stat project vuvu
TRANSCRIPT
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INTRODUCTION
The question of link between inflation and economic growth has been widelydebated. In early 1980 many economist thought rise on inflation has a positive
effect on economic growth. But they seemed to change their views in mid-1990 as
increase on inflation has negative impact on economic growth. A great economist
once said The notion that inflation fosters growth has died a long, difficult death
in economics. For thirty years, evidence has piled up against the idea. Certainly, in
these decades, dozens of countries tried to fertilize their economies with inflation
and harvested only weeds and misery.
The project examines the effect of inflation on economic growth using annual
historical data for the period of 1982-2000 from Australian bureau of statistic. Its
illustrate inflation variability by using the coefficient of correlation of inflation. Its
discussed about the uncertainty between inflation and economic growth.
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AIMS
In this report we are aiming to compare economic growth and inflation of Australia from 1981 to
2000. This study sought to determine...
The relationship between inflation rate and economic growth
Expectable tendencies of the inflation and GDP
Study the past behavior of GDP and inflation
Forecast the trends.
On this report, there are calculations based on some of important three statistical methods and have made
decisions regarding calculations. The statistical methods are as flows
Measuring Dispersion
Correlation Analysis
Time Series Analysis and forecasting
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Measuring Dispersion
Measures of dispersion are descriptive statistics that describe how similar a set of
scores are to each other.
The more similar the scores are to each other, the lower the measure of
dispersion will be
The less similar the scores are to each other, the higher the measure of
dispersion will be
In general, the more spread out a distribution is, the larger the measure of
dispersion will be
Dispersion for Economic growth
2.5 + 2.6 / 2 = 2.55 Middle number Q2
-1.5
-1.4
0.2
0.8
1.5
2
2.2
2.4
2.5
2.5
2.6
2.9
2.9
3.1
3.4
3.6
3.6
3.9
4.7
5.2
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1) Range = maximum valueminimum value
= 5.2 (1.5)
= 6.7
2) Interquartile Range (IQR)
Q1 = n/2 + n/2 +1
Q1 = 10/ 2 + 10/2 +1
= 5thand 6th
= 1.5 + 2 / 2
= 1.75
Q3 = n/2 + n/2 +1
Q3 = 10/ 2 + 10/2 +1
= 5thand 6th
Q3 = 3.4 + 3.6
2
= 3.5
IQR = Q3 Q1
= 3.51.75
= 1.75
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Standard deviation
Mean = 47.1 / 20 = 2.35
( )-1.5 2.35 -3.85 14.8225
-1.4 2.35 -3.75 14.0625
0.2 2.35 -2.15 4.6225
0.8 2.35 -1.55 2.4025
1.5 2.35 -0.85 0.7225
2 2.35 -0.35 0.1225
2.2 2.35 -0.15 0.0225
2.4 2.35 0.05 0.0025
2.5 2.35 0.15 0.0225
2.5 2.35 0.15 0.0225
2.6 2.35 0.25 0.0625
2.9 2.35 0.55 0.3025
2.9 2.35 0.55 0.3025
3.1 2.35 0.75 0.5625
3.4 2.35 1.05 1.1025
3.6 2.35 1.25 1.5625
3.6 2.35 1.25 1.5625
3.9 2.35 1.55 2.40254.7 2.35 2.35 5.5225
5.2 2.35 2.85 8.1225
58.33
( )
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Dispersion for Inflation rate
Q2 Middle number
3) Range = maximum valueminimum value
= 12.2 (2.1)
= 10.1
4) Interquartile Range (IQR)
Q1 = n/2 + n/2 +1
Q1 = 10/ 2 + 10/2 +1
= 5thand 6th
= 2.8 +2.9 / 2
= 2.85
2.1
2.3
2.3
2.62.8
2.9
3
3
3.6
3.7
4.5
4.6
4.7
5.2
5.2
5.9
6.7
8.1
8.5
12.2
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Q3 = n/2 + n/2 +1
Q3 = 10/ 2 + 10/2 +1
= 5thand 6th
Q3 = 5.2 + 5.9
2
= 5.55
IQR = Q3 Q1
= 5.55 2.85
= 2.7
Standard deviation
Mean = 93.9 / 20 = 4.695
( )2.1 4.69 -2.59 6.7081
2.3 4.69 -2.39 5.7121
2.3 4.69 -2.39 5.7121
2.6 4.69 -2.09 4.3681
2.8 4.69 -1.89 3.5721
2.9 4.69 -1.79 3.2041
3 4.69 -1.69 2.8561
3 4.69 -1.69 2.85613.6 4.69 -1.09 1.1881
3.7 4.69 -0.99 0.9801
4.5 4.69 -0.19 0.0361
4.6 4.69 -0.09 0.0081
4.7 4.69 0.01 0.0001
5.2 4.69 0.51 0.2601
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5.2 4.69 0.51 0.2601
5.9 4.69 1.21 1.4641
6.7 4.69 2.01 4.0401
8.1 4.69 3.41 11.6281
8.5 4.69 3.81 14.5161
12.2 4.69 7.51 56.4001
125.77
( )
Coefficient of variation
Coefficient variation for economic growth
The coefficient of variation for economic growth is 72.34%
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Coefficient of variation for inflation rate
The coefficient of variation for inflation rate is 53.3 %
Findings:-
After considering above calculations it is seen that the economic growth hasgreater relative variation than inflation rate.
