An Statistical Analysis Of Funds Allocated To The Restoration Of Heritage Buildings In Trinidad And Tobago

TITLE: FUNDS FOR LONG TERM PROJECTS: THE RESTORATION OF HERITAGE BUILDINGS

Julianna Vanessa Baptiste

University of the West Indies Economic Statistics (EC23J)

2005

1

TABLE OF CONTENTS LIST OF ILLUSTRATIONS ...................................................................................... 4 INTRODUCTION........................................................................................................ 4 PROBLEMS AND ISSUES RELATED TO THE DATABASE ............................... 5 RECOMMENDATIONS ........................................................................................... 7 ANALYSIS OF DATA... ............................................................................................. 9 MOVING AVERAGE……………………………………………………………..9 SIMPLE EXPONENTIAL SMOOTHING .............................................................. 15 TREND ANALYSI/REGRESSION AND FORECASTS ....................................... 18 ANALYSIS AND CONCLUSION ........................................................................... 21

LIST OF ILLUSTRATIONS

FIGURE

TITLE

PAGE

1

MOVING AVERAGE FOR TRINIDAD ................................................. 9

2

MOVING AVERAGE FOR TOBAGO .................................................. 10

3

MOVING AVERAGE FOR TRINIDAD AND TOBAGO..................... 11

4

SIMPLE EXPONENTIAL SMOOTHING FOR TRINIDAD ................ 15

5

SIMPLE EXPONENTIAL SMOOTHING FOR TOBAGO ................... 16

6

SES FOR TRINIDAD AND TOBAGO .................................................. 17

7

TREND ANALYSIS PLOT FOR TRINIDAD ....................................... 18

8

TREND ANALYSIS PLOT FOR TOBAGO .......................................... 19

9

TREND ANALYSIS PLOT FOR TRINDAD AND TOBAGO ............. 20

10

RESIDUAL PLOTS FOR TRINIDAD ................................................... 21 2

11

FITTED LINE PLOTS FOR TRINDAD ................................................ 21

12

RESIDUAL PLOTS FOR TOBAGO ..................................................... 22

13

FITTED LINE PLOTS FOR TOBAGO ................................................. 22

14

RESIDUAL PLOTS FOR TRINDAD AND TOBAGO ......................... 23

15

FITTED LINE PLOTS FOR TRINIDAD AND TOBAGO .................... 23

TABLE 1 RAW DATA FOR FUNDS ALLOCATED TO LONG TERM PROJECTS (1973-2005).............................................................................................................. 12 2

FIVE POINT MOVING AVERAGE FOR LONG TERM PROJECTS . 13

3

INTRODUCTION

The assigned project was to collect statistical data for Funds allocated to Long Term Projects. In particular, funds allocated to the restoration of Heritage Buildings in Trinidad and Tobago from 1970 to 2005.

The organizations approached to source data were: 1. The Central Bank of Trinidad and Tobago (CBTT) 2. The Central Statistical Office (CSO) 3. The Ministry of Finance

Efforts were made to source the data from the Central Bank. However, the data was not available and it was advised that the data be sourced from the Central Statistical Office (CSO).

Numerous attempts were made to source data from the CSO. However, upon further investigation it was realized that the CSO only had data for the years 2002-2004. According to the CSO, this was the only data which was sent to them by the Ministry of Finance.

The Ministry of Finance was finally approached and proved to be very helpful in providing estimates and actual funds utilized in the restoration of heritage buildings in Trinidad and Tobago. However, for a number of years, actual funds utilized in both Trinidad and Tobago were not recorded as such for those years the estimates were utilized. Although the 4

estimates for funds do not guarantee that these were the actual amounts spent, it was the closest possible data to the actual funds and thus it was utilized where the actual amounts were not available.

