INTRODUCTION
Ethiopia's agriculture plays a crucial role in its economy, contributing 83.9% of exports and providing 80% of employment While most agricultural output is consumed domestically, a significant portion of exports comes from a small cash-crop sector Over recent decades, the agriculture industry has rapidly expanded, aiding in poverty reduction However, it faces challenges such as drought, soil degradation from overgrazing, deforestation, high taxation, and inadequate infrastructure.
Agriculture plays a vital role in Nigeria's economy, employing around 35% of the population as of 2020 The sector comprises four main subsectors: crop production, livestock production, forestry, and fishing, with livestock and crop farming serving as its backbone As Nigeria's population continues to grow, the agricultural sector is expected to expand to meet increasing demand However, it faces significant challenges, including an outdated land tenure system, limited irrigation development, slow technology adoption, high input costs, and inadequate storage facilities.
Nigerian and Ethiopian data used in this report originate entirely from genuine and reputable sources and range the years 1997 to 2018:
AAGR% of GDP) (Use agriculture, forestry, and fishing, value added (% of GDP from world bank indicator)
GDP per capita growth rate (annual %)
Foreign direct investment, net inflow (% of
Employment in Agriculture (% of total employment)
Agricultural raw materials exports (% of merchandise exports)
CO2 emission (metric tons per capita)
Urban population (% of total population)
Between 2004 and 2005, the dataset for 'Agricultural raw materials exports' was unavailable due to restrictions imposed by the Nigerian government (FAO 2013) To complete the dataset, this report opted to replace the missing data with figures from either 2003 or 2006 The 2003 data reflects a value of 0.01%, while the 2006 data shows 0.36%, indicating a 0.3% change For consistency and ease of calculations, this report will utilize the 2003 data, although this replacement may lead to some inaccuracies in the overall findings.
DESCRIPTIVE ANALYSIS
Table 2: The central tendency of two countries Agricultural Annual Growth Rate
Minimum value Compare Lower threshold
Maximum value Compare Upper threshold
Table 3: Outliers identification for the datasets.
Applying the IQR rule reveals two outliers in the data set, leading to the decision to use the median as the measure of central tendency, as it remains unaffected by outliers The median agricultural growth rate for Nigeria is 24.569%, which is significantly lower than Ethiopia's 41.348%, highlighting Nigeria's reduced agricultural growth rate.
Agriculture, forestry, and fishing, value added (% of GDP) Nigeria Comparison Ethiopia
Table 4 Table of comparison with all the measures of two countries of Variation in terms of t% of GDP of Agricultural Annual Growth Rate
The Interquartile Range (IQR), which measures the spread of the central 50% of data while excluding outliers, serves as the optimal variation metric for Nigeria and Ethiopia Nigeria's IQR stands at 5.342, which is lower than Ethiopia's IQR of 6.022, suggesting that the central data distribution in Ethiopia exhibits a greater spread.
(Unit: % of GDP) Left side Right side Conclusion Skewness
Q1-Min vs Max-Q3 1.252 < 10.381 Right- skewed
Median-Q1 vs Q3-Median 3.327 > 2.015 Left- skewed
Table 5: Table of comparison between Nigeria Box-and-Whisker plot values to determine skewness.
(Unit: % of GDP) Left side Right side Conclusion Skewness
Q1-Min vs Max-Q3 7.448 < 9.447 Right- skewed
Median-Q1 vs Q3-Median 2.788 < 3.234 Right- skewed
Table 6: Table of comparison between Ethiopia Box-and-Whisker plot values to determine skewness.
Tables 3,4 show that two countries box-plot are positively-skewed However, figure 1 depicts that Nigeria values are more concentrated in the left tail of the distribution than Ethiopia values.
In Nigeria, the first 25% of data shows a sparse distribution, while the final 25% is highly scattered In contrast, Ethiopia's box plot indicates a more balanced distribution, featuring approximately equal tails on both the right and left sides.
