Data Analysis and Forecasting: A Practical Assignment

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DATA ANALYSIS AND FORECASTING

Table of Contents
QUESTION 1................................................................................................................................... 2
QUESTION 2................................................................................................................................... 3
Column Chart.............................................................................................................................3
Line Chart...................................................................................................................................3
QUESTION 3................................................................................................................................... 4
I. Mean...................................................................................................................................4
II. Median................................................................................................................................5
III. Mode...............................................................................................................................6
IV. Range.............................................................................................................................. 6
V. Standard deviation..............................................................................................................7
Question 4..................................................................................................................................... 8
Linear Forecasting Model.......................................................................................................... 8
I. Steps to calculate m value..................................................................................................9
II. Steps to calculate c value..................................................................................................10
III. Using the calculated ‘m’ and ‘c’ values forecast the weather indicators for day 15 and
day 23...................................................................................................................................... 11
REFERENCES.................................................................................................................................12
1

QUESTION 1
This assignment includes the weather data that is humidity for ten consecutive days between
14th Jan 2018 to 23rd Jan 2018 for London UK.
Table 1 Humidity in London (in %), 14 Jan to 23 Jan 2018
Number of days Humidity in London (in %)
14-Jan-2018 70
15-Jan-2018 82
16-Jan-2018 62
17-Jan-2018 60
18-Jan-2018 64
19-Jan-2018 64
20-Jan-2018 95
21-Jan-2018 96
22-Jan-2018 66
23-Jan-2018 86
Source: Timeanddate, 2019
2

QUESTION 2
Column Chart
14-Jan-18
15-Jan-18
16-Jan-18
17-Jan-18
18-Jan-18
19-Jan-18
20-Jan-18
21-Jan-18
22-Jan-18
23-Jan-18
0
20
40
60
80
100
120
Humidity in London
Series 1
Line Chart
14-Jan-18
15-Jan-18
16-Jan-18
17-Jan-18
18-Jan-18
19-Jan-18
20-Jan-18
21-Jan-18
22-Jan-18
23-Jan-18
0 20 40 60 80 100 120
Humidity in London
Series 1
3

QUESTION 3
I. Mean
Number of days Humidity in London (in %)
14-Jan-2018 70
15-Jan-2018 82
16-Jan-2018 62
17-Jan-2018 60
18-Jan-2018 64
19-Jan-2018 64
20-Jan-2018 95
21-Jan-2018 96
22-Jan-2018 66
23-Jan-2018 86
Total 745
All the percentage of humidity in London will be summed up to find the arithmetic mean
The formula for Mean =
x= 1
n ∑
i=1
n
( x )
Mean = 745/10
Mean = 74.5 %
Arithmetic mean ( x) is 74.5 %.
4

II. Median
The humidity percentage is sorted in ascending order to identify median
Number of days Humidity in London (in %)
17-Jan-2018 60
16-Jan-2018 62
18-Jan-2018 64
19-Jan-2018 64
22-Jan-2018 66
14-Jan-2018 70
15-Jan-2018 82
23-Jan-2018 86
20-Jan-2018 95
21-Jan-2018 96
Here it is noticed that there are two middle numbers 66 and 70. The average of the two middle
numbers will be calculated to find the median.
Median= (66+70)
2
Median= 68
The median is 68 per cent.
5

III. Mode
A set of data’s mode is the number with high frequency. In the above table for humidity in
London, 64 is the mode as it occurs twice while the rest occurred only one time.
IV. Range
Range refers to the difference between the highest and lowest values in a set of data (Groebner
et al., 2013). The humidity percentage of London is ordered in ascending order.
Number of days Humidity in London (in %)
17-Jan-2018 60
16-Jan-2018 62
18-Jan-2018 64
19-Jan-2018 64
22-Jan-2018 66
14-Jan-2018 70
15-Jan-2018 82
23-Jan-2018 86
20-Jan-2018 95
21-Jan-2018 96
Here the highest value is 96 and the lowest value is 60
So,
Range = Highest Value – Lowest Value
Range = 96 - 60
Range = 36
6

V. Standard deviation
Table 2 Table for Standard Deviation
Humidity in London (in %) =
x
( x−x )
x= 74.5
( x−x ) 2
70 -4.5 20.25
82 7.5 56.25
62 -12.5 156.25
60 -14.5 210.5
64 -10.5 110.25
64 -10.5 110.25
95 20.5 420.25
96 21.5 462.25
66 -8.5 72.25
86 11.5 132.25
Total - 1750.75
Formula for standard deviation (Groebner et al., 2013) =
s(σX)= √ 1
n−1 ∑
i=1
n
( x−x ) 2
s ( σX ) = √ 1750.75
10−1
s ( σX )= √194.53
s ( σX ) =13.947
Hence the variance is 194.53 and the standard deviation is the square root of 194.53 = 13.947.
7

Question 4
Linear Forecasting Model
14-Jan-18
15-Jan-18
16-Jan-18
17-Jan-18
18-Jan-18
19-Jan-18
20-Jan-18
21-Jan-18
22-Jan-18
23-Jan-18
0
20
40
60
80
100
120
Humidity in London
Humdity in london
The equation of straight line =
y=mx+c
Where,
m = slope/ gradient
c= y-intercept/ bias (where the line crosses the y-axis) (Xie et al., 2018)
Equation of Straight Line (y = mx + b)
In the given assignment, let’s consider the humidity at day 1st the starting point and humidity at
day 10th as ending point.
The coordinates of the start and end points will be
(x1, y1)= (1, 70)
(x2, y2)= (10, 86)
8

Where,
X represents the number of days
Y represents humidity in London
The first step is to get hands on the formula in the form of y=mx+c where x is known value
and y is predicted value (Xie et al., 2018).
I. Steps to calculate m value
M is the slope or gradient which is calculated as dividing the change in y by change in x
m= c h ange∈ y
c h nage ∈x
m= ( y 2− y 1 )
( x 2−x 1 )
Here,
x1=1,
y1=70,
x2=10,
y2=86
m= ( 86−70 )
( 10−1 )
m= 16
9
m=1.78
Hence, m (slope/ gradient) is 1.78
9

II. Steps to calculate c value
The y-intercept/ bias is c which is calculated by using the formula y− y 1=m ( x−x 1 )
Given,
m= 1.78,
(x1, y1)= (1, 70)
So,
y− y 1=m ( x−x 1 )
y−70=1.78 ( x−1 )
y−70=1.78 x−1.78
y=1.78 x−1.78+70
y=1.78 x−68.22
This can be written in the form of y=mx+c as
y=1.78 x + (−68.22 )
So, c (y-intercept/ bias) is -68.22
10

III. Using the calculated ‘m’ and ‘c’ values forecast the weather indicators
for day 15 and day 23
To calculate the prediction y for any input value x, the below are
m (slope/ gradient) is 1.78 and c (y-intercept/ bias) is -68.22
FORECAST THE WEATHER INDICATORS FOR DAY 15
Here, x= 15
y=1.78 x + (−68.22 )
y=1.78∗15+ (−68.22 )
y=26.7−68.22
y=−41.52
FORECAST THE WEATHER INDICATORS FOR DAY 23
Here, x= 15
y=1.78∗23+ (−68.22 )
y=¿40.94-68.22
y=−27.28
11