Statistical Problem Solving homework
mansour
ma_2025_project_1_example.docMA 2025 Project 1 Example
Description
A statistical study was done on average temperatures in Fort Wayne for the month of November.
Statistical Tools Summary
· Created a time series plot of the temperature data over time (sec. 1.1)
· Calculated a five-number summary of the temperature data (sec. 1.2)
· Determined the form of the relationship between time and temperature based on the creation of a scatterplot (sec. 2.1)
· Determined the direction and strength of the relationship between time (X) and temperature (Y) based on the calculation of a Pearson correlation coefficient (sec. 2.2)
· Determined the linear regression equation for time (X) and temperature (Y), calculated R-squared, and interpreted it by giving a non-statistical explanation (sec. 2.3)
Data set
|
Day in November |
Daily average temp in FTW |
|
1 |
42 |
|
2 |
40 |
|
3 |
36 |
|
4 |
34 |
|
5 |
32 |
|
6 |
34 |
|
7 |
41 |
|
8 |
38 |
|
9 |
44 |
|
10 |
59 |
|
11 |
60 |
|
12 |
46 |
|
13 |
29 |
|
14 |
32 |
|
15 |
34 |
|
16 |
38 |
|
17 |
40 |
|
18 |
40 |
|
19 |
42 |
|
20 |
47 |
|
21 |
44 |
|
22 |
46 |
|
23 |
42 |
|
24 |
31 |
|
25 |
35 |
Findings
The time series plot of the temperature data over time:
2
4
2
2
2
0
1
8
1
6
1
4
1
2
1
0
8
6
4
2
6
0
5
5
5
0
4
5
4
0
3
5
3
0
D
a
y
i
n
N
o
v
e
m
b
e
r
D
a
i
l
y
a
v
e
r
a
g
e
t
e
m
p
i
n
F
T
W
T
i
m
e
S
e
r
i
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s
P
l
o
t
o
f
D
a
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l
y
a
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g
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t
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m
p
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F
T
W
The five-number summary of the temperature data:
Minimum Q1 Median Q3 Maximum
29.00 34.00 40.00 44.00 60.00
The form, direction, and strength of the relationship between time and temperature based on the creation of a scatterplot and the calculation of a Pearson correlation coefficient:
2
5
2
0
1
5
1
0
5
0
6
0
5
5
5
0
4
5
4
0
3
5
3
0
D
a
y
i
n
N
o
v
e
m
b
e
r
D
a
i
l
y
a
v
e
r
a
g
e
t
e
m
p
i
n
F
T
W
S
c
a
t
t
e
r
p
l
o
t
o
f
D
a
i
l
y
a
v
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r
a
g
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t
e
m
p
i
n
F
T
W
v
s
D
a
y
i
n
N
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m
b
e
r
Form: linear
Direction: positive
Strength: weak, r = 0.032
The linear regression equation for time (X) and temperature (Y), calculated R-squared, and a non-statistical explanation:
Daily average temp in FTW = 39.8 + 0.033 Day in November
R-Squared = 0.1%
Explanation: 0.1% of temperature is determined by the day of the month
Conclusions
The time series plot showed a distinct increase and sharp decrease in the middle of the month. The day of the month had almost no influence on the average temperature.
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