Figure 1 Box-plot of Nigeria and Ethiopia
MULTIPLE REGRESSION
Multiple regression is a statistical method used to analyze the relationship between one dependent variable and several independent variables In this study, it will evaluate the impact of various factors on the agricultural annual growth rates (AAGR) of Ethiopia and Nigeria The AAGR serves as the dependent variable (Y), while nine other identified factors act as independent variables (X).
5,6) To arrive at the final regression model, this report uses the backward elimination method
To enhance the accuracy of the regression analyses, independent variables (X) that are not significant at the 0.05 level will be excluded, focusing solely on those that correlate with the dependent variables (Y) Furthermore, to mitigate the impact of outliers on the results, the years 1997 and 2002 will be omitted from the analysis for both nations.
Final regression output Table 8 Nigeria independent and dependent variables
Table 7 Ethiopia independent and dependent variables
Agriculture, forestry, and fishing, value added (% of GDP) / Agricultural Annual Growth Rate
2 Urban population (% of total population) X
Agriculture, forestry, and fishing, value added (% of GDP) /
2 Foreign direct investment, net inflows (% of GDP) X
Employment in agriculture (% of total employment) (modeled ILO estimate)
4 Urban population (% of total population) X
Scatter plot and line fit plots
Figure 2 : Ethiopia's final regression output applying the application of the backward elimination technique
Figure 3 Line fit plot between FDI (% of GDP) and AAGR (% of GDP)
Figure 4 Line fit plot between Average of Temperature (Celsius) and AAGR (% of GDP)
Figure 5 Line fit plot between Urban population (% of total population) and AAGR (% of GDP)
The figure 3,4,5,6 illustrate that, while employment in agriculture exhibits a positive correlation,
Foreign Direct Investment (FDI), urban population, and average temperature are negatively correlated with the Average Annual Growth Rate (AAGR) Specifically, an increase in agricultural employment is associated with a higher AAGR Conversely, rising levels of FDI, urban population, and average temperature lead to a decline in AAGR Additionally, regression analysis and line fit plots provide further insights into these relationships.
Predicted agriculture, forestry, and fishing, value added (% of GDP) / Predicted Agricultural Annual Growth Rate
Foreign direct investment, net inflows (% of GDP)
Employment in agriculture (% of total employment)
Figure 6 Line fit plot between Employment in Agriculture (% of total employment) and AAGR (% of GDP)
Urban population (% of total population) Average of Temperature - (Celsius)
The relationship between employment in agriculture and average temperature appears contradictory when analyzed through linear fit plots This inconsistency may arise from the use of a linear regression model that considers only one independent and one dependent variable, while multiple independent variables are present In contrast, multiple regression accounts for the correlations among these independent variables, leading to more accurate results However, it is important to acknowledge that this analysis carries a 5% margin of error, highlighting the need for careful interpretation of regression coefficients.
73.196, indicating that when all independent variables are 0, the predicted AAGR will take
73.196% of GDP This is explainable as agriculture is known as the backbone of Ethiopia’s economy (Welteji 2018).
The analysis indicates that a 1% increase in Foreign Direct Investment (FDI) could lead to a 1.509% decrease in the Average Annual Growth Rate (AAGR) of GDP, assuming other factors remain constant This trend is attributed to the agriculture sector's diminishing contribution to GDP, which has fallen to 30% over the past two decades, prompting a shift of FDI from agriculture to non-agricultural sectors (Eshetu & Mehare, 2020).
The analysis indicates that a 1% increase in employment within the agricultural sector is associated with a projected average annual growth rate (AAGR) decrease of 1.072% of GDP, assuming other factors (x1, x3, x4) remain constant This highlights the unproductive nature of agriculture, suggesting that additional employment in this sector has a minimal impact on overall industry growth.
The anticipated average annual growth rate (AAGR) is projected to decline by 3.544% of GDP with a 1% increase in the urban population, assuming other factors remain constant Urbanization significantly affects Ethiopians, as the nation heavily depends on agriculture for economic growth and employs a substantial portion of its workforce (Agwu & Anugwa 2021, Yalew 2020) Furthermore, rising urbanization is likely to reduce productivity among agricultural workers, leading to the urbanization of agricultural regions that already experience low production levels (Ergen 2016).
