Results.ipynb

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    "# <span style = \"color:red;\">INTERMEDIATE CERTIFICATE IN DATA SCIENCE - FINAL PROJECT</span>\n",
    "# <span style = \"color:#1A237E;\">Problem Statement</span>\n",
    "To explore the relationship between poverty indicators and credit access among Kenyan households.\n",
    "## <span style = \"color:green;\">Explanation</span>\n",
    "Poverty is a major issue in Kenya, with a large portion of the population living below the poverty line. \n",
    "The government has put in place policies and programs to alleviate poverty, but their effectiveness is \n",
    "not well known. The study aims to investigate the factors \n",
    "that affect credit access among Kenyan households and assess how credit access affects poverty levels \n",
    "in the country."
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    "# <span style = \"color:#1A237E;\">Summary of Hypotheses</span>\n",
    "## <span style = \"color:green;\">Hypothesis One</span>\n",
    "### <span style = \"color:brown;\">Null Hypothesis</span>\n",
    "Households in counties with lower headcount rates are less likely to access credit.\n",
    "### <span style = \"color:brown;\">Alternative Hypothesis</span>\n",
    "Households in counties with higher headcount rates are less likely to access credit.\n",
    "### <span style = \"color:brown;\">Relevance</span>\n",
    "In Kenya, poverty is more prevalent in some counties compared to others. \n",
    "Therefore, it is hypothesized that households in poorer counties will have less access to credit, \n",
    "which may worsen their poverty status.\n",
    "## <span style = \"color:green;\">Hypothesis Two</span>\n",
    "### <span style = \"color:brown;\">Null Hypothesis</span>\n",
    "Households in counties with higher poverty gaps are more likely to access credit.\n",
    "### <span style = \"color:brown;\">Alternative Hypothesis</span>\n",
    "Households in counties with higher poverty gaps are less likely to access credit.\n",
    "### <span style = \"color:brown;\">Relevance</span>\n",
    "Poverty gaps measure the depth of poverty, indicating how far the poor are from the poverty line. \n",
    "If households are far from the poverty line, they may face more difficulties accessing credit, \n",
    "thereby exacerbating their poverty situation.\n",
    "## <span style = \"color:green;\">Hypothesis Three</span>\n",
    "### <span style = \"color:brown;\">Null Hypothesis</span>\n",
    "1. There is no significant relationship between Headcount Rate (%) and Severity of Poverty (%).\n",
    "2. There is no significant relationship between Poverty Gap (%) and Severity of Poverty (%).\n",
    "3. There is no significant relationship between Distribution of the Poor (%) and Severity of Poverty (%).\n",
    "### <span style = \"color:brown;\">Alternative Hypothesis</span>\n",
    "1. There is a significant relationship between Headcount Rate (%) and Severity of Poverty (%).\n",
    "2. There is a significant relationship between Poverty Gap (%) and Severity of Poverty (%).\n",
    "3. There is a significant relationship between Distribution of the Poor (%) and Severity of Poverty (%).\n",
    "### <span style = \"color:brown;\">Relevance</span>\n",
    "By exploring the relationships between poverty indicators, such as headcount rate, poverty gap, and distribution of the poor, with the severity of poverty, we can gain insights into the key drivers of poverty in the country and inform policy and intervention strategies.\n",
    "## <span style = \"color:green;\">Hypothesis Four</span>\n",
    "### <span style = \"color:brown;\">Null Hypothesis</span>\n",
    "There is no significant difference between the proportion of households that accessed credit between \n",
    "those that sought credit and those that did not seek credit\n",
    "### <span style = \"color:brown;\">Alternative Hypothesis</span>\n",
    "There is a significant difference between the proportion of households that accessed credit between \n",
    "those that sought credit and those that did not seek credit\n",
    "### <span style = \"color:brown;\">Relevance</span>\n",
    "This hypothesis aims to investigate the factors that affect credit access among Kenyan households, \n",
    "with a focus on the impact of seeking credit. It is hypothesized that households that have sought \n",
    "credit before are more likely to access credit in the future.\n",
    "## <span style = \"color:green;\">Hypothesis Five</span>\n",
    "### <span style = \"color:brown;\">Null Hypothesis</span>\n",
    "The distribution of the poor is not correlated with credit access.\n",
    "### <span style = \"color:brown;\">Alternative Hypothesis</span>\n",
    "The distribution of the poor is correlated with credit access.\n",
    "### <span style = \"color:brown;\">Relevance</span>\n",
    "Poverty is distributed unevenly across different parts of Kenya. This hypothesis seeks to explore \n",
    "whether there is a relationship between the distribution of poverty and credit access in Kenya."