Problems and Issues related to the database 1. The timeliness of CSO‟s data collection has significantly deteriorated over the last 3 decades and more. The data concerning the allocation of funds to the restoration of Heritage Buildings was only available for the years 2002-2004. CSO Had no other records for funds allocated to the restoration Heritage Buildings. This to an extent however, is understandable mainly because „the Central Statistical Office is subject to several resource constraints –human, physical and financial – and this has had a deterious effect on its output.‟ 1

2. The Central Bank can by error be considered as an institution where data and statistics can be found with reference to funding for the restoration of Heritage Buildings. Being an organization that provides data for the public, staff at the Central Bank should at least be familiar with the fundamental data characteristics associated with such issues as funds allocated to the restoration of long term projects. Furthermore, at the Ministry of Finance where the data was found, the library staff had no idea where exactly to look for data concerning funding for long term projects. The time taken to look for the books with data concerning Long

1

Forde P. (1996) “Challenges and Problems in Forecasting Caribbean Economics: Some Data Issues: - Pg. 110

5

Terms projects is time wasted. Staff should at least be trained to know where exactly this data is located.

3. The data produced by the Ministry of Finance was recorded without a great deal of consideration for the accurate assignment of funds to the restoration of Heritage Buildings. The data was recorded without any significant analysis by the Ministry of Finance. There were no attempts to make any relevant comparisons for different time periods. Additionally, the data recorded was annual data there were no monthly or quarterly data to be found for funds utilized in the restoration of heritage buildings.

4. „Data series that is non existent, or plagued by missing values, or is too short cannot create an appropriate Time Series.‟2 For a number of years Actual funds allocated to the restoration of Heritage buildings in both Trinidad and Tobago was not recorded. Although it can be argued that these projects are long term so one wouldn‟t know the actual funds utilized, from as far back as the year1971 in both Trinidad and Tobago actual funds utilized in the restoration of Heritage Buildings were not recorded. One would imagine that for the earlier years actual amounts utilized would be recorded, this however was not the case. Therefore, where the actual amounts were not recorded the estimates had to be utilized.

5. The utilization of Estimates in the place where the actual amount were not recorded poses a serious problem when creating forecasts for the data. This is because, if the 2

Patrick K. (2003) “Data limitations in Modeling the Caribbean Economies” –pg 1

6

difference between the actual amount and the estimate is very large, forecasts would not be accurate. For Trinidad the difference between the estimates and the actual amounts was not sizeable. For Tobago however, the difference between the estimated and actual funds (from the data available) was very considerable.

6. „Government may have hardware and software that are not compatible with the rudimentary backbone of information systems being put in place today.‟ 3 This was evident from the fact that the Ministry of Finance did not have a computer system in place whereby the public could access data from as far back as 1970. In order to get data one had to search through a number of books and compile data this was very time consuming.

Recommendations 1. With the advancement of technology, The Central Statistical Office and other statistical organizations should acquire increased technological capacity so that data can be electronically obtained. Also, this is a more efficient means of processing, compiling and storing data. In this way if data can be produced and accessed electronically time would not be wasted waiting for data to be recorded and published in hard copy books. And therefore, the CSO would not have to wait very long for the Ministry of Finance to send data for The Long term Funds utilized in the restoration of Heritage Buildings.

3

Bashey A.L (2003) “Criteria for the Efficient Coordination of the Activities for Data Collection and the Design of Instruments for Mapping and Data Collection applicable to Countries of the Caribbean” –pg 7

7

2. The critical issue of missing data where it should be available can be lessened by a great degree if Statisticians and Research Officers of all three organizations develop efficient means/tools of collecting data and ensuring that this data is accurate. Thus for more years actual amounts can be available and one would not have to rely on unreliable estimates.

3. Coordination is effective as is the sharing of information between parties. All three organizations should develop a networking system to ensure efficient and coordination and communication between all three organizations. At present there is no networking system between the CSO and the Ministry of Finance. A networking system should be developed between the CSO and The Ministry of Finance and employees should be trained to utilize the system. Not only would the wastage of money and manpower be reduced, but workers would become more skilled.

8

The following is an analysis of the data for ‘Trinidad’ ‘Tobago’ and ‘Trinidad and Tobago’ using Moving Averages, Single Exponential Smoothing, Regression and Trend Analysis. MA for funds Allocated to the Restoration of Heritage Buildings in Trinidad Variable A ctual Smoothed

9000000 8000000 7000000

Trinidad

6000000 5000000

Mov ing A v erage Length 5

4000000 3000000

A ccuracy Measures MA PE 1.23391E+02 MA D 1.06778E+06 MSD 4.19994E+12

2000000 1000000 0 1970

1976

1982

1988 Year

1994

2000

Above is a graphical representation of the Five-Point Moving Average for Funds allocated to the restoration of Heritage Buildings in Trinidad4 during the years 1970-2005. From this graph it can be seen that for the raw data (denoted in black) for the first ten (10) years (1970-1980) data was relatively stationery at a low level. There was a gradual increase between the years 1980 and 1982 followed by a sharp decrease between 1982 and 1983 after which the data continuously fluctuated at a low level until 2000. There was then a sharp increase between the years 2000 to 2003. The data continued to gradually increase until it peaked at 2004 then slightly decreased between years 2004 to 2005.

