shalinitmth522

Shalini_Talluri_MTH 522 Project 3

Geospatial analysis is a powerful approach for unraveling insights from data that possesses a geographic component. It involves the examination and interpretation of information in relation to its spatial context. This technique utilizes various tools and technologies, including GPS data, satellite imaging, and Geographic Information Systems (GIS), to analyze and visualize data on maps. The integration of location-based data enables professionals across diverse fields such as epidemiology, logistics, environmental science, and urban planning to gain a comprehensive understanding of complex issues.

By leveraging geospatial analysis, practitioners can identify patterns, correlations, and trends that may remain hidden in traditional data analysis methods. The spatial perspective allows for a deeper exploration of relationships between data points, leading to informed decision-making. For instance, in epidemiology, tracking disease outbreaks geographically can provide critical insights into the spread and containment of diseases.

One of the key strengths of geospatial analysis lies in its ability to display data visually on maps. This visualization aids in recognizing spatial patterns, trends, and interconnections between geographical features that might not be evident in tabular data. As a result, experts can uncover valuable information and relationships that contribute to a more holistic understanding of the underlying dynamics.

A particular kind of machine learning system called a decision tree represents decisions and their possible outcomes using a structure resembling a tree. The algorithm recursively partitions the data according to particular attribute values, beginning with the root node that contains the whole dataset. Every decision node is a test point for an attribute, and every leaf node represents the outcome or final choice.

In a decision tree journey, start at the root node, dividing data based on attributes. Move through decision points (internal nodes) making choices guided by attribute values. Reach leaf nodes, representing final outcomes in classification or numerical values in regression. Decide paths at each point with the algorithm selecting features to create internally similar yet different groups. This recursive exploration continues until a stopping point is reached, like a specified depth, sample size, or when further splits add little value to group differences.

In today’s class the graph depicting median home prices serves as a roadmap, delineating market highs and lows and offering insights into economic dynamics. Ascending prices often signal a robust economy, reflecting confident buyers and high demand for homes. Conversely, price decreases or plateaus may indicate a cooling market, potentially influenced by evolving consumer sentiments or economic challenges. However, these trends are interconnected with various economic factors such as interest rates, employment rates, and the overall economic condition. A strong job market, for instance, can empower individuals to purchase homes, thereby driving up prices. Similarly, fluctuations in interest rates not only impact prices but also play a role in motivating or dissuading potential buyers.

Notably, seasonal variations in the housing market were observed, indicating potential price impacts during periods of heightened activity throughout the year. Understanding these nuances in housing prices provides valuable insights into both the real estate market and the broader economic landscape. This analysis is beneficial for buyers, sellers, investors, and policymakers, empowering them to make informed decisions in a dynamic and ever-changing market.

I have established parameters for a Seasonal AutoRegressive Integrated Moving Average (SARIMA) model to forecast the “hotel_avg_daily_rate” time series, taking into account the obvious seasonality in the data, using standard procedures and autocorrelation analysis (ACF and PACF plots). Finding ARIMA parameters (p, d, q) and seasonal parameters (P, D, Q, S) from PACF and ACF plots is the process of parameter selection.

The SARIMA model will be fitted to the training set using the chosen parameters, and model validation will entail predicting the test set and comparing results to the real values. Forecasts for the upcoming 12 months, including expected values, 95% confidence intervals, and the Root Mean Squared Error (RMSE) as a gauge of predictive accuracy, have been produced following the fitting of the SARIMA model. An indicator of how well the model predicts data is the RMSE, which is roughly 13.12. A lower value suggests a better fit.

I will use line charts and other visualizations to compare growth rates as I use time series analysis to look at trends in the overall earnings for each department over time. By quantifying the variation in earnings changes over time and finding outliers with noticeably high or low growth in relation to other departments, statistical approaches such as calculating the coefficient of variation can be applied. Regression analysis in particular will be used in statistical modeling to obtain insights into the primary drivers of overtime pay. This method makes it possible to investigate factors such as years of service, department, and job category in order to determine how they relate to overtime compensation. The correlation between each independent variable (job type, experience, etc.) and the dependent variable (overtime compensation) will be estimated using multiple linear regression.