The predicted Average Annual Growth Rate (AAGR) is expected to rise by 4.831% of GDP for each one-degree Celsius increase in temperature, assuming other factors remain constant However, this claim contradicts numerous reports indicating that higher temperatures diminish soil nutrients, negatively impacting agricultural and animal productivity (Ketema and Negeso 2020) Consequently, the validity of coefficient b4 appears questionable, potentially due to a 5% margin of error in the findings Additionally, it is essential to clarify the coefficient of determination in this context.
The R-squared value of 0.888 suggests that 88.8% of the variation in Ethiopia's Average Annual Growth Rate (AAGR) can be attributed to factors such as Foreign Direct Investment (FDI), agricultural employment, average temperature, and urban population The remaining 11.2% of the variation is likely influenced by other factors not covered in this report.
Scatter plot and line fit plots:
Figure 7: Nigeria's final regression output applying the application of the backward elimination technique
The urban population line fit plot reveals a negative correlation, indicating that an increase in the agricultural annual growth rate corresponds to a decrease in urban population Additionally, the plot shows moderate linear correlations, suggesting that fluctuations in urban population significantly influence changes in the agricultural annual growth rate This relationship can be further analyzed through the regression equation and a comparison with line fit plots.
Predicted agriculture, forestry, and fishing, value added (% of GDP) / Predicted Agricultural Annual Growth Rate Urban population (% of total population)
AAGR Moreover, line fit plot of the variable also shows negative correlation with AAGR. c Regression coefficient interpretation
Figure 8 Line fit plot between Urban population (% of total population) and AAGR (% of GDP)
The projected Average Annual Growth Rate (AAGR) for Nigeria's agricultural sector is expected to reach 42.028% of GDP when all independent variables are set to zero This significant growth potential is largely attributed to the challenges faced by the sector, including recurring flooding, insurgencies from Boko Haram, and conflicts between herders and local farmers, which have adversely impacted agricultural productivity (ITA 2021).
A 1% increase in the urban population is projected to lead to a 0.428% decline in the Average Annual Growth Rate (AAGR) of GDP, indicating that urban expansion negatively impacts agricultural land (Oloukoi, Oyinloye & Yadjemi, 2014).
The R-squared value of 0.443 indicates that 44.3% of the fluctuations in Nigeria's Agricultural Annual Growth Rate are attributable to changes in the urban population, while the remaining 55.7% is influenced by other factors not addressed in this analysis.
REGRESSION CONCLUSION
The regression analysis reveals distinct differences between Ethiopia and Nigeria regarding significant independent variables affecting their growth Ethiopia identifies four key variables: Foreign Direct Investment (FDI), average temperature, employment in agriculture, and urban population In contrast, Nigeria highlights only one significant variable: urban population Despite the variation in the number of impactful factors, both countries share urban population as a common variable, which exerts a substantial negative influence on the Average Annual Growth Rate (AAGR) for both nations at a 0.05 significance level.
The urban population in Nigeria has a lesser impact on the Average Annual Growth Rate (AAGR) compared to Ethiopia, with coefficients of -0.428 and -3.544, respectively This disparity is attributed to Ethiopia's significantly lower urban population proportion from 1998 to 2018 Consequently, Nigeria's high urban population suggests that urbanization will minimally affect agricultural land In contrast, Ethiopia's nascent urbanization presents a more substantial impact on its agricultural landscape.
Ethiopia's coefficient of determination (R square) stands at 88.8%, significantly higher than Nigeria's 44.3%, indicating that a greater proportion of variance in the dependent variable can be explained by the independent variable in Ethiopia (Corporate Finance Institute, n.d.) According to Frost (2015), a larger R square suggests a closer alignment between expected and actual data, implying that Ethiopia's predictions of AAGR variables are likely to be more accurate than those of Nigeria Despite potential errors stemming from two predicted data points in Nigeria and the insignificant coefficient of average temperature in Ethiopia, the fact that Ethiopia's R square is double that of Nigeria suggests that any errors in predictions are relatively minor.
