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16th Oct 2023

This report leverages Cohen’s d, a powerful statistical tool for measuring effect sizes, to enhance the analysis of the police shootings dataset. Cohen’s d proves invaluable in quantifying the practical significance of various factors in the context of lethal force incidents involving law enforcement officers. It goes beyond statistical significance to offer a tangible understanding of these factors’ real-world implications, allowing for a nuanced examination of demographics, armed status, mental health, threat levels, body camera usage, and geographic factors in relation to the likelihood of these incidents.

By employing Cohen’s d, we can quantitatively assess the magnitude of differences between groups or conditions in the dataset, moving beyond simplistic binary comparisons to comprehend the intricate dynamics at play. This approach sheds light on the influence of demographics, such as age, gender, and race, on the occurrence of lethal force incidents, revealing potential disparities and their practical relevance. Ultimately, it provides a holistic perspective and aids in identifying meaningful patterns and significant variables that impact these incidents, offering a more comprehensive understanding of the complex factors shaping the occurrence of lethal force incidents involving law enforcement officers.

By October 16, 2023.  No Comments on 16th Oct 2023  Uncategorized   

13th Oct 2023

The dataset in question offers a comprehensive overview of incidents involving lethal force by law enforcement officers in the United States during various dates in 2015, serving as a valuable resource for understanding the complexities surrounding these events. Each dataset entry contains vital information, including the incident date, manner of death (such as shootings or taser use), and details about the individuals involved, including their armed status, age, gender, race, and indications of mental illness. It also notes whether the officers had body cameras, crucial for assessing transparency and accountability.

Geospatial analysis reveals the geographic distribution of these incidents, showing their occurrence in various U.S. cities and states. This geographical data forms a foundation for investigating regional disparities, clustering patterns, and trends in lethal force incidents. The dataset’s demographic diversity is notable, encompassing individuals of various ages, genders, and racial or ethnic backgrounds. Analyzing this diversity can unveil potential discrepancies in how these incidents affect different demographic groups, while also providing an opportunity to investigate the role of mental health conditions and perceived threat levels. The temporal aspect is equally significant, enabling the examination of trends and changes in the frequency and nature of these incidents over time.

In summary, this dataset is a valuable resource for researchers, policymakers, and the general public interested in gaining insights into law enforcement activities in the United States. It allows for the exploration of demographic, geographic, and temporal patterns and forms the basis for conducting statistical analyses to draw meaningful conclusions about the use of lethal force by law enforcement officers.

By October 13, 2023.  No Comments on 13th Oct 2023  Uncategorized   

11th Oct 2023

Clustering is a fundamental technique used in data analysis and machine learning to group similar data points together based on their shared characteristics or features. Its primary goal is to uncover underlying patterns and structures within a dataset, making complex data more understandable and interpretable.

There are various key types of clustering methods available. Hierarchical clustering forms a tree-like structure of clusters by either merging individual data points into clusters (agglomerative) or dividing one large cluster into smaller ones (divisive). K-Means clustering partitions data points into ‘k’ clusters based on their proximity to cluster centroids, making it suitable for large datasets. DBSCAN identifies clusters as dense regions separated by sparser areas and is robust to outliers. Mean-Shift clustering assigns each data point to the mode of its local probability density function and is useful for non-uniformly distributed data. Spectral clustering transforms data into a low-dimensional space using eigenvalues and then applies a clustering algorithm. Fuzzy clustering allows data points to belong to multiple clusters with varying degrees of membership, which is helpful when data points exhibit mixed characteristics. Agglomerative clustering, similar to hierarchical clustering, starts with individual data points as clusters and merges them iteratively based on their similarity. The choice of clustering algorithm depends on the specific dataset characteristics and analysis objectives.

By October 11, 2023.  No Comments on 11th Oct 2023  Uncategorized   

6th Oct 2023

In our project, we aimed to predict diabetes by analyzing data on inactivity, obesity levels, and corresponding diabetes rates in different counties. We initially attempted simple linear regression models but found them insufficient, noticing heteroskedasticity in the data. Upon closer inspection, we determined that a quadratic model, enhanced by an interaction term, was more accurate for predicting diabetes.

We identified counties with complete data for all three parameters and tested various models, including the quadratic one, using cross-validation to assess their test errors. With more data, a broader trend might emerge, allowing for a simpler and more accurate model. This summarizes our project’s findings, suggesting the potential for further exploration with additional data.