Clustering techniques, particularly k-means, can be very useful in investigating the possible relationship between variables such as job type and years of experience and overtime compensation. Based on several data variables like average base salary, overtime to base pay ratio, and variations over time, these algorithms can identify departments that share similar compensation patterns. Policymakers can learn about common trends in compensation by grouping departments together. This will help them make data-driven decisions regarding the uniformity of pay scales and salaries throughout the local government.

In Today’s i have learnt about Time series. Time series refers to a chronological sequence of data points that consist of measurements or observations made at consistent and regularly spaced intervals. This form of data is extensively applied across diverse fields like environmental science, biology, finance, and economics. When dealing with time series, the fundamental objective is to comprehend the inherent patterns, trends, and behaviors that may be present in the data across time. Time series analysis encompasses activities such as modeling, interpreting, and forecasting future values by drawing insights from historical trends. Forecasting the project lifecycle entails anticipating future trends or results based on historical data. The lifecycle generally encompasses phases like gathering data, conducting exploratory data analysis (EDA), choosing a model, training the model, validating and testing, deploying, monitoring, and maintenance. This cyclical approach ensures accurate and up-to-date forecasts, necessitating regular revisions and adjustments.

Baseline models act as straightforward benchmarks or points of reference for more intricate models. They offer a basic level of prediction, aiding in the assessment of the effectiveness of more advanced models.

In Today’s class, we delved into the captivating realm of time series analysis. This advanced statistical field provides valuable insights into the evolution of data over time, equipping us with the skills to forecast future patterns based on historical data. We explored essential tools like moving averages and autoregressive models, which act as magical instruments allowing us to decipher the mysteries embedded in sequences of data points.

The significance of time series analysis extends beyond mathematical concepts to real-world applications, such as identifying trends in weather or the stock market. The ability to recognize patterns, seasonal variations, and anomalies in data emerges as a superpower in the realm of data science. This superpower empowers us to make informed decisions and plan for the future by leveraging the knowledge gained from historical data.

Shalini Talluri _MTH522-Project-2

Shalini Talluri_Mth522_Project-1

Today i have learnt about how the decision tree method works by asking a dataset a series of questions in order to predict a target variable based on features of the observations. It starts with a question, like “Can the animal fly?” then goes on to segment data and refine it further with other questions before arriving at prediction endpoints. The decision tree, which has been trained on labeled data, determines which questions are the most informative and which order is best for accurate predictions. It makes predictions using the learnt structure when faced with fresh, unlabeled input. Decision trees are transparent, which makes them easier to read and gives insight into the reasoning behind the decisions made. Because of their versatility, comprehensibility, and effectiveness in classification and regression problems, decision tree algorithms are widely used in machine learning.

An advanced data analysis technique called geographic or spatial clustering concentrates on finding patterns and groupings within geographical or spatial data sets. Finding locations on a map where data points show similarities is the main goal in order to provide a detailed understanding of spatial distribution. Geographic clustering has applications in many different domains in real life. It aids in the identification of areas with comparable demographic traits or infrastructure requirements in urban development. This method is used in epidemiology to identify geographic areas where a given disease is more prevalent, which helps with focused public health initiatives. Marketing campaigns can be targeted more precisely when regional concentrations of customer behavior are understood.

Geographic clustering has drawbacks despite its benefits. It is important to handle spatial autocorrelation and account for scale effects when making decisions on distance measures and methods. Meaningful application depends on how interpretable clusters are and how applicable the patterns found are in real-world scenarios.

A t-test’s reliability must be ensured by carefully taking into account a number of important parameters. First and foremost, it is important to presume that every group has a normal distribution. This can be evaluated using instruments such as histograms, Q-Q plots, or statistical tests like the Shapiro-Wilk test. Tests such as Levene’s test can also be used to confirm the consistency of variances between groups, particularly in independent two-sample t-tests. Another important point to make is that each group’s observations should remain independent of one another, meaning that the existence or importance of one observation should not affect the significance of another within the same group. In order to guarantee that each prospective subject has an equal chance of being selected and to enhance the generalizability of study findings, randomized data collection is essential. In addition, the t-test works well with continuous data where the predictor variable has two levels and the result variable is continuous. Finally, the existence of extreme values, or outliers, can distort the mean and standard deviation and adversely affect the reliability of the t-test results. This emphasizes the significance of detecting and controlling such values prior to doing the study. Through careful evaluation of these factors, researchers can maintain the validity of their t-test findings and derive significant insights from their statistical analyses.

