warmest waters are near the equator and the coldest waters are in the
Arctic and Antarctic regions. To examine this claim, an experiment has been designed and the
following data has been collected from coastal areas in the southern hemisphere for 5
consecutive years in the middle of November. The recorded temperatures are all averages
across the 5 years of data.
Coastal ocean
Surface
Temperature
Latitude
44
42
40
38
36
34
32
30
28
26
24
22
20
18
16
14
12
10
8
6
14.1
15.2
16.2
17.5
18
21
22.1
23.8
24.5
24.2
24.4
26
26.9
28.2
28.5
28.8
29.8
29.8
31.2
32.5
.
Coastal Air
Temperature
●
16
17
15
15
18.5
22
24.5
24
25
26.5
30
31.6
30.4
33.5
Note: Temperature.xlsx is also attached.
a) Convert the latitude numerical variable to a categorical variable
with 4 levels (very low, low, moderate, high), using a statistical software package.
Find the overall mean, group means, and group standard deviations
using the statistical package.
33
32
32
33.5
34
30
Conduct an ANOVA test to find the possible impact of latitude on
coastal ocean surface temperature.
Write the assumptions of the model, write out the model in cell
means/classical/regression form,
conduct the analysis in a statistical software package, run the
Tukey HSD test if needed,
and state a conclusion based on the output.
b) Plot a scatterplot with coastal ocean surface temperature
(horizontal axis) and costal air
temperature (vertical axis). Interpret the output.
c) State all possible ways to categorise both latitude and coastal ocean surface
temperature to design a two-way ANOVA to test their impact on costal air
temperature with the following conditions:
Both independent variables must be changed to categories;
The design must be balanced;
All 20 observations must be used.
d) Which one of the designs from part c of this question works?
Why? Note: calculate and use the error df(s) to answer this question.
e) Run this two-way ANOVA design and state your conclusion.

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Follow-up Question

c) State all possible ways to categorise both latitude and coastal ocean surface
temperature to design a two-way ANOVA to test their impact on costal air
temperature with the following conditions:
• Both independent variables must be changed to categories;
• The design must be balanced;
All 20 observations must be used.
d) Which one of the designs from part c of this question works?
Why? Note: calculate and use the error df(s) to answer this question.
e) Run this two-way ANOVA design and state your conclusion.

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