By October 9, 2023.  No Comments on 6th Oct 2023  Uncategorized   

4th Oct 2023

Skewness is a statistical measure used to assess the shape of a data distribution, indicating whether it is skewed to the left (negatively skewed), to the right (positively skewed), or if it exhibits a roughly symmetrical pattern. In a positively skewed distribution, the right-side tail of the data is longer or heavier than the left side, with most data points concentrated on the left. Conversely, a negatively skewed distribution has a longer or heavier left-side tail and most data points on the right. A distribution is considered perfectly symmetrical when its skewness value is zero.

Kurtosis is a statistical measure used to assess how the tails of a data distribution compare to those of a normal distribution. It helps determine if the data has either heavier tails (leptokurtic) or lighter tails (platykurtic) than a standard normal distribution. When kurtosis is positive (leptokurtic), it suggests that the distribution has fatter tails and a more peaked central region compared to a normal distribution. Conversely, a negative kurtosis (platykurtic) suggests that the distribution has thinner tails and a flatter central region compared to a normal distribution. In a standard normal distribution, the kurtosis value is 3 (referred to as excess kurtosis), so any deviation from this value, whether greater or smaller, indicates how far the data distribution deviates from the normal pattern.

By October 9, 2023.  No Comments on 4th Oct 2023  Uncategorized   

MTH Project 1

MTH_Pjt1

MTH Project 1

By October 9, 2023.  No Comments on MTH Project 1  Uncategorized   

22nd Sept 2023

P-value:

  • A measure that aids in assessing the significance of a specific finding in a statistical investigation is the p-value (probability value).
  • It quantifies the evidence that refutes a null hypothesis. The null hypothesis frequently presupposes that the data are devoid of any influence or connection.
  • A low p-value (usually less than 0.05) denotes statistical significance and shows substantial evidence opposing the null hypothesis.
  • However, a high p-value indicates that there is little evidence to support the null hypothesis and that the result is not statistically significant.

R-squared:

  • In regression analysis, the R-squared statistic is used to assess how well a model fits the data.
  • It shows how much of the variance in the dependent variable, which is the variable being predicted, can be attributed to the model’s independent variables, or predictor variables.
  • Higher numbers suggest a better fit, and R-squared values range from 0 to 1. An R-squared of 1 indicates that the model perfectly explains the data’s variance, whereas a value of 0 indicates that the model cannot account for any data’s variation.
  • R-squared is used to measure how well a model fits observed data, although it is not always a reliable indicator of how well a model predicts the future.

By October 7, 2023.  No Comments on 22nd Sept 2023  Uncategorized   

2nd Oct 2023

Regularization is a technique that is used to prevent overfitting in predictive models. Overfitting occurs when a model learns to fit the training data too closely, capturing noise and making it perform poorly on new, unseen data. Regularization introduces a penalty term to the model’s loss function, discouraging it from learning overly complex patterns. Two common forms of regularization are L1 regularization (Lasso) and L2 regularization (Ridge), which add constraints to the model’s coefficients to reduce their magnitude. By doing so, regularization helps strike a balance between fitting the training data well and maintaining the model’s ability to generalize to new data, ultimately improving its performance on unseen examples.

By October 3, 2023.  No Comments on 2nd Oct 2023  Uncategorized   

29th Sept 2023

Mean Square Error (MSE) is a widely used mathematical metric in statistics and machine learning to measure the average squared difference between the values predicted by a model and the actual observed values in a dataset. To compute MSE, you take the difference between each predicted value and its corresponding actual value, square those differences to eliminate negative values, sum up all the squared differences, and then divide by the number of data points. A smaller MSE indicates that the model’s predictions are closer to the actual values, while a larger MSE suggests greater prediction errors. MSE is particularly useful for assessing the quality of regression models and quantifying their overall accuracy.

By October 3, 2023.  No Comments on 29th Sept 2023  Uncategorized   

27th Sept 2023

Cross-validation is a crucial technique in machine learning used to assess the performance and generalization of a predictive model. It involves splitting the dataset into multiple subsets, typically a training set and a validation set, several times. The model is trained on different combinations of these subsets, allowing it to learn and evaluate its performance on various portions of the data. This process helps detect overfitting (when the model performs well on the training data but poorly on new data) and provides a more robust estimate of a model’s accuracy. Common types of cross-validation include k-fold cross-validation, where the data is divided into k subsets, and leave-one-out cross-validation, where each data point serves as the validation set once. Cross-validation is essential for selecting the best model and hyperparameters while ensuring the model’s ability to generalize to unseen data.

By September 28, 2023.  No Comments on 27th Sept 2023  Uncategorized