Accurate analysis depends on how anomalies and null data are managed in data arrays. Observations that considerably deviate from the majority are referred to as anomalies. These can be visually spotted using dispersion diagrams or numerically using techniques such as standard scores. Exclusion is one management strategy that eliminates abnormal observations, but it carries a risk of losing valuable data. Limit setting places deviants on thresholds, quantization reclassifies continuous variables, and modulation uses transformations to reduce variability.

There are three types of null observations: MNAR (non-random nullity), MAR (random nullity), and MCAR (completely random nullity). Graphic utilities and pandas are examples of tools that can be used for identification. Complete record exclusion is one simple management strategy that runs the risk of significant data attrition. While statistical value replacement fills nullities with mean, median, or modality, which is ideal for MCAR, pairwise exclusion makes use of the data that is already available for analysis. Iterative substitution creates several estimates for every null space, predictive model substitution uses models to estimate and populate null spaces, and progressive/regressive fill uses adjacent data for chronological arrays.

In today’s class i have learnt about a statistical technique known as Analysis of Variance, or ANOVA, is essential for comparing means among three or more groups in order to ascertain if observed differences are truly significant or are merely random variation. It assesses the likelihood that the variation between these groups is the result of true differences versus random variation. Creating a null hypothesis, which assumes no substantial differences, and an alternative hypothesis, which suggests differences, are the steps in the process. Next, a low p-value (often less than 0.05) suggests that the observed differences are not random, according to the computation of the F-statistic, a ratio of variances. When an ANOVA indicates significance, post-hoc analyses such as the Bonferroni or Tukey’s HSD tests assist in identifying which particular groups’ means differ. Due to the higher potential of false positives, multiple comparisons should be used with caution.

In today’s class we studied about different clustering methods.

• K-Means is like a way of putting data into groups where each group is centered around a point, usually the average of the data in that group. It tries to make the total distance between data points and their group centers as small as possible.
• K-Medoids is quite similar to K-Means, but instead of using the average as the center of each group, it picks the data point that’s right in the middle of each group. This is handy when you want your clustering to be less affected by outliers, which are data points that are very different from the rest.
• Now, DBSCAN is a different approach. It focuses on areas where data points are packed closely together and separated by areas with fewer data points. It’s especially good when your data forms clusters with irregular shapes and when there might be some noise, which are those random data points that don’t belong to any clear group. DBSCAN uses two important things: how close data points need to be to be considered part of the same group (epsilon distance) and how many data points you need in a cluster for it to be called a “dense” region.

So, these methods help us put data into groups, but they do it in slightly different ways, and you might choose one over the other depending on your data and what you want to find.

In today’s class we discussed about K-Means clustering it is like a secret codebreaker for our data. It’s cool technique in machine learning that helps us uncover hidden patterns in our datasets. With K-Means, we can group similar data points together and really get to know them better. So, let’s dive into what K-Means is all about, what we can do with it, and how it actually works.

K-Means clustering is all about taking a bunch of data and dividing it into these neat little groups called clusters. We do this by repeatedly assigning data points to the cluster that’s closest to them, adjusting the cluster centers, and then doing it all over again until things settle down. In the end, we end up with a bunch of clusters, and each cluster is like a family of data points that are more like each other than they are like anyone in the other families. It’s a way to bring order to our data and find the hidden connections within it. The starting points for clusters and the selection of K (the number of clusters) play a critical role. Varying initial choices can lead to different results, and the algorithm might get stuck in certain solutions. Additionally, K-Means assumes that clusters are round and have consistent sizes.

In a nutshell, K-Means clustering is a valuable tool for uncovering patterns and gaining insights from data. When used thoughtfully and while acknowledging its limitations, it can provide a clearer understanding of complex datasets. This makes it a fundamental technique in the fields of data analysis and machine learning.

The Washington Post’s extensive dataset on fatal police shootings offers a valuable opportunity to dive deep into the demographics of the victims and their connection to these incidents.

In this we have learn’t about Hyperparameter tuning, sometimes called hyperparameter optimization, it is a crucial part of developing machine learning models. Hyperparameters are special settings that we choose before we start training a model. They’re like the dials and switches that control how the model learns and, ultimately, how well it works.

Examples of these hyperparameters include things like how quickly the model learns (learning rate), how many hidden layers a neural network has, how many decision trees are in a random forest, and how much regularization is applied in linear regression.

