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Ordinary Least Square Method

Embark on a comprehensive journey through the world of the Ordinary Least Square Method. Crucial to Business Studies, this statistical technique is thoroughly examined in this resource. Beginning with its key principles and application, you will delve into regression analysis aspects, practical examples and case studies. Evaluating its benefits and drawbacks, you'll also gain clear insights on conducting linear regression using the Ordinary Least Square Method. A must-read guide for anyone seeking a detailed understanding of this vital statistical tool.

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Jetzt kostenlos anmeldenEmbark on a comprehensive journey through the world of the Ordinary Least Square Method. Crucial to Business Studies, this statistical technique is thoroughly examined in this resource. Beginning with its key principles and application, you will delve into regression analysis aspects, practical examples and case studies. Evaluating its benefits and drawbacks, you'll also gain clear insights on conducting linear regression using the Ordinary Least Square Method. A must-read guide for anyone seeking a detailed understanding of this vital statistical tool.

residual error

- \(y_i\) refers to the observed value of the dependent variable,
- \(x_i\) is the value of the independent variable,
- \(a\) and \(b\) are parameters to be estimated that represent the intercept and slope of the regression line respectively.

It interesting to note that the OLS method belongs to the broader field of linear regression analysis and is the simplest and most common estimator in which the two βs are chosen to minimize the square of the distance between the predicted and actual output variables.

Consider a supermarket aiming to estimate how the price of its leading product affects the sales. The store has recorded the number of product units sold and their specific prices. By applying the OLS method, the supermarket can predict sales volumes at different price levels.

- Plot data points for the independent variable (Price) and the dependent variable (Sales).
- Calculate the slope and intercept of the line of best fit using the formula provided earlier.
- Generate predicted values for each X value using your line of best fit, resulting in a sales forecast.

A **regression line** is a straight line that best represents the data on a scatter plot. This line may pass through some of the points, none of the points, or all of the points. It provides a visual demonstration of the correlation between two parameters.

- \(y_i\) is the dependent variable (the variable you are trying to predict or explain),
- \(x_i\) is the independent variable (the predictor or explanatory variable),
- \(a\) and \(b\) are constants representing the y-intercept and the slope of the regression line respectively, and
- \(e_i\) is the residual.

- Linearity: The relationship between the independent and dependent variables is linear.
- Independence: The residuals are independent, i.e., the residuals from one prediction have no effect on the residuals from another.
- Heteroscedasticity: The variance of the errors is constant across all levels of the independent variables.
- Normality: The errors of the prediction will be normally distributed.

Month | Advertising Expenditure (£) | Consultations |

1 | 100 | 40 |

2 | 120 | 45 |

3 | 150 | 50 |

4 | 180 | 60 |

5 | 200 | 75 |

Employing the above mathematical relationships, you may reach a model like \(y = 2x + 10\). This regression equation signifies that for each £1 increase in advertising, consultations rise by approximately two.

Month | Website Visits | Product Sales |

1 | 3500 | 200 |

2 | 5000 | 250 |

3 | 4000 | 220 |

4 | 4500 | 230 |

5 | 6000 | 300 |

If your calculated regression equation is \(y = 0.03x + 50\), it conveys that each additional website visit leads to an increase in sales by approximately 0.03 units.

**Ordinary Least Square Method:** It offers a way to estimate the parameters in a linear regression model by minimising the sum of the squares of the observed residuals in the given model.

- \(y_i\) represents the dependent variable,
- \(x_i\) represents the independent variable,
- \(a\) is the y-intercept,
- \(b\) is the slope of the line, and
- \(e_i\) symbolises the error term.

**Step 1 - Gather Data:**Engage in comprehensive data collection of the variables in question.**Step 2 - Plot Scatter Diagram:**Plot the collected data points on a graph, with the independent variable on the x-axis and the dependent variable on the y-axis.**Step 3 - Calculate Slope and Intercept:**Use OLS formulas to calculate the slope (\(b\)) and y-intercept (\(a\)) of the regression line.**Step 4 - Plot the Regression Line:**Draw the line of best fit on the graph using the computed slope and intercept.**Step 5 - Make Predictions:**Use the generated line to predict the dependent variable's value for different independent variable values.

- The Ordinary Least Square Method (OLS Method) is a statistical tool used to draw correlations between variables and enhance the accuracy of predictions in business studies. It supports crucial business decisions based on data-driven insights.
- OLS Method of regression involves minimization of the sum of the squares of the differences, or residuals, between observed and predicted values of data, helping establish relationships between different variables.
- The concept of 'best-fitting line' or regression line is central to OLS. A regression line is a straight line that best represents data on a scatter plot, showing the correlation between two parameters. In OLS regression, the regression line minimizes the sum of the squares of the vertical residuals.
- The OLS method has underlying assumptions, including linearity, independence, heteroscedasticity, and normality for optimum function. However, it relies heavily on these assumptions and might produce biased or inefficient estimates if they are not met.
- Despite the simplicity, efficiency, interpretability, flexibility, and scalability of OLS, it has potential drawbacks. These include sensitivity to outliers, heavy reliance on observed data, and limitation in dealing with complex, nonlinear relationships between variables.

In Business Studies, the Ordinary Least Square Method is commonly used in regression analysis to predict future sales, costs or profits by establishing relationships between variables. It enables better business decision-making by helping understand and quantify the impact of one business variable on another.

The Ordinary Least Square Method aids business forecasting decisions by providing a statistical technique used to estimate the relationships among variables. It helps predict future business outcomes and enables businesses to plan based on historical data trends.

The Ordinary Least Square Method can lead to misleading results if data is non-linear, has multicollinearity issues, or contains outliers. It also assumes a constant variance and correlation between variables, which may not always be accurate in real-world business scenarios.

Yes, the Ordinary Least Square Method can be used in risk management within businesses. It is often applied in regression analysis to predict and quantify different types of risks, such as financial, operational, or market-related risks.

The primary assumptions made when using the Ordinary Least Square Method in business analytics are linearity, independence, homoscedasticity (equal variance), normality of errors, and absence of multicollinearity.

Flashcards in Ordinary Least Square Method15

Start learningWhat is the main objective of the Ordinary Least Square (OLS) Method?

The main objective of the OLS Method is to find the best possible line of fit for a set of data points by minimising the sum of squares of the residuals, or the differences between actual and predicted values.

In the context of the Ordinary Least Square (OLS) Method formula, what do 'a' and 'b' represent?

In the OLS method formula, 'a' and 'b' are parameters to be estimated which represent the intercept and the slope of the regression line respectively.

How can the Ordinary Least Square Method be used in Business Studies?

In Business Studies, the Ordinary Least Square Method can be used to draw correlations between variables and assist in making accurate forecasts. An example could be understanding how changing a product price (independent variable) affects its sales (dependent variable).

What is the Ordinary Least Square Method (OLS) of regression?

The Ordinary Least Square Method (OLS) of regression is a statistical tool that minimises the sum of the squares of the differences, or residuals, between observed and predicted data values. It is used to establish relationships between different variables.

What are the key assumptions of the Ordinary Least Square Method?

The key assumptions of the Ordinary Least Square Method are: the linearity of the relationship between variables, independence of residuals, constant variance of errors (heteroscedasticity), and the normal distribution of prediction errors.

What is a regression line in the context of Ordinary Least Square Method regression analysis?

A regression line is a straight line that best represents the data on a scatter plot, providing a visual demonstration of the correlation between two parameters. It is determined by minimising the sum of the squares of the vertical residuals.

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