Statistical Project

ACKNOWLEDGEMENT I would like to thank all those people who helped me complete my project. A few names that I would like to mention are Sir Shahid kamal for helping me decide which variables to choose for comparison. Then I would like thank my friend, Fatima Liaqat, Usama Tariq, Daneya Ehson for solving all my problems and queries.

OBJECTIVES • The main objective is to compare the GDP growth% of Pakistan and India since 1961-2003. • To find out the relationship between Pakistan GDP growth% and India’s GDP growth%. • To see the trend in the distribution of the both countries GDP growth% from 1961-2003. • To find the relationship of the no. of years with Pakistan’s GDP growth%. • To find out the relationship of the no. of years with India’s GDP growth%.

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METHODOLOGY Series Name

Years

GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %) GDP growth (annual %)

1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Pakistan 5.987344761 4.48285997 8.688826947 7.569758157 10.41936837 5.789951795 5.400612596 7.233220928 5.507899633 11.35346172 0.468372549 0.813406409 7.064263854 3.54019171 4.211415634 5.156189587 3.94769829 8.048533622 3.758435565 10.21570404 7.920763572 6.537486802 6.778378338 5.065205603 7.592114701 5.501653664 6.452343023 7.625278781 4.959768894 4.458586816 5.061567753 7.705897824 1.757747697 3.737415554 4.962609149 4.846581284 1.014396016 2.550234294 3.660132744 4.260088011 1.860002383 3.219026738 5.149463052

India 3.867614237 3.131273149 6.278014612 7.436833348 -2.40939267 -0.169065256 7.792848241 3.471278961 6.54238601 5.172337845 1.710305404 -0.578152621 3.162698092 1.187949725 9.165505222 1.707244733 7.231877433 5.735009778 -5.242170339 6.689499811 6.36104433 3.65602743 7.078159273 4.124118353 5.629585098 4.836803037 4.268812872 9.859558909 6.442423543 5.808784537 0.906745997 5.271619713 4.870194972 7.463629804 7.645754747 7.394667316 4.478169835 5.987373201 7.128722755 3.94200669 5.151948677 4.1 8.6

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• The scatter plot was made by the help of the stats graphics. This graph shows the relationship between the two variable i.e. (positive relationship or negative relationship) • The histogram shows the maximum and minimum value in the distribution. •

The hypothesis testing proves if null hypothesis should be accepted or not.

• The density plot proves the density of the data from 1971-2002 for both the variables • The box and whisker plot shows whether the distribution is positively skewed or negatively skewed. The two samples are compared by the difference in: • Mean: It is the value obtained by dividing the sum of the observations by their number. •

Median: It is a value which divides a data set that have been ordered, into two equal parts, one part comprising of observations greater than and other part smaller than it.

• Mode: The value which occur most frequently in a set of data. When the mean>median>mode then the data is to positively skewed And if it is mode>median>mean then data is said to be negatively skewed. • Standard deviation: It is the positive square root of the variance. This shows the deviation of the data from its median.

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•

Coefficient of skew ness: Any deviation from symmetry is called skew ness. The coefficient of skew ness in only considered when the numbers of value are greater than 30. If the numbers of values are less than 30 then you consult the box and whisker diagram.

• Range: The difference between the largest and the smallest value in a set of data. • Percentiles: The ninety nine values dividing the data into hundred equal parts. • Geometric mean: It is the positive nth root of their product.

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Pakistan Statistics: Count = 43 Average = 5.40312 Median = 5.14946 Mode = Geometric mean = 4.62733 Variance = 6.22732 Standard deviation = 2.49546 Standard error = 0.380554 Minimum = 0.468373 Maximum = 11.3535 Range = 10.8851 Lower quartile = 3.75844 Upper quartile = 7.23322 Interquartile range = 3.47479 Skewness = 0.194787 Stnd. skewness = 0.521458 Kurtosis = 0.0519473 Stnd. kurtosis = 0.0695331 Coeff. of variation = 46.1855% Sum = 232.334

The positive value of skew ness shows that the distribution of GDP growth% is positively skewed and the positive value shows that the graph is leptokurtic.