The main goal of hyperparameter tuning is to find the best combination of these settings that makes the machine learning model perform its absolute best on a particular task or dataset. This means we carefully try out different combinations of these settings to find the one that gives us the highest accuracy, the lowest errors, or the best results for the specific problem we’re working on. By doing this, hyperparameter tuning makes sure our model can make accurate predictions on new data it has never seen before, improving its overall performance and adaptability.

Today in class, we were introduced to GeoPy, a Python library that helps with geocoding. The professor demonstrated how GeoPy can be used to map data points. By using GeoHistogram, Geopositioning and other data sources Python developers can easily find the coordinates of addresses, cities, countries, and landmarks all across the world with Geopy.

A GeoHistogram is like a specialized tool for solving a common educational issue. Think of it as a graph that helps us understand how data is spread out. In this case, we’re looking at how data is distributed across different places on a map. For example, you could use a GeoHistogram to show how the population is distributed among various cities or regions. In this graph, the number of people would be shown on one side (up and down), while the locations like cities or regions would be shown along the other side (left and right). Each bar in the graph represents the population of a specific place, and the height of the bar tells you how many people live there. It’s a visual way to see where more or fewer people are in a geographic area.

Additionally, we studied clustering approaches. We discovered that there were just four clusters by integrating GeoPy with the DBSCAN technique (Density-Based Spatial Clustering of Applications with Noise). DBSCAN is a wonderful tool for discovering diverse shaped clusters and even isolated data points since it excels at clustering together data points that are close to one another.

In today’s class Data on police shootings throughout the previous year is under investigation. We start by gathering data and making sure it is accurate. Then, in order to comprehend the material more fully, we make use of numerical and visual aids. We investigate information such as who was injured, where the occurrences happened, and whether any patterns have emerged. In order to identify any alterations, we also examine how these data evolve over time. We would like to know if there are some demographics that are more impacted than others, as well as the outcomes for the law enforcement personnel engaged in these kinds of incidents. We also examine how these incidents are received by the community and whether it has an impact on any modifications to police protocols.

Once our research is complete, we disseminate our findings and make sure to conduct it impartially and accurately by consulting with specialists. We produce detailed reports and visual aids to help communicate the insights we have drawn from the data. The report offers a thorough and interesting overview of our work, and these visualizations aid in making our key conclusions more understandable. Throughout the entire process, it is essential that we handle the data with sensitivity, remain objective when interpreting the findings, and take ethical considerations into account when doing our research. Accurate insights into this delicate and complex problem may only be obtained through rigorous data analysis carried out with ethical responsibility.

In this class, we reviewed Project 2 dataset, which shows the police interactions with individuals wielding weapons or displaying violent intent. Each incident is described through various factors like date, time, location, threat type, and whether injuries or shootings occurred.

The dataset predominantly focuses on encounters within the United States, with notable concentrations in Texas and California. Gun violence emerged as the most prevalent threat, closely followed by knife-related threats. Interestingly, in most instances, the individuals involved were not shot or injured. It’s important to emphasize that this dataset represents a limited sample of all police encounters. Additionally, it lacks contextual details regarding each interaction, such as the individual’s mental state or whether they were under the influence of substances.

In summary, the data showcases the frequency of police engagements with individuals brandishing weapons or exhibiting threatening behavior. Yet, deriving definitive conclusions from this dataset remains challenging due to the absence of critical contextual information for each encounter.

In this class, my main focus was on advancing our project by delving into the data provided by the Diabetes Atlas and the CDC for the year 2018. These datasets offered valuable insights into the prevalence of diabetes across various U.S. counties, accompanied by intriguing metrics such as the Social Vulnerability Index (SVI). My primary task involved integrating these datasets using the county FIPS codes.

Regularization is indeed a vital technique in machine learning and statistical analysis used to mitigate overfitting, a common problem where a model performs exceedingly well on the training data but poorly on unseen or test data due to excessive complexity and fitting noise in the training data. The fundamental idea behind regularization is to introduce an additional term to the standard loss function, often called the regularization term, which penalizes the model for being too complex or having large parameter values. This penalty discourages the model from fitting noise or learning intricate patterns that might be specific to the training data but not generalizable to new, unseen data.

There are several types of regularization techniques, but two of the most common are L1 and L2 regularization:

L1 Regularization : L1 regularization adds the absolute values of the coefficients of the model’s parameters to the loss function. Mathematically, it adds the sum of the absolute values of the coefficients (often referred to as the L1 norm) multiplied by a hyperparameter, typically denoted as alpha, to the standard loss function.