Ethiopia's agriculture is more advanced than Nigeria's, yet Nigeria's economic standing is perceived to be superior (Georank n.d) This disparity arises from Nigeria's robust heavy industries, which contribute significantly more to its GDP compared to agricultural development (trade.gov n.d) Consequently, the R-squared implications for both countries are reinforced.
TIME SERIES AND CONCLUSION
Figure 9 Comparison of Ethiopia and Nigeria urban population (worldbank n.d)
Figure 10 Ethiopian and Nigerian AAGR (% of GDP) line chart
Between 1997 and 2018, Ethiopia's average annual growth rate (AAGR) surpassed that of Nigeria, with Ethiopia showing greater economic stability Nigeria experienced a peak-to-trough disparity of 16.98%, while Ethiopia's decline was less pronounced The stability of Ethiopia's economy can be attributed to its agricultural sector, which accounts for 40% of the GDP, 80% of exports, and employs over 75% of the workforce, as reported by US Aid in 2022.
Between 1997 and 2002, Ethiopia saw a notable decline in its Average Annual Growth Rate (AAGR), while Nigeria experienced an increase during the same period However, from 2003 to 2018, Nigeria's AAGR decreased by 12.63%, and Ethiopia's dropped by 6.18% This decline in AAGR for both nations is linked to rising urban populations The Multiple Regression analysis indicates a significant negative relationship between urbanization and agricultural growth Specifically, from 2003 to 2008, Ethiopia's urban population increased by 5.45%, and Nigeria's by 12.98%, contributing to the reduced AAGR Ergen (2016) highlights that urbanization adversely affects agricultural growth rates by depleting the workforce in rural areas.
From Appendix A, the significant trend models for both countries are linear and exponential.
Y The AAGR for both countries from 1997 to 2018
T Time period order for each year from 1997 to 2018
Figure 11 Regression output for Nigeria’s linear model
In 1996, the Average Annual Growth Rate (AAGR) of GDP was 29.615%, indicated by the intercept of 0.615 The slope of -0.421 demonstrates a negative relationship, suggesting that the AAGR is projected to decrease by 0.421% for each passing year.
Figure 12 Regression output for Nigeria’s exponential model Linear Format:
This means that AAGR falls by a factor of 0.984 each month As such, by the end of every year,the AAGR is 1.6% lower
Figure 13 Regression output for Ethiopia’s linear model Formula and Explanation:
In 1996, designated as T=0, the Average Annual Growth Rate (AAGR) of GDP was 47.909% The intercept value indicates this initial growth rate, while the slope of -0.570 signifies that the AAGR decreases by 0.570% for each subsequent year, highlighting a negative correlation over time This analysis can be further explored through an exponential model.
Figure 14 Regression output for Ethiopia’s exponential model Linear Format:
This means that the AAGR falls by a factor of 0.986 each month As such, by the end of every
The accuracy of a trend model is evaluated through its error measurement, with Mean Absolute Deviation (MAD) and Sum of Squared Errors (SEE) being the most effective metrics A model with smaller errors is deemed more reliable (Bartlett & Frost, 2008) However, due to the presence of outliers in the AAGR data sets for Ethiopia and Nigeria, SEE is not applicable as it is sensitive to such anomalies Consequently, MAD emerges as the preferred metric for comparing trend models in this context (Mathews, 2018).
Table 12 Comparing MAD for Nigeria’s significant trend models
Since the Linear trend model has the smallest result of MAD, it is considered as the most suitable trend model to predict AAGR in Nigeria
Table 13 Comparing MAD for Ethiopia’s significant trend models
Because the Linear trend model has the smallest MAD, it is regarded as the best-suited trend model for predicting Ethiopia's AAGR.
Linear trend formula Y= 29.615 - 0.421T will be used to estimate the AAGR in Ethiopia.
Time period (T) Agricultural annual growth rate predicted value (Y)
Table 14 Predicted AAGR values for Nigeria
Linear trend formula YG.909-0.570T will be used to estimate the AAGR in Ethiopia.
Time period (T) Agricultural annual growth rate predicted value (Y)
Table 15 Predicted AAGR values for Ethiopia
After using the Linear Trend Formula to estimate the AAGR in Nigeria and Ethiopia, these predictions are made:
In 2022 (T = 26), it is predicted that the AAGR in Nigeria and Ethiopia are 18.699% and 33.089% respectively.
