Wind Speed Prediction using Linear Forecasting Model

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NUMERACY AND DATA ANALYSIS
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Contents
QUESTION 1................................................................................................................................... 3
QUESTION 2................................................................................................................................... 4
COLUMN CHART........................................................................................................................ 4
BAR CHART.................................................................................................................................4
QUESTION 3................................................................................................................................... 5
I. MEAN.................................................................................................................................. 5
II. MEDIAN.............................................................................................................................. 6
III. MODE.............................................................................................................................. 7
IV. RANGE............................................................................................................................. 7
V. STANDARD DEVIATION....................................................................................................... 8
QUESTION 4................................................................................................................................... 9
LINEAR FORECASTING MODEL...................................................................................................9
I. STEPS FOR CALCULATING THE VALUE OF m......................................................................11
II. STEPS FOR CALCULATING THE VALUE OF c.......................................................................12
III. USING THE VALUEWS CALCULATED FOR “m” & “c” TO PREDICT THE WIND SPEED FOR
DAY 14 AND 21........................................................................................................................ 13
REFERENCES.................................................................................................................................14
2

QUESTION 1
This table includes the weather data of wind speed for ten consecutive days from 23rd
September 2019 to 2ND October 2019 for England, United Kingdom.
NUMBER OF DAYS WIND SPEED IN ENGLAND (in km/h)
23-Sep-2019 23
24-Sep-2019 22
25-Sep-2019 21
26-Sep-2019 24
27-Sep-2019 24
28-Sep-2019 23
29-Sep-2019 19
30-Sep-2019 21
1-Oct-2019 19
2-Oct-2019 20
Table 1: Wind Speed in England (in km/h), 23RD Sep to 2nd Oct 2019
(Source: St. James's, England, United Kingdom, 2019)
3

QUESTION 2
COLUMN CHART
23-Sep-19
24-Sep-19
25-Sep-19
26-Sep-19
27-Sep-19
28-Sep-19
29-Sep-19
30-Sep-19
1-Oct-19
2-Oct-19
0
5
10
15
20
25
30
Wind Speed in England
Wind Speed
4

BAR CHART
23-Sep-19
24-Sep-19
25-Sep-19
26-Sep-19
27-Sep-19
28-Sep-19
29-Sep-19
30-Sep-19
1-Oct-19
2-Oct-19
0 5 10 15 20 25 30
Wind Speed in England
Wind Speed
QUESTION 3
I. MEAN
NUMBER OF DAYS WIND SPEED IN ENGLAND (in km/h)
23-Sep-2019 23
24-Sep-2019 22
25-Sep-2019 21
26-Sep-2019 24
27-Sep-2019 24
28-Sep-2019 23
29-Sep-2019 19
30-Sep-2019 21
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1-Oct-2019 19
2-Oct-2019 20
TOTAL 216
All the values of the wind speed would be summed up to find the arithmetic mean of the data
given:
FORMULA FOR MEAN =
x= 1
n ∑
i=1
n
( x )
Mean = 216/10
= 21.6%
Arithmetic Mean (x) = 21.6%
II. MEDIAN
The values of wind speed is arranged in the ascending order to find out the median
NUMBER OF DAYS WIND SPEED IN ENGLAND (in km/h)
29-Sep-2019 19
1-Oct-2019 19
2-Oct-2019 20
25-Sep-2019 21
30-Sep-2019 21
24-Sep-2019 22
23-Sep-2019 23
28-Sep-2019 23
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26-Sep-2019 24
27-Sep-2019 24
In this table, it can be inferred that there are two middle numbers available that is 21 and 22
(Siegel, 2016).Therefore, the average would be calculated of these two middle numbers to
identify the value of mean.
Median= (21+22)
2
Median= 21.5
The median is 21.5 per cent
7

III. MODE
Mode is calculated on the basis of the number having the highest frequency (Schabenberger
and Gotway, 2017).In the table above for wind speed in England, the modes are 9, 21, 23 & 24
are they occurring more than one time.
IV. RANGE
Range can be referred to as the difference between the highest value and the lowest value in
the given data (Li et al., 2019).The values of the wind speed of England are provided in the
ascending order below:
NUMBER OF DAYS WIND SPEED IN ENGLAND (in km/h)
29-Sep-2019 19
1-Oct-2019 19
2-Oct-2019 20
25-Sep-2019 21
30-Sep-2019 21
24-Sep-2019 22
23-Sep-2019 23
28-Sep-2019 23
26-Sep-2019 24
27-Sep-2019 24
In the given table the highest value is 24 and the lowest value is 19.
Range = Highest Value – Lowest Value
Range = 24-19
Range = 5
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V. STANDARD DEVIATION
WIND SPEED IN ENGLAND (in
km/h) = x
( x−x )
x= 21.5
( x−x )2
23 1.5 2.25
22 0.5 0.25
21 -0.5 0.25
24 2.5 6.25
24 2.5 6.25
23 1.5 2.25
19 -2.5 6.25
21 -0.5 0.25
19 -2.5 6.25
20 -1.5 2.25
TOTAL - 32.5
STANDARD DEVIATION FORMULA =
s(σX)= √ 1
n−1 ∑
i=1
n
( x−x ) 2
s ( σX )= √ 32.5
10−1
s ( σX )= √3.611
s ( σX )=¿ 1.900
Thus, the variance is 3.611 and standard deviation is the square root of 3.611 = 1.900.
9

QUESTION 4
LINEAR FORECASTING MODEL
23-Sep-19
24-Sep-19
25-Sep-19
26-Sep-19
27-Sep-19
28-Sep-19
29-Sep-19
30-Sep-19
1-Oct-19
2-Oct-19
0
5
10
15
20
25
30
Chart Title
Wind Speed
The equation regarding straight line is =
Wherein,
m = slope/ gradient
c= y-intercept/ bias (where the line crosses the y-axis)
Equation of Straight Line (y = mx +c)
In the above assignment, the wind speed at day 1st is considered as the starting point and wind
speed at day 10th is considered as the ending point (Luo et al., 2018).
The coordinates of the start and end points will be
(x1, y1)= (1, 23)
(x2, y2)= (10, 20)
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y=mx+c

Where,
X represents the number of days
Y represents wind speed in England
The first step is to comprehend the formula in the form of y=mx+c where x is known value
and y is predicted value.
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I. STEPS FOR CALCULATING THE VALUE OF m
m is considered as the slope which is calculated by dividing the change in y by the changes
made in x
m= change ∈ y
chnage∈ x
m= ( y 2− y 1 )
( x 2−x 1 )
Where,
x1=1
y1=23
x2=10
y2=20
m= ( 20−23 )
( 10−1 )
m=−3
9
m=−0.33
Thus, the value of m (slope) is -0.33
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