The modified loss function with L1 regularization is: L_loss = Original_loss + alpha * sum(|coefficients|).

L2 Regularization : L2 regularization adds the squared values of the coefficients of the model’s parameters to the loss function. Mathematically, it adds the sum of the squared values of the coefficients (often referred to as the L2 norm) multiplied by a hyperparameter, alpha, to the standard loss function.

The modified loss function with L2 regularization is: L_loss = Original_loss + alpha * sum(coefficients^2).

Shalini Talluri MTH522-Project-1

In today’s class, we have discussed about cross-validation using a dataset that focuses on three key health variables: obesity, inactivity, and diabetes. We meticulously examined 354 individuals’ data, thoroughly measuring these health aspects.

Our main goal is to construct predictive models that provide deeper insights into how these health variables interrelate. To achieve this, we’re considering a diverse range of polynomial models, spanning from simple linear models to more intricate ones, extending up to a degree of 4. This variety enables us to explore and grasp the complexity of our dataset.

To effectively assess and select the most suitable model that aligns with our data, we’ve adopted a 5-fold cross-validation technique. In this process, we segment our dataset into five sections or “folds.” Subsequently, we train and test our polynomial models five times, each time utilizing a distinct fold as the test set, while utilizing the remaining four folds for training. This systematic approach aids us in gauging how effectively our models can adapt to new, unseen data.

Our primary objective is to pinpoint the polynomial model that accurately represents our data. We evaluate model performance using common statistical measures like mean squared error or R-squared, providing insights into how well our models match the actual data.

To delve deeper and visually comprehend patterns and distributions within the dataset, we’ve constructed a 3D scatter plot. In this visualization, every data point is illustrated as a black dot, and the three axes showcase the values for obesity, inactivity, and diabetes. This graphical representation helps us identify any noticeable trends or groupings in the data.

In essence, our analysis revolves around selecting the most fitting polynomial model to elucidate the relationships among obesity, inactivity, and diabetes. We utilize the robust approach of cross-validation to meticulously assess these models, while our 3D scatter plot aids in grasping the fundamental patterns and tendencies in these health-related variables.

In this class I have learnt about Cross-Validation and Bootstrap, k-Fold Cross-Validation.

Cross-Validation- Cross-validation is a method employed in both machine learning and statistical modeling to evaluate how effectively a predictive model will perform on data it hasn’t seen before, allowing for an assessment of its performance and applicability. Instead of a single train-test split, cross-validation involves repeating the training and validation process multiple times, each time using a different subset of the data as the testing/validation set and the remaining data for training.

Bootstrap- Bootstrap is akin to a clever data illusion, conjured by crafting “simulated” datasets from our original data through random selection with replacement. This technique proves particularly useful in situations where data is limited. By scrutinizing these simulated datasets, We can determine the level of confidence we can place in our model’s outcomes. It’s comparable to having our model revisit its assignments multiple times, ensuring a comprehensive understanding of the subject matter.

k-Fold Cross-Validation- It is a common technique used in machine learning for model evaluation. It involves partitioning the dataset into ‘k’ equally sized folds, where ‘k’ is a specified number. The model is trained ‘k’ times, each time using a different fold as the validation set and the remaining data as the training set. The results from the ‘k’ iterations are then averaged to obtain a single performance metric for the model. This method provides a robust assessment of the model’s performance and is especially useful for optimizing hyperparameters and understanding how the model generalizes to unseen data.

In this class I have learnt about t-test.

A t-test is like being a detective in statistics. Suppose we have two sets of data, and we are curious if they’re truly different or just a coincidence. The t-test comes to the rescue. We start with a guess called the “null hypothesis,” assuming there’s no actual difference between the groups. Then, we collect data and crunch the numbers to get a special value called the “t-statistic.” This value indicates how significant the differences between the groups are. If the t-statistic is large and the groups are notably different,  we get a small “p-value,” which is like a hint. A small p-value implies the groups are likely genuinely different, not by chance. If the p-value is less than a number we pick (usually 0.05), we can confidently say the groups differ, and we reject the null hypothesis. But if the p-value is large, it suggests the groups might not differ much, and we lack enough proof to reject the null hypothesis. Essentially, the t-test guides us in determining if what we observe in our data is a genuine difference or just a random outcome.