In 2023 (T = 27), it is predicted that the AAGR in Nigeria and Ethiopia are 18.248% and 32.519% respectively.
In 2024 (T = 28), it is predicted that the AAGR in Nigeria and Ethiopia are 17.828% and 31.949% respectively.
From 2022 to 2024, both countries are predicted to experience a downward trend in the AAGR However, with a confidence level of 95%, the actual growth rate can be different from these predictions.
OVERALL CONCLUSION
Multiple regression analysis highlights the substantial contribution of agriculture to the GDP growth of Ethiopia and Nigeria However, the report overlooks urban challenges faced by both countries, leading to potential inaccuracies in its findings This discrepancy may stem from Ethiopia's heavy reliance on agriculture, which plays a crucial role in its GDP and employment, whereas Nigeria tends to prioritize heavy industries over agricultural development.
Agriculture plays a vital role in alleviating poverty and enhancing food security in developing countries, yet these nations continue to face numerous challenges (Nori & Farinella 2020) The Foreign and Commonwealth Office (FCO) highlights that the adoption of specialized techniques and advanced technology has transformed agricultural practices and productivity in Asia and Latin America, leading to significant improvements in the sector.
"green revolution" (Hoskins 2009) However, Africa as a whole, and particularly Nigeria and Ethiopia, have not seen the emergence of distinctly African green revolution technology.
Enhanced plant breeding research is essential, particularly when considering the unique soil types of both nations (Osaki et al 1991) The consortium of agricultural research facilities indicates that every dollar invested in this research yields a remarkable six-fold return.
As the effects of climate change on weather patterns grow more prominent, increased irrigation will be required On average, irrigated farms yield 90% more than nearby rain-fed farmland.
As soil fertility declines, the demand for fertilizers rises, necessitating government action to provide the right type and amount of fertilizer at optimal prices and times Implementing fertilizer education programs not only supports environmental sustainability but has also been shown to significantly increase average incomes, with a study in East Africa indicating a 61% income boost (Banayo et al 2020).
Our research highlights significant similarities between Nigeria and Ethiopia, as both are developing countries with African heritage that heavily depend on agriculture Consequently, it is evident that technology and education play crucial roles in driving the Annual Agricultural Growth Rate (AAGR) in these nations.
Enhancing agricultural production efficiency is essential for fostering pro-poor economic growth Research by Thirtle et al (2003) highlights the positive correlation between agriculture and technology, demonstrating that from 1985 to 1993, a 1% rise in crop yields led to a reduction of 0.6 to 1.2% in the number of people living on less than $1 per day (Lenne 2007) Thus, the adoption of technology significantly boosts agricultural productivity.
Agricultural education encompasses subjects like biology, chemistry, physics, and business management, aiming to integrate knowledge from various fields Research indicates that farmers with higher education levels make more informed decisions, leading to improved resource utilization across farms of all sizes (Asadullah & Rahman 2009) Furthermore, education plays a crucial role in diminishing information asymmetry related to input and output quality, enabling educated farmers to allocate limited resources more effectively (Reimers & Klasen 2013).
APPENDICES
The backward elimination technique is a statistical method used to remove non-essential features that do not significantly impact the dependent variable or output prediction Starting with a full model that includes all independent variables, the technique identifies non-significant variables based on t-values, p-values, and a predetermined alpha level Variables with p-values exceeding the alpha level are systematically eliminated, beginning with the one having the smallest absolute value, and a new model is developed This iterative process continues until all remaining independent variables are statistically significant, at which point the backward elimination process is complete.
Since Nigeria missed 2014 and 2015 data for “Agriculture raw materials exports”, this report will used 2013 data instead (as explained above) Additionally, the multiple regression will omit
1997 and 2002 as they contain outliers.
The report utilizes the Backward Elimination method to analyze data from Ethiopia and Nigeria, focusing on nine variables (X1 to X9) to identify significant independent factors influencing the Agricultural Annual Growth Rate (AAGR) (Y) by evaluating p-values against a threshold of 0.05.