4

A 3-pt, 5-pt and 7-pt MA was attempted for all data series ; 5-pt chosen because it does not leave too much randomness in the trend cycle estimate and because of its longer length.

9

The five point Moving Average (denoted in red) is used to remove any irregularity in the raw data. It is L shaped in nature due to low stationery effect between the years 1970 to 1980 and the significant increase between the years 2000 to 2003.

MA for funds Allocated to the Restoration of Heritage Buildings in Tobago Variable A ctual Smoothed

600000 500000

Tobago

400000 300000 Mov ing A v erage Length 5

200000 100000

A ccuracy Measures MA PE 1.94246E+02 MA D 1.45668E+05 MSD 4.04949E+10

0 1970

1976

1982

1988 Year

1994

2000

Above is a graphical representation of the Five-Point Moving Average for Funds allocated to the restoration of Heritage Buildings in Tobago during the thirty-five year period under investigation. In studying this graph one could see that for the raw data, the first eights (8) years (1970-1978), data fluctuated at a low stationery point (under $100,000) as shown by the first eight black dots on the Graph. There was then a sharp increase between the years 1978-1979, then a slight fall up to 1980, followed by a marked decrease in 1981, with a sharp increase in 1982. The data then decreased considerably between the years 1982 to 1983. There was a slight recovery to 1984, followed by a downward trend between 1984 10

and 1986, followed by a recovery to 1987. This was followed by sharp increase to 1988 where it peaked and a decreased to 1989. For the next eight years (1989 to 1996), the data continued to fluctuate but at a low stationery point. Furthermore, between the years 1996 to 2005 the data continued to fluctuate, however these fluctuations where more significant. The smoothed data of the Five-point MA (denoted by the red plot), reflects the trend of the raw data by removing irregularity. The MA depicts the stationery (fluctuation) trend in the first few years, followed by the uninterrupted fluctuations which followed throughout the rest of the raw data.

MA for funds for the Restoration of Heritage Buildings in Trindad and Tobago Variable A ctual Smoothed

9000000

Trinidad and Tobago

8000000 7000000 6000000 5000000

Mov ing A v erage Length 5

4000000 3000000 2000000

A ccuracy Measures MA PE 1.60809E+02 MA D 1.35727E+06 MSD 5.47775E+12

1000000 0 1970

1976

1982

1988 Year

1994

2000

The graph above represents the Five-point Moving Average of the funds allocated to the restoration of Heritage Buildings in Trinidad and Tobago for the thirty-five year period under investigation. In examining the three MA graphs, one can conclude that the raw data from Tobago had very little effect on the pattern of the raw data from Trinidad except for 11

the year 1980 where for Tobago there was a sharp increase up to 1980 (as shown in black dots above) whereas for Trinidad, this year was a low stationery data point. The graph for funds allocated to the restoration of Heritage Buildings in Trinidad and Tobago is approximately identical to graph for funds allocated in Trinidad. For the first nine years the raw data in the graph above data is stationery almost constant. There is a sharp increase in 1980, followed by a plunge in 1981 and subsequent recovery in 1982 followed by a sharp decrease in 1983. The data then continues to fluctuate at a low stationery level between the years (1982 to 2000). There is then a sharp increase between the years 2000 to 2003 followed by a decrease and subsequent recovery.

The Five-Point Moving Average (denoted in red) is L-Shaped in nature, except between the years 1978 to 1982 where there is a gradual increase and decrease. This is due to significant fluctuations in the raw data between the years 1978 and 1983.

