stat project vuvu

8/11/2019 Stat Project vuvu

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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.

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