❖ Step 1: State the Null and Alternative Hypothesis
- Do not reject Null when p-value larger than or equal to = 0.05�
- Reject Null when p-value smaller than = 0.05�
❖ Step 2: Run the Regression Model with the full 9 variables
In the analysis, most variables exhibit p-values exceeding 0.05, with the exceptions being urban population and foreign direct investment (FDI) Significantly, CO2 emissions present the highest p-value at 0.883 and the lowest absolute t-statistic of 0.883, indicating that CO2 emissions will be prioritized for elimination in the study.
❖ Step 3: Run the Regression Model with k-1 (eight) variables:
After removing CO2 emissions from the analysis, urban population and foreign direct investment (FDI) remain the only variables with a p-value less than 0.05 In contrast, GDP per capita growth exhibits the highest p-value of 0.796 and the lowest absolute t-statistic of 0.265, leading to its elimination from the study.
❖ Step 4: Run the Regression Model with k-2 (seven) variables:
Figure 15 The Regression Model of Ethiopia with full 9 variables
Figure 16 The Regression Model of Ethiopia with 8 variables
Following the removal of two variables, the analysis reveals that only three out of seven variables maintain a p-value exceeding 0.05 Consequently, with the highest p-value of 0.302 and the lowest absolute t-Stat of 1.079, the export of agricultural raw materials will be the next variable to be excluded from the model.
❖ Step 5: Run the Regression Model with k-3 (six) variables:
Currently, two variables have p-values exceeding 0.05, prompting the continuation of the backward elimination process The variable with the highest p-value of 0.218 and the lowest absolute t-statistic of 1.293, which is Inflation in consumer prices, will be the next to be removed from the analysis.
❖ Step 6: Run the Regression Model with k-3 (five) variables:
Figure 17 The Regression Model of Ethiopia with 7 variables
Figure 18 The Regression Model of Ethiopia with 6 variables
Figure 19 The Regression Model of Ethiopia with 5 variables
Average rainfall is the only variable with p-value greater than 0.05 The report will eliminate it.
❖ Step 7: Run the Regression Model with k-3 (four) variables:
As can be seen, there are four significant variables left, with p-value smaller than 0.05 Therefore, the Backward elimination process ends
In summary, Foreign Direct Investment (FDI), agricultural employment, urban population, and average temperature significantly influence the Average Annual Growth Rate (AAGR) in Ethiopia At a 5% significance level, these four variables demonstrate a meaningful relationship with AAGR, highlighting their importance in understanding Ethiopia's economic dynamics.
❖ Step 1: State the Null and Alternative Hypothesis
- Do not reject Null when p-value larger than or equal to = 0.05�
- Reject Null when p-value smaller than = 0.05�
❖ Step 2: Run the Regression Model with the full 9 variables
Figure 20 The Regression Model of Ethiopia with four variables
In the analysis, most variables exhibit p-values exceeding 0.05, with the exceptions being GDP per capita growth, average rainfall, and average temperature Particularly, CO2 emissions stand out with the highest p-value of 0.883 and the lowest absolute t-statistic of 0.900, indicating that CO2 emissions will be prioritized for elimination in the study.
❖ Step 3: Run the Regression Model with k-1 (eight) variables:
After removing CO2 emissions, GDP per capita growth, inflation, consumer prices, and average rainfall—four variables with p-values below 0.05—the analysis reveals that employment in agriculture has the highest p-value of 0.774 and the lowest absolute t-Stat of 0.294 Consequently, employment in agriculture will be excluded from the study.
Figure 21 The Regression Model of Ethiopia with full 9 variables
Figure 22 The Regression Model of Ethiopia with 8 variables
❖ Step 4: Run the Regression Model with k-2 (seven) variables:
After eliminating two variables, the analysis reveals that only two of the seven variables have a p-value exceeding 0.05 The variable with the highest p-value of 0.842 and the lowest absolute t-statistic of 1.204, Foreign Direct Investment, Net Inflows, will be the next to be removed from the model.