Table 1: Raw Data for Funds for Long Term Projects: The Restoration of Heritage Buildings Years (1970-2005) ( 1970-2005) Year Estimate Actual Trinidad Estimate Actual Tobago Trinidad

1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983

Trinidad

Trinidad

71060 70299 116894 118942 131904 152927 174855 100000 180000 150000 248200 1500000 2500000 120000

66331 * 115489 125642 129721 * * * * 140319 * * * *

66331 70299 115489 125642 129721 152927 174855 100000 180000 140319 248200 1500000 2500000 120000

Tobago

Tobago

50000 50000 10000 75000 70000 35000 72000 58000 90000 528056 350000 245000 500000 60000

8583 * 6617 63026 64060 27476 61646 * * * * 25671 386000 60000

12

8583 50000 6617 63206 64060 27476 61646 58000 90000 528056 350000 25671 386000 60000

and Tobago 74914 120299 122106 188848 193781 180403 236501 158000 270000 668375 5982000 1525671 2886000 180000

1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

350000 145000 200000 190000 1000000 895000 785000 175700 500000 220000 400000 575000 1900000 739000 700000 5260000 1260000 10525000 7856821 8158000 9200000 8700000

* 130000 * * 903800 442552 * * 243048 95814 399985 468011 436351 * * 1145211 587754 1671680 * * * *

350000 130000 200000 190000 903800 442552 785000 175700 243048 95814 399985 468011 436351 739000 700000 1145211 587754 1671680 7856821 8158000 9200000 8700000

75000 815000 641000 100000 600000 100000 85000 50000 913000 60000 12500 60000 60000 500000 100000 120000 200000 500000 500000 500000 50000 300000

74452 60000 24000 * * * 89700 * 75000 12500 * 60000 * * * * * * * 50000 * *

74452 60000 24000 100000 600000 100000 89700 50000 75000 12500 12500 60000 60000 500000 100000 120000 200000 500000 500000 50000 50000 300000

Table2: Five-Point Moving Average for Funds for Long Term Projects: The Restoration of Heritage Buildings between the years 1970-2005 Year

1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982

Trinidad

Tobago

Trinidad and Tobago

Raw Data

5-Pt MA

Raw Data

Raw Data

Raw Data

5-pt MA

66331 70299 115489 125642 129721 152927 174855 100000 180000 140319 248200 1500000 2500000

* * 101496 118816 139727 136629 147501 149620 168675 433704 913704 901704 943640

8583 50000 6617 63206 64060 27476 61646 58000 90000 528056 350000 25671 386000 13

* * 38493 42272 44601 54878 60236 153036 217540 210345 275945 269945 179225

74914 120299 122106 188848 193781 180403 236501 158000 270000 668375 5982000 1525671 2886000

* * 139990 161087 184328 191507 207737 302656 1462975 1720809 2266409 2248409 2199625

424452 190000 224000 290000 1503800 542552 874700 225700 318048 108314 412485 528011 496351 1239000 800000 1157211 787754 2171680 8356821 8208000 9250000 9000000

1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

120000 350000 130000 200000 190000 903800 442552 785000 175700 243048 95814 399985 468011 436351 739000 700000 1145211 587754 1671680 7856821 8158000 9200000 8700000

920000 660000 198000 354760 373270 504270 499410 510020 348423 339909 276512 328642 427832 548669 697715 721663 968729 2392293 3883893 5494851 7117300 * *

60000 74452 60000 24000 100000 600000 100000 89700 50000 75000 12500 12500 60000 60000 500000 100000 120000 200000 500000 500000 50000 50000 300000

14

121225 120890 63690 171690 176800 182740 187940 65440 47940 42000 44000 129000 146500 168000 196000 284000 284000 274000 260000 280000 290000 * *

180000 424452 190000 224000 290000 1503800 542552 874700 225700 318048 108314 412485 528011 496351 1239000 800000 1157211 787754 2171680 8356821 8208000 9250000 9000000

1041225 780890 260690 526450 550070 687010 687350 692960 413863 387849 318512 372642 556832 695169 844115 896063 1231129 2654693 4136293 5754851 7397300 * *