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02. Time Series
A time series is a collection of observations of well-defined data items obtained throughrepeated measurements over time. For example, measuring the value of retail sales each
month of the year would comprise a time series. This is because sales revenue is welldefined, and consistently measured at equally spaced intervals. Data collected irregularly oronly once are not time series.
An observed time series can be decomposed into three components :
Long Term Trend Influences:
The 'long term' movement in a time series without calendar related and irregular
effects, and is a reflection of the underlying level.
( over a period of 10 years or more )
Secular Trends
eg : population growth,
price inflation
general economic changes
Cyclical Movements
Short Term Trend Influences:
Seasonal Variation
Eg : Weather fluctuations that are representative of the season
Start and end of the school term
Christmas
Irregular Variations
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Trend Analysis
Trend analysis is often used to predict future events, it could be used to estimate uncertain
events in the past, such as how many ancient kings probably ruled between two dates,
based on data such as the average years which other known kings reigned.
Time series data trends can categorised as, Straight line (linear) trends , or
Curved (non linear) trends.
When most of organizations are making their decisions for future ideally they are using trend
analysis. They can surely measure that what kind of things, that they should ready to face in
future successfully. They can estimate their budget also based on estimated values which they
having through trend analysis.
As a example when we look at infrastructure planning of government, they have to spend more
money for the materials. So, it is very important to have an idea about future constructions.
Straight line Trends
When data shows upward and downward trend changing with time, that set of data can use below this
method. There are four ways that we can analyze liner trend.
Free hand graphical method.
Semi average Least squares
Moving average
Data range that we are going to use is total revenues of McDonald's regarding several years. Let's
sort out that data range for Least squares method .
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Year Economic growth Inflation
1981 -1.5 12.2
1982 2 8.5
1983 3.6 5.2
1984 2.5 4.5
1985 3.6 5.2
1986 3.9 3.6
1987 1.5 3.7
1988 5.2 4.6
1989 2.2 5.9
1990 0.8 8.1
1991 -1.4 6.7
1992 0.2 4.7
1993 2.5 3
1994 4.7 2.3
1995 2.9 2.9
1996 2.6 3
1997 3.4 2.8
1998 2.9 2.6
1999 2.4 2.3
2000 3.1 2.1
Least Squares Method
This method uses to mathematical formula to generate a straight trend line.
Formula for the Least Squares Method is,
y = a + bx
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We can calculate a by using,
a = y
n
To calculate b we can use,
b = x . y
x^2
To calculate Trend line Equation we have to make table as below,
Regarding to our data range,
Years become as x
Revenue become as y
When we calculate b we have to multiply x with y . But, it is unable to multiply
years (x) with revenue (y). Hence we are coding years then multiply with revenue. Codingyears are become as x
If there is odd numbers of years, we have find midpoint of years and that mid -yearis coding as 0 . From there codes spread as -3, -2, -1, 0, 1, 2, 3, ...
If there is even numbers of years, we divide years to same parts and at their start to
code as -5, -3, -1, 1, 3, 5, .... ( no code of 0 )
Year
Code(x)
Inflation(y1)
GDP(y2)
x.y1 x.y2 X^2
1981 -192.1 -1.5
-39.9 28.5 361
1982 -172.3 -1.4
-39.1 23.8 289
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1983 -152.3 0.2
-34.5 -3 225
1984 -132.6 0.8
-33.8 -10.4 169
1985 -112.8 1.5
-30.8 -16.5 121
1986 -9 2.9 2 -26.1 -18 811987 -7
3 2.2-21 -15.4 49
1988 -53 2.4
-15 -12 25
1989 -33.6 2.5
-10.8 -7.5 9
1990 -13.7 2.5
-3.7 -2.5 1
1991 14.5 2.6
4.5 4.5 1
1992 34.6 2.9
13.8 9.7 9
1993 5 4.7 2.9 23.5 14.5 25
1994 75.2 3.1
36.4 21.7 49
1995 95.2 3.4
46.8 30.6 81
1996 115.9 3.6
64.9 39.6 121
1997 136.7 3.6
87.1 50.7 169
1998 158.1 3.9
121.5 58.5 225
1999 178.5 4.7
144.5 79.9 289
2000 1912.2 5.2
231.8 98.8 361
Total 93.9 44.6 520.1 375.5 2660
years Code (X)
2001 21
2002 23
2003 25
Now we can calculate Trend line equation with the help of table.
y = a + bx ,
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a = y
n
= 93.9
20
= 4.7
b = x.y
x^2
= 520.1
2660
= 0.196
y = a + bx
y = 4.7 + 0.196 x
The Trend Line Equation is : y = 4.7 + 0.196 x
After having Trend Line Equation line we can calculate revenue for given years.
Years that we are pointing also must be code for calculations.
Let's estimate total revenue for year 2001 & 2003 .