In this lecture  I have learned about T-Test – A Statistical Tool for Comparing Groups.

The statistical hypothesis test known as the t-test is used to evaluate whether there is a significant difference between the means of two groups. For comparing means and determining the significance of observed differences, it is a crucial statistical tool that is applied widely in many different domains.

There are two main types of t-tests:

1. Independent Samples T-Test: This type of t-test is used when we want to compare the means of two independent groups or populations. It’s often applied when comparing two different treatments, groups of people, or any situation where the samples are independent of each other.
2. Dependent Samples T-Test: This type of t-test is used when the samples are dependent or related in some way (e.g., before and after measurements on the same individuals). It’s often used in situations where we want to determine if there’s a significant difference between two measurements taken on the same individuals or objects.

The t-test assesses whether the observed difference between the means is likely to be due to chance (random variability) or if it’s likely to represent a true difference in the populations. The result of a t-test is usually reported as a p-value, which indicates the probability of observing the given difference (or a more extreme difference) if the null hypothesis is true. If the p-value is below a predetermined significance level (e.g., 0.05), you reject the null hypothesis in favor of the alternative hypothesis, suggesting that there is a significant difference between the groups. If the p-value is above the significance level, you fail to reject the null hypothesis, indicating that there is no significant difference.

Linear regression with two predictor variables:

Multiple linear regression is the term frequently used to describe linear regression with two predictor variables. In this case, a single result or dependent variable is what we are attempting to predict using at least two independent factors. Multiple linear regression takes the following general form:

y=β0​+β1​x1​+β2​x2​+ϵ

where:

• $y$ is the dependent variable (what you’re trying to predict),
• x1and x2​ are the two independent variables (predictors),
• β0​ is the intercept (the value of $y$ when both x1​ and x2​ are zero),
• β1​ and β2​ are the coefficients associated with x1​ and x2​, respectively, representing the change in $y$ for a one-unit change in x1​ or x2​,
• $ϵ$ is the error term.

Overfitting: Overfitting occurs when a model becomes overly complex and fits too closely to the noise or idiosyncrasies present in the training dataset. This noise is essentially the random variations or errors that naturally exist in real-world data. When a complex model tries to capture this noise along with the actual underlying relationship between variables, it “memorizes” the peculiarities of the training data, including the noise, instead of capturing the true patterns.

In today’s class I have learnt about Null Hypothesis and P- Value.

Null Hypothesis-The null hypothesis is that the new approach doesn’t actually affect students’ marks when two groups of students are being compared, one using the new method and the other the old one. Therefore, the null hypothesis serves as our baseline and is what we will test. You might reject the null hypothesis and declare that something unusual or noteworthy is occurring if our data and analysis support this. If not, we can accept the null hypothesis and state, “Looks like there’s no real difference or effect.”

P- Value- A p-value helps in determining whether a study’s findings are the result of pure random chance or if something significant is actually occurring. Consider trying a new drug: a small p-value indicates that the drug is likely to work, whereas a large one indicates that the drug may not be doing much. Scientists utilize p-values to determine whether or not they should believe their findings, but they must also consider how significant those findings are in the actual world in addition to what the p-value indicates.

From the CDC 2018 diabetes dataset I understood that we have data on %diabetes, %obesity, and %inactivity, but only 354 rows contain information for all three variables. Out of these 1370 data points related to %inactivity, all of them also include data for %diabetes.

The correlation between %diabetes and %inactivity is about 0.44, indicating a moderate positive relationship. %diabetes data is slightly skewed with a kurtosis of approximately 4, while %inactivity data is skewed in the opposite direction with a kurtosis of about 2. A linear regression model suggests that around 20% of the variation in %diabetes can be attributed to %inactivity. However, the residuals from the linear model do not follow a normal distribution and exhibit heteroscedasticity, meaning that their variability changes with %inactivity values.

This heteroscedasticity violates a key assumption of linear regression, raising concerns about the reliability of the model. For Further analysis or alternative modeling approaches may be needed for more dependable predictions.

The relationship between a dependent variable which is also known as the target or outcome variable and one or more independent variables known as predictors or features is modeled using the core statistical and machine learning approach of linear regression. A simple linear regression method is a prediction of quantitative response Y based on a single predictor variable, X. It presumes that the relationship between X and Y is roughly linear.

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