❖ Step 5: Run the Regression Model with k-3 (six) variables:
With the highest p-value (0.735) and lowest absolute t-Stat (0.345), agricultural raw materials exports will
Figure 23 The Regression Model of Ethiopia with 7 variables
Figure 24 The Regression Model of Ethiopia with 6 variables
❖ Step 6: Run the Regression Model with k-3 (five) variables:
With the highest p-value (0.384) and lowest absolute t-Stat (0.899), Foreign direct investment, net inflows exports will be eliminated next.
❖ Step 7: Run the Regression Model with k-3 (four) variables:
With the highest p-value (0.217) and lowest absolute t-Stat (1.288), average of temperature will be eliminated next.
❖ Step 8: Run the Regression Model with k-3 (three) variables:
Figure 25 The Regression Model of Ethiopia with 5 variables
Figure 26 The Regression Model of Ethiopia with four variables
In this step, the variable GDP per capita growth will be eliminated as it has a p-value (0.069) higher than Significance Level.
❖ Step 9: Run the Regression Model with k-3 (two) variables:
In this step, the variable average of rainfall will be eliminated as it has a p-value (0.073) higher than Significance Level.
❖ Step 10: Run the Regression Model with k-3 (two) variables:
Figure 27 The Regression Model of Ethiopia with three variables
Figure 28 The Regression Model of Ethiopia with two variables
As can be seen, there is only one significant variable left, with p-value smaller than 0.05 Therefore, the Backward elimination process ends
In summary, the urban population significantly influences the Average Annual Growth Rate (AAGR) in Nigeria, with statistical analysis at the 5% significance level indicating it as the sole impactful variable.
Appendix B: Hypothesis testing for significant trend
A regression model is deemed statistically significant when its significance F value is less than 0.05, as noted by Kenton (2021) This article will adhere to this criterion, specifically analyzing the datasets from Nigeria and Ethiopia to evaluate their significance.
(Linear trend exists between AAGR and Time - Year)
(Linear trend does not exist between AAGR and Time - Year)
As Significance F(0.001) < 0.05, is rejected and we can conclude at 95% certainty that the Linear trend between AAGR and Time - Year is significant
Figure 29 The Regression Model of Ethiopia with one variable
Figure 30 Regression output for Nigeria’s linear model
(Exponential trend exists between AAGR and Time - Year)
(Exponential trend does not exist between AAGR and Time - Year)
The significance level of F(0.004) indicates that the null hypothesis is rejected, while the P-values for the variables Time Period (0.860) and T^2 (0.287) are significantly greater than 0.05 Consequently, we can confidently conclude that the quadratic trend variables are insignificant, leading to the determination that the quadratic trend does not effectively predict the variance of the Average Annual Growth Rate (AAGR).
Figure 31 Regression output for Nigeria’s quadratic model
(Exponential trend exists between AAGR and Time - Year)
As Significance F(0.001) < 0.05, is rejected and we can conclude at 95% certainty that the Exponential trend between AAGR and Time - Year is significant
Figure 32 Regression output for Nigeria’s exponential model
(Linear trend exists between AAGR and Time - Year)
(Linear trend does not exist between AAGR rate and Time - Year)
As Significance F(0.001) < 0.05, is rejected and we can conclude at 95% certainty that the Linear trend between AAGR and Time - Year is significant
Figure 33 Regression output for Ethiopia’s linear model
(Exponential trend exists between AAGR and Time - Year)
(Exponential trend does not exist between AAGR and Time - Year)
The significance level of F(0.004) indicates a rejection of the null hypothesis, while the P-values for the variables Time Period (0.472) and T^2 (0.742) are significantly higher than 0.05 Consequently, we can assert with 95% confidence that the quadratic trend variables are insignificant, leading to the conclusion that the quadratic trend does not effectively predict the variance of the Average Annual Growth Rate (AAGR).
Figure 34 Regression output for Ethiopia’s quadratic model
(Exponential trend exists between AAGR and Time - Year)
(Exponential trend does not exist between AAGR and Time - Year)
As Significance F(0.001) < 0.05, is rejected and we can conclude at 95% certainty that the Exponential trend between AAGR and Time - Year is significant
Figure 35 Regression output for Ethiopia’s exponential model