Calculations
If x = 21 ( code for 2001 )
y = 4.7 + 0.196 x
y = 4.7 + 0.196 * 21
y = 8.82
Estimated inflation rate for year 2001 8.82
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If x = 25 ( code for 2003 )
y = 4.7 + 0.196 x
y = 4.7 + 0.196 * 25
y = 9.6
Estimated inflation rate for year 2003 9.6
These figures show estimated inflation rate for 2001 & 2003. Figures are calculated byusing Lest Squared Method. However from these figures much reliable estimated value is
8.82 regarding to 2001.
Then we can apply it to estimate GDP also.
y = a + bx ,
a = y
n
= 44.6
20
= 2.23
b = x.y
x^2
= 375.52660
= 0.141
y = a + bx
y = 2.2 + 0.14 x
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The Trend Line Equation is : y = 2.2 + 0.14 x
After having Trend Line Equation line we can calculate revenue for given years.
Years that we are pointing also must be code for calculations.
Let's estimate total revenue for year 2001 & 2003 .
Calculations
If x = 21 ( code for 2001 )
y = 2.2 + 0.14 x
y = 2.2 + 0.14 * 21
y = 5.14
Estimated GDP rate for year 2001 5.14
If x = 25 ( code for 2003 )
y = 2.2 + 0.14 x
y = 2.2 + 0.14 * 25
y = 5.7
Estimated GDP rate for year 2003 5.1
These figures show estimated inflation rate for 2001 & 2003. Figures are calculated byusing Lest Squared Method. However from these figures much reliable estimated value is5.14 regarding to 2001.
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Correlation Analysis
Year Economic growth Inflation1981 -1.5 2.1
1982 -1.4 2.31983 0.2 2.31984 0.8 2.61985 1.5 2.81986 2 2.91987 2.2 31988 2.4 31989 2.5 3.6
1990 2.5 3.71991 2.6 4.51992 2.9 4.61993 2.9 4.71994 3.1 5.21995 3.4 5.21996 3.6 5.91997 3.6 6.71998 3.9 8.11999 4.7 8.5
2000 5.2 12.2
-4
-2
0
2
4
6
8
10
12
14
1980 1985 1990 1995 2000 2005
Economic growth
inflation
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Pearson product-moment correlation coefficient.
Inflation Economic Growth
y ( ) (y-) ( ) (y-) ( (y12.5 -1.5 4.97 2.31 7.23 -3.81 52.27 14.52 -27
8.5 2 4.97 2.31 3.53 -0.31 12.46 0.1 -1.
5.2 3.6 4.97 2.31 0.23 1.29 0.053 1.66 0
4.5 2.5 4.97 2.31 -0.47 0.19 0.22 0.04 -0.
5.2 3.6 4.97 2.31 0.23 1.29 0.053 1.66 0
3.6 3.9 4.97 2.31 -1.37 1.59 1.87 2.53 -2.
3.7 1.5 4.97 2.31 -1.27 -0.81 1.61 0.66 1.
4.6 5.2 4.97 2.31 -0.37 2.89 0.14 8.35 -1.
5.9 2.2 4.97 2.31 0.93 -0.11 0.86 0.01 0
3.1 0.8 4.97 2.31 3.13 -1.51 9.8 2.28 -4.
6.7 -1.4 4.97 2.31 1.73 -3.71 2.99 13.76 -6.
4.7 0.2 4.97 2.31 0.95 -2.11 0.9 4.45 -
3 2.5 4.97 2.31 -1.97 0.19 3.88 0.04 -0.
2.3 4.7 4.97 2.31 -2.67 2.39 7.13 5.71 -6.
2.9 2.9 4.97 2.31 -2.07 0.59 4.28 0.35 -1.
3 2.6 4.97 2.31 -1.97 0.29 3.88 0.08 -0.
2.8 3.4 4.97 2.31 -2.17 1.09 4.71 1.19 -2.
2.6 2.9 4.97 2.31 -2.37 0.59 5.62 0.35 -1.
2.3 2.4 4.97 2.31 -2.67 0.09 7.13 8.1 -0.
2.1 3.1 4.97 2.31 -2.87 0.79 8.24 0.62 -2.
128.1 66.46 -57
= -57.73
128.10*66.46
= -0.6257
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Spearman rank correlation coefficient.
EconomicGrowth
inflation Difference D Squared Total
1 20 -19 361
6 19 -13 169
16.5 14.5 2 4
9.5 11 -1.5 2.25
16.5 14.5 2 4
18 9 9 81
5 10 -5 25
20 12 8 64
7 16 -9 81
4 18 -14 1962 17 -15 225
3 13 -10 100
9.5 7.5 2 4
19 2.5 16.5 272.25
12.5 6 6.5 42.25
11 7.5 3.5 12.25
15 5 10 100
12.5 4 8.5 72.25
8 2.5 5.5 30.25
14 1 13 169 2014.5
=1- 6*2014.5
20(400-1)
= -0.5147
We can interpret this as a high negative correlation relationship between economic
growth and inflation. When the GDP gose up inflation is going down according to the
correlation.
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Conclusion
According to the all calculations it is evident that GDP rate goes up and while inflation
goes down in the time period.