SES for Trinidad Using alpha .2 Variable A ctual Smoothed

9000000 8000000

Trinidad Raw Data

7000000 6000000 5000000 4000000 Smoothing Constant Alpha 0.2

3000000 2000000

A ccuracy Measures MA PE 2.18302E+02 MA D 1.03470E+06 MSD 4.07534E+12

1000000 0 1970

1976

1982

1988 Year

1994

2000

The graph above represents the Simple Exponential Smoothing for funds allocated to the Restoration of Heritage Buildings in Trinidad during the years 1970 to 2005. An alpha (α) of 0.2 was used because it derived a smoother curve that was less sensitive to the conditions of the raw data5. Additionally, F1 was derived from obtaining the average of all thirty-five (35) observations. As a result of this, the smoothed curve (in red) begins relatively higher than the first observation. The smoothed series slightly decreases until it is surpassed by the raw data after the 11th year, where the significant increase then decrease gradually pulled this line upwards then downwards, until the smoothed series once again surpasses the raw data. This however is not for long, as the raw data continues to fluctuate at a low level the smoothed series adjusts accordingly. This continues until the year 2000

5

A large α of 0.8 and a small of 0.2 was chosen and compared for all the data series: it was decided that the smaller alpha of 0.2 would be utilized since the large alpha was much too sensitive to the conditions of the raw data.

15

where the raw data surpasses the smoothed series, here, the smoothed series increases significantly. This is due to the sharp increase in the raw data from the year 2000.

SES for Tobago Using alpha .2 Variable Actual Smoothed

600000

Tobago Raw Data

500000 400000 300000 200000

Smoothing Constant Alpha 0.2

100000

Accuracy Measures MAPE 2.51148E+02 MAD 1.33633E+05 MSD 3.32947E+10

0 1970

1976

1982

1988 Year

1994

2000

Above is a graphical representation of the Simple Exponential Smoothing for Funds utilized in the restoration of Heritage Buildings in Tobago. As in the exponential smoothing for Trinidad, an alpha (α) of 0.2 was used, while the average of all thirty-five (35) observations was used for F1. As with Trinidad, the smoothed series (in red) begins relatively higher than the raw data, however for most of the years the raw data surpassed the smoothed series because of it significant fluctuations. However, for the years 1984 to 1986 and again for the years 1989 to 1996, the smoothed series surpassed the raw data in a decreasing trend due to the low fluctuating levels of the raw data. In the final eight years because of the significant fluctuations of the raw data, this line remained higher than the

16

smoothed series except for the year 1998, 1999, and again for the years 2003 and 2004 where the raw data plunged making the smoothed series surpass it.

SES for Trinidad and Tobago Using alpha .2 Variable Actual Smoothed

9000000

Triniad and Tobago

8000000 7000000 6000000 5000000 4000000

Smoothing Constant Alpha 0.2

3000000 2000000

Accuracy Measures MAPE 2.36806E+02 MAD 1.28501E+06 MSD 5.06700E+12

1000000 0 1970

1976

1982

1988 Year

1994

2000

The graph above represents the Simple Exponential Smoothing of the Funds utilized in the Restoration of Heritage Buildings in Trinidad and Tobago during the years 1970 to 2005. The shape of this smoothed series resembles the smoothed series of Trinidad. This proves that the data of Tobago had little impact on the pattern of Trinidad‟s data series. Furthermore, one can conclude that more funds were allocated to the restoration of Heritage buildings in Trinidad.

According the figure above, the smoothed series slightly decreases until it is surpassed by the raw data in 1989, where the significant increase then decrease gradually pulled this line 17

upwards then downwards, until the smoothed series once again surpasses the raw data. This however is not for long, as the raw data continues to fluctuate at a low level the smoothed series moves and adjusts accordingly. This continues until the year 2000 where the raw data surpasses the smoothed series, the smoothed series increases significantly this is due to the sharp increase in the raw data from the year 2000.

Trend Analysis Plot for Trinidad Linear Trend Model Yt = -1364717 + 147646*t

10000000

Variable A ctual Fits Forecasts

Trinidad Raw Data

8000000

A ccuracy Measures MA PE 4.62392E+02 MA D 1.60106E+06 MSD 4.26175E+12

6000000 4000000 2000000 0

1970

1976

1982

1988 Year

1994

2000

2006

Forecast 2006: $4,098,190

The graph represents a trend analysis and forecast for funds allocated to the restoration of Heritage Buildings in Trinidad during the years 1970 to 2005. As seen above, there is an obvious increasing trend in the series. This resulted in a forecast for 2006 of $4,098,190 for funds allocated to the restoration of Heritage Buildings. This forecast suggests a decrease from 2005.

