How can you use linear regression for both prediction and inference?

To put it in simple words, Linear regression estimates a line that best fits most of the points in the data set. Once estimated, this line can now be used to forecast new values of the dependent variable, given new set of independent variables. This line has the general form of y=mx+b, where m and b are interpreted to get some empirical relationship between the dependent variable and the independent variables. This has a significant weightage for most of the data analysis/business analysis problem, which gives us an idea of the association of various traits (not causation).

Linear regression (LR) fits a line through data points to minimize the distance, described by y = mx + b. For prediction, LR forecasts new 'y' values given new 'x' values. For inference, it interprets 'm' and 'b' to understand the relationship between 'x' and 'y'. Techniques: Ensure data is clean, check assumptions (linearity, independence, homoscedasticity, normality), and use libraries like scikit-learn and statsmodels. Example: In marketing, predicting sales from advertising spend aids budget allocation. For inference, understanding factors like social media vs. TV ads informs strategic decisions. Validate models with new data and adjust using R-squared and p-values.

Linear regression fits a straight line through the data points, minimizing the distance between the line and the actual data points. This line represents the equation y = mx + b, where y is the dependent variable you're trying to predict, x is the independent variable, m is the slope, and b is the intercept. The slope (m) tells you how much the dependent variable changes on average for a one-unit increase in the independent variable. The intercept (b) represents the predicted value of y when the independent variable (x) is zero.

Once, a regression line is estimated, it then can be used to predict future data points (in the sense, use unseen data to give new result). While this is quite useful, caution must be taken while estimating the regression equation, as it may sometimes result in overfitting the dataset with which it was trained(used to forecast the line). This gets a impeccable accuracy and fit on the training set, but it works poorly on the unseen (test) data set.

When using linear regression for prediction, the goal is to forecast future data points. For example, predict future sales based on advertising spend by fitting a regression line to historical data. After establishing the regression equation, input new advertising spend values ('x') to predict sales ('y').Techniques: Ensure the model is well-fitted and validated. Use training and test sets to check for overfitting or underfitting. Regularization techniques like Ridge or Lasso regression can help.Example: In retail, forecasting next quarter's sales based on this quarter's advertising spend aids budget planning.Update the model with new data to improve accuracy. Validate using metrics like RMSE and MAE.

The most important segment here is model deployment. This means integrating the model with specific tools and data for predictions and making the actual predictions. Model deployment is not an easy task and required years of experience in multiple fields such as Data Science, Domain knowledge and even software engineering to be done correctly.

If i may add here, the domain knowledge and reasoning are very important to be combined with the statistical segment of the inference. Remember, every inference has two segments, which is extracting the insights from the data and the reasoning segment too.

The slopes(co-efficient terms) help interpret the association of various explanatory variables with the explained variable. Here, it can't be stressed enough, to understand that the co-efficient terms talk about co-relation(association) and co-relation doesn't imply causation. In multiple instances, it is misinterpreted as causation, which is faulty. To establish causal relationships, it is imperative to deep dive further to analyse taking into account the data set relevance and business context.

Before using linear regression for prediction or inference, it's essential to ensure that several key assumptions are satisfied. These assumptions include linearity, independence, homoscedasticity (constant variance of errors), and normality of error terms. If these assumptions are violated, the results may be biased or inaccurate. Certain forms of visualization help verify the veracity of the claim of the assumptions being held in place

In my opinion, this is the most important step in the complete cycle. This step requires one to first understand the context of the analysis, what the ask is and how the variables weigh in to predict what has to be predicted. It is imperative, to remove redundant variables(think of them as proxy of some other variable, or the explained variable itself. Hence, removing them won't be of any harm to the analysis), fill in the missing data (wherever possible), detect and remove outliers, and transform variables(if required).

Linear regression assumes a linear relationship between variables. Visualizing the data through scatter plots is crucial to identify non-linear patterns that might require more complex models. Outliers, data points far from the majority, can skew the regression line. Techniques like winsorization or truncation can be used to address outliers, but tread carefully to avoid discarding valuable information. For example, if you are predicting house prices based on square footage. Here, data cleaning might involve removing outliers representing mansions or very small sheds, as these would distort the linear relationship between typical house sizes and prices.

Metrics like R-squared tell you how well the model explains the variance in the dependent variable. A high R-squared indicates good predictive power, but it doesn't guarantee perfect predictions. Hypothesis testing allows you to assess if the relationship between variables is statistically significant or simply due to chance. P-values less than a threshold (e.g., 0.05) indicate a statistically significant relationship. The slope and intercept of the regression line provide valuable insights. In the house price example, the slope would tell you the average price increase per square foot, while the intercept would represent the predicted price for a house with zero square footage (which wouldn't be meaningful but helps interpret the slope).