Confidence interval: 95.0% confidence interval for mean: 5.40312 +/- 0.76799 [4.63513, 6.17111] 95.0% confidence interval for standard deviation: [2.05761, 3.17175]

The confidence interval of mean shows that we are 95% sure that our mean lies between 5.40312 +/- 0.76799 and we are 95% sure that our value of standard deviation lies between the interval (2.05761, 3.17175).

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Percentiles of Pakistan 1.0% = 0.468373 5.0% = 1.0144 10.0% = 1.86 25.0% = 3.75844 50.0% = 5.14946 75.0% = 7.23322 90.0% = 8.04853 95.0% = 10.2157 99.0% = 11.3535

Hypothesis testing for Pakistan Sample mean = 5.40312 Sample median = 5.14946 T-test -----Null hypothesis: mean = 5.40312 Alternative: not equal Computed t statistic = 0.00000603954 P-Value = 0.999995 Do not reject the null hypothesis for alpha = 0.05.

The confidence interval of mean shows that we are 95% sure that our mean lies between 5.40312 +/- 0.76799. Our assumption was that our mean is equal 5.40312 and our alternative was that our mean is not equal to 5.40312. The hypothesis testing result shows that we accept the null hypothesis and reject the alternative hypothesis.

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Histogram for Pakistan

frequency

18 15 12 9 6 3 0 -1

2

5

8

11

14

Pakistan

It’s showing positively change.

Plot of Pakistan vs Years 12

Pakistan

10 8 6 4 2 0 1960

1970

1980

1990

2000

2010

Years

Its positive low co-relation. It’s showing that the increase in GDP growth% is not as good as it should increase as no. of years is increasing.

Box-and-Whisker Plot

0

2

4

6

8

10

12

Pakistan

Its shows that it’s positively skewed because the mean lies on the right side of the median.

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India Statistics: Summary Statistics for india Count = 43 Average = 4.71837 Median = 5.17234 Mode = Geometric mean = Variance = 9.44783 Standard deviation = 3.07373 Standard error = 0.46874 Minimum = -5.24217 Maximum = 9.85956 Range = 15.1017 Lower quartile = 3.47128 Upper quartile = 7.07816 Interquartile range = 3.60688 Skewness = -1.12651 Stnd. skewness = -3.01574 Kurtosis = 1.73695 Stnd. kurtosis = 2.32496 Coeff. of variation = 65.1439% Sum = 202.89

The negative value of skew ness shows that the distribution of GDP growth% is negatively skewed and the positive value shows that the graph is platy-kurtic.

Confidence interval: 95.0% confidence interval for mean: 4.71837 +/- 0.945957 [3.77242,5.66433] 95.0% confidence interval for standard deviation: [2.53442,3.90675]

The confidence interval of mean shows that we are 95% sure that our mean lies between 4.71837 +/- 0.945957 and we are 95% sure that our value of standard deviation lies between the interval [2.53442, 3.90675]

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Percentiles of India 1.0% = -5.24217 5.0% = -0.578153 10.0% = 0.906746 25.0% = 3.47128 50.0% = 5.17234 75.0% = 7.07816 90.0% = 7.64575 95.0% = 8.6 99.0% = 9.85956

Hypothesis Tests for India Sample mean = 4.71837 Sample median = 5.17234 t-test -----Null hypothesis: mean = 4.71837 Alternative: not equal Computed t statistic = 0.00000678732 P-Value = 0.999995 Do not reject the null hypothesis for alpha = 0.05.

The confidence interval of mean shows that we are 95% sure that our mean lies between 4.71837 +/- 0.945957. Our assumption was that our mean is equal 4.71837 and our alternative was that our mean is not equal to 4.71837. The hypothesis testing result shows that we accept the null hypothesis and reject the alternative hypothesis.

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Plot of india vs Years 10

india

6 2 -2 -6 1960

1970

1980

1990

2000

2010

Years

Box-and-Whisker Plot

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2

6

10

india

its showing that mean is less than median and as mean lies on the left hand side so its negatively skewed. Histogram for india frequency

15 12 9 6 3 0 -6

-3

0

3

6

9

12

india its showing that it is increasing positively.

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