18

Trend Analysis Plot for Tobago Linear Trend Model Yt = 68192.9 + 4448.23*t

Variable A ctual Fits Forecasts

600000

Tobago Raw Data

500000

A ccuracy Measures MA PE 2.37823E+02 MA D 1.28274E+05 MSD 2.81116E+10

400000 300000 200000 100000 0 1970

1976

1982

1988 Year

1994

2000

2006

Forecast for 2006: $232,778

Above is a graphical representation of the linear trend analysis and forecast for funds allocated to the restoration of Heritage Buildings in Tobago during the years 1970 to 2005. The series shows an obvious increasing trend that resulted in a forecast for 2006 of approximately $232,778 for funds allocated to the restoration of Heritage Buildings. This forecast also suggests a decrease from the 2005.

19

Trend Analysis Plot for Trinidad and Tobago Linear Trend Model Yt = -951782 + 141381*t

10000000

Variable A ctual Fits Forecasts

Trinidad and Tobago

8000000

A ccuracy Measures MA PE 3.42601E+02 MA D 1.73876E+06 MSD 5.19604E+12

6000000 4000000 2000000 0 1970

1976

1982

1988 Year

1994

2000

2006

Forecast for 2006: $4,330,968

The graph above represents a linear trend analysis and forecast for funds allocated to the restoration of Heritage Buildings in Trinidad and Tobago during the years 1970 to 2005. The combination of the two data series caused the trend to make a significant slant upwards. This variant in the trend line shows the minute effect that Tobago has on the total figure for the two islands combined. The forecast for Trinidad and Tobago is $4,330,968 for funds allocated to the restoration of Heritage Buildings in 2006, which is equal to the sum of the forecasts for each country separately. This forecast assumes an increase from 2005, continuing the upward trend in the raw data.

20

Residual and Fitted line Plot Analysis

Residual Plots for logten(Trinidad Raw Data) Normal Probability Plot of the Residuals 99

0.0 -0.5

10 -1.0

-0.5

0.0 Residual

0.5

-1.0

1.0

5.0

5.5 6.0 Fitted Value

6.5

Residuals Versus the Order of the Data 1.0

12

0.5

Residual

Frequency

Histogram of the Residuals 16

8 4

S R-Sq R-Sq(adj)

10000000

0.5

Trinidad Raw Data

Residual

Percent

50

0

logten(Trinidad Raw Data) = - 658.0 + 201.2 logten(Years)

1.0

90

1

Fitted Line Plot for Trinidad

Residuals Versus the Fitted Values

1000000

100000

0.0 -0.5

-1.0

-0.5

0.0 Residual

0.5

1.0

-1.0

1970 1

5

10

15 20 25 Observation Order

30

35

1980

1990 Years

2000

2010

Above are graphical representations of firstly the residual plots6 for raw data7 of Trinidad and secondly the fitted line plot for Trinidad. R-sq8 for the linear regression model for Trinidad Raw data is 56.8%, this means that 56.8% of the total variation of the dependant variable Y (Raw data Trinidad) is explained by the variable X (Years). However the model does not explain 43.2% of the total variation Y. Thus R-sq% = 56.8% is not a very good fit of the raw data for Trinidad

The graph representing the normal probability plot generally forms a straight line except for the end points which display some curvature. As the number of observations moves upward there is significant non-linearity and variation (as seen in the dotted line). The graph representing the residual versus fit (dotted line) does not have any recognizable

6

Residual Plots are being utilized to examine the goodness of fit of the regression model. The variables (raw data) was transposed by calculating the Logs in order for analysis to be easier 8 R-sq, the coefficient of determination is measure of the degree of fit (quality) of the linear regression model. 7

21

0.409478 56.8% 55.6%

pattern. There are also a few outliers (six). There is a series of increasing points between the fitted values of 5.7 and 6.3 this represents some error that is not random.

The Histogram of the residuals, (below the normal probability plot) does not have very long tails as such, the data is not skewed. The first bar (-1.0) is far from the other bars therefore these points are outliers. The Residuals versus the order of the data is a plot of all residuals in the order that the data was collected (from 1975-2005). There is some positive correlation, this is indicative of the cluster of residuals in the same sign this can be seen by the cluster of residuals between the third and the sixth observations.