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    "# <span style = \"color:#1A237E;\">Summary of observations and inferences</span>\n",
    "### <span style = \"color:green;\">Hypothesis One</span>\n",
    "1. The `mean proportion of households that sought and accessed credit` for counties with `Headcount \n",
    "Rate >= 50%` is `72.17%`, while the `mean proportion of households that sought and accessed credit` \n",
    "for counties with `Headcount Rate < 50%` is `89.50%`.\n",
    "2. The correlation coefficient is `-0.4777`, which indicates _a moderate negative correlation between \n",
    "the `Headcount Rate (%)` and the `Proportion of households that sought credit (%)`_. \n",
    "3. The `p-value` is `0.0379`, which is _below_ the commonly used threshold of `0.05`. This suggests \n",
    "that _the observed correlation between the two variables is statistically significant_, and not \n",
    "likely to have occurred by chance.\n",
    "4. The `t-value` is `-2.368`, which indicates that _the means of the two groups are significantly \n",
    "different from each other_. \n",
    "5. The `p-value` is `0.038`, which is `below the commonly used threshold` of `0.05`. \n",
    "This suggests that _the difference in means between the two groups is statistically significant_, and not \n",
    "likely to have occurred by chance.\n",
    "### <span style = \"color:green;\">Hypothesis Two</span>\n",
    "1. The Pearson correlation coefficient between the `Poverty Gap (%)` and `Proportion of households that \n",
    "sought credit (%)` is `-0.4777`, which means that there is a moderate negative correlation between \n",
    "these two variables. This indicates that as the `Poverty Gap (%)` increases, the `Proportion of \n",
    "households that sought credit (%)` _decreases_, and vice versa.\n",
    "2. The `p-value` is `0.000684`, which is less than the commonly used threshold of `0.05`. This suggests \n",
    "that the observed correlation between the two variables _is statistically significant_, and not \n",
    "likely to have occurred by chance.\n",
    "### <span style = \"color:green;\">Hypothesis Three</span>\n",
    "1. **Severity_of_Poverty:** Has a _strong positive correlation_ with the `Headcount_Rate` and `Poverty_Gap`, and a _moderate positive correlation_ with the `Distribution_of_the_Poor` - important indicators.\n",
    "2. **Poverty_Gap:** Has a _strong positive correlation_ with the `Headcount_Rate` and `Severity_of_Poverty`, and a moderate positive correlation with the `Distribution_of_the_Poor`.\n",
    "3. **Distribution_of_the_Poor:** Has a moderate positive correlation with the `Severity_of_Poverty`, `Number of Poor (ths)`, and `Poverty_Gap` - may be a useful predictor.\n",
    "\n",
    "<br>The `R-squared` value of the model is `0.882`, which indicates that _`88.2%` of the variation in the dependent \n",
    "variable is explained by the independent variables in the model_. \n",
    "<br>The `adjusted R-squared` value of `0.874` also suggests that _the model is a good fit for the data_. \n",
    "<br>The `F-statistic` and its associated `p-value` indicate that _the model is statistically significant_.\n",
    "<br>`Poverty Gap (%)` has a `positive coefficient of 0.7962`, indicating that an _increase in poverty \n",
    "gap leads to an increase in severity of poverty_. \n",
    "<br>`Distribution of the Poor (%)` has a `negative coefficient of -0.1028`, indicating that _an \n",
    "increase in the proportion of the poor in more vulnerable sections of society leads to a decrease in the \n",
    "severity of poverty_ (interesting). \n",
    "<br>However, `Headcount Rate (%)` has a coefficient of only `0.0102`, which \n",
    "is `not statistically significant`, and therefore, we _cannot infer any significant relationship \n",
    "between headcount rate and severity of poverty_.\n",
    "<br>\n",
    "<br>\n",
    "The RMSE value of `1.7863860335702446` is **moderately high**, which suggests that _the model may not be \n",
    "suitable for accurately predicting the severity of poverty based on these independent variables \n",
    "alone_. \n",
    "<br>Therefore, it may be necessary to explore other variables that could be relevant to predicting \n",
    "poverty severity.\n",
    "### <span style = \"color:green;\">Hypothesis Four</span>\n",
    "1. The results of the **chi-square test** show that the `chi-square statistic` is `0.01275` and the `p-value` is `0.910`. \n",
    "2. The `p-value` is greater than the typical significance level of `0.05`, indicating that there is not enough \n",
    "evidence to reject the null hypothesis.\n",
    "3. A `t-statistic` of `infinity` and a `p-value` of `0` indicates a likelihood of very few observations \n",
    "in one of the groups, which can led to unstable estimates.\n",
