Solution

Solution

Building a statistical model (for example linear regression) involves these steps:

Step 1: Define the Problem Understand what you want to predict and which factors matter. Example: grocery expenses may depend on family size, location, or income. For a fruit stall, customers (independent variable $X$) affect daily earnings (dependent variable $Y$).

Step 2: Collect Data Gather related data. For the stall, record customers and earnings for several days (Table 5.3). Data should later be cleaned and prepared so errors and missing values do not mislead the model.

Step 3: Choose an Algorithm Choose a method that fits the problem. Linear regression is used when one numeric variable is predicted from another. Logistic regression is used for yes/no outcomes.

Step 4: Train the Model The model learns from the collected data. For simple linear regression the line is $Y = \beta_{0} + \beta_{1} X + \epsilon$. In the stall example, every $5$ extra customers add $200$ Rs, so $\beta_{1} = 40$, and $\beta_{0} = 100$, giving $\text{Earnings} = 100 + 40 \times \text{Customers}$.

Step 5: Evaluate the Model Test on new or unseen data. If $28$ customers visit and actual earnings are $1{,}250$ Rs, the model predicts $1{,}220$ Rs; the error is $-30$ Rs. Error metrics measure how far predictions are from actual values; accuracy metrics measure how often classifications are correct.

Use more data, relevant extra factors, and regular updates to improve the model.