Residual Plots for logten(Tobago Raw Data) 99

1.0

90

0.5

10 1

-1.0

-0.5

0.0 Residual

0.5

4.6

4.8 5.0 Fitted Value

5.2

Residuals Versus the Order of the Data 1.0

9

0.5

6

0.486267 12.6% 10.0%

100000

10000

0.0 -0.5

3 0

R-Sq R-Sq(adj)

-0.5

12 Residual

Frequency

Histogram of the Residuals

S

0.0

-1.0

1.0

1000000

Tobago Raw Data

50

Fitted Line Plot for Tobago logten(Tobago Raw Data) = - 255.4 + 78.91 logten(Years)

Residuals Versus the Fitted Values

Residual

Percent

Normal Probability Plot of the Residuals

-1.0

-0.5

0.0 Residual

0.5

1.0

-1.0

1970 1

5

10

15 20 25 Observation Order

30

35

1980

1990 Years

2000

2010

Above are graphical representations of firstly the residual plots for the Log of Tobago raw data and secondly the fitted line plot for Tobago. R-sq for the linear regression model for Tobago Raw data is 12.6%, this means that 12.6% of the total variation of the dependant variable Y (Raw data for Tobago) is explained by the variable X (Years). However the 22

model does not explain 87.4% of the total variation Y. Thus R-sq% = 12.6% is a poor fit of the Raw data for Tobago.

The graph representing the normal probability plot generally forms a straight line. As the number of observations moves upward there is some non-linearity and variation (dotted line). The graph representing the Residual versus fit (dots only) does not have any recognizable pattern. There are also a few outliers (six). There is a series of increasing points between the fitted values of 5.4 and 5.6; there is also a predominance of negative points this is indicative of error that is not random.

The Histogram of the residual, does not have very long tail thus, the data is not very skewed. There are no separate bars; this means that there are few outliers. The Residuals versus the order of the data is a plot of all residuals in the order that the data was collected. According to the data, there is negative correlation; this is indicated by the rapid changes in signs of the consecutive residuals.

Residual Plots for logten(Trinidad and Tobago) Normal Probability Plot of the Residuals

Fitted Line Plot for Trinidad and Tobago

Residuals Versus the Fitted Values

logten(Triniad and Tobago) = - 559.9 + 171.5 logten(Years)

99

R-Sq(adj)

0.0 -0.5

10 1

0.5

-1.0 -1.0

-0.5

0.0 0.5 Residual

1.0

5.0

Histogram of the Residuals

5.5 6.0 Fitted Value

6.5

Residuals Versus the Order of the Data

12 Residual

Frequency

1.0 9 6 3 0

Triniad and Tobago

Residual

Percent

50

S R-Sq

10000000

1.0

90

1000000

0.5

100000

0.0 -0.5

1970

-1.0 -1.0

-0.5

0.0 0.5 Residual

1.0

1

5

10

15 20 25 Observation Order

30

35

23

1980

1990 Years

2000

2010

0.457499 43.4% 41.7%

Above are graphical representations of firstly the residual plots for logs of Trinidad and Tobago raw data and secondly the fitted line plot for Trinidad and Tobago. R-sq for the linear regression model for Trinidad and Tobago Raw data is 43.4%, this means that 43.4% of the total variation of the dependant variable Y (Raw data for Trinidad and Tobago) is explained by the variable X (Years). However the model does not explain 56.6% of the total variation Y. Thus R-sq% = 56.6% is not a very good fit for the raw data of Trinidad and Tobago.

The graph representing the normal probability plot generally forms a straight line. As the number of observations moves upward there is some non-linearity and variation. The graph representing the Residual versus fit (dots only) does not have a recognizable pattern. There are only three outliers and as in the graph for Trinidad, there is a series of increasing and decreasing points; this indicates that there is some error that is not random.

The Histogram of the residuals, has a bit of a long tail on the right side this is indicative of some skewness. As in the histogram for Trinidad, the first bar (-1.0) is far from the other bars therefore these points are outliers. The Residuals versus the order of the data is a plot of all residuals in the order that the data was collected (from 1975-2005). Here, there is some positive correlation, this is indicative of the cluster of residuals in the same sign.

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