    "<br>However, this can be interpreted as there being _there is a significant difference between the \n",
    "means of the two groups_ being compared.\n",
    "4. The probability of accessing credit given that an individual sought credit is `9/(9+0) = 1` \n",
    "which means that all individuals who sought credit also accessed credit. \n",
    "5. The probability of seeking credit given that an individual did not \n",
    "access credit is `0/(0+35) = 0`, which means that no individuals who did not access credit sought credit.\n",
    "### <span style = \"color:green;\">Hypothesis Five</span>\n",
    "1. A correlation coefficient of `0.005` indicates _a very weak positive correlation_ between the two \n",
    "variables, **while** the p-value of `0.972` suggests that _the correlation is not statistically significant_ \n",
    "at the standard significance level of `0.05`. \n",
    "2. This means that there is no evidence to suggest that the two variables are related to each other.\n",
    "Based on the contingency table and the conditional probabilities, there appears to be a relationship \n",
    "between seeking credit and accessing credit. \n",
    "3. However, the results of the chi-square test are not consistent with this conclusion, likely due to the \n",
    "small sample size."
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    "# <span style = \"color:#1A237E;\">Aggregate conclusions</span>\n",
    "1. Household credit access in Kenya is negatively correlated with the headcount rate in a county. \n",
    "Households in counties with higher headcount rates are less likely to access credit.\n",
    "2. Poverty gap is also negatively correlated with the proportion of households that sought credit in Kenya. \n",
    "Households in counties with higher poverty gaps are less likely to access credit.\n",
    "3. The relationship between credit access and poverty levels in Kenya is inconclusive based on the available data.\n",
    "4. There is no significant difference between the proportion of households that accessed credit between those that sought credit and those that did not seek credit.\n",
    "5. The distribution of the poor is not significantly correlated with credit access in Kenya.\n",
    "6. There is a positive relationship between poverty gap and severity of poverty.\n",
    "7. The variation in the severity of poverty can be explained by the independent variables in the model.\n",
    "8. An increase in the poverty gap leads to a higher severity of poverty.\n",
    "9. An increase in the proportion of the poor in more vulnerable sections of society is associated \n",
    "with a decrease in the severity of poverty.\n",
    "10. There is insufficient evidence to support a significant relationship between headcount rate and \n",
    "severity of poverty."
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    "# <span style = \"color:#1A237E;\">Recommendations</span>\n",
    "### <span style = \"color:brown;\">Increase credit access in areas with high poverty rates</span>\n",
    "Since households in counties with higher poverty rates are less likely to access credit, the government \n",
    "and NGOs should focus on increasing credit access in these areas. This can be done through initiatives \n",
    "such as microfinance programs, community-based credit schemes, and government-led credit programs.\n",
    "\n",
    "### <span style = \"color:brown;\">Address the issue of poverty gap</span>\n",
    "Households in counties with higher poverty gaps are less likely to access credit. Additionally, there \n",
    "is a  positive relationship between poverty gap and severity of poverty.\n",
    "<br>Therefore, the government and NGOs should focus on reducing the poverty gap in these areas. \n",
    "This can be done through measures such as income redistribution, social safety nets, and \n",
    "targeted poverty alleviation programs.\n",
    "\n",
    "### <span style = \"color:brown;\">Collect more data</span>\n",
    "The relationship between credit access and poverty levels in Kenya is inconclusive based on the \n",
    "available data. Therefore, the government and NGOs should collect more data on credit access and \n",
    "poverty levels to gain a better understanding of the relationship between the two.\n",
    "\n",
    "### <span style = \"color:brown;\">Target vulnerable populations</span>\n",
    "The negative relationship between the distribution of the poor and severity of poverty suggests \n",
    "that efforts should be made to target and support vulnerable populations. This can be done \n",
    "through social welfare programs, skill development initiatives, and providing opportunities \n",
    "for income generation in marginalized communities."
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