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What you should know
By the end of this subtopic, you should be able to:
apply simple linear regression in a given context (AO2, AO4)
https://quizlet.com/pa/804917851/43-sales-forecasting-flash-cards/?i=4jrhob&x=1jqt
Correlation
The relationship between two sets of numbers or variables, such as sales revenue at different times of the year.
Cyclical variations
The recurring fluctuations in sales revenues due to the trade cycle (or business cycle).
Extrapolation
A forecasting technique that identifies the trend from using past data and then extending this trend line to predict future sales.
Random variations
Irregular, erratic, or unexpected fluctuations in sales revenues, caused by unexpected and unpredictable factors.
Range
The difference between the highest and the lowest values in a data set.
Sales forecasting
A quantitative technique used to predict a firm’s level of sales revenue over a given time period.
Seasonal variations
Foreseeable periodic fluctuations in sales revenues over a known period of time, such as certain months or times of the year.
Time series analysis
A statistical technique used to identify trends in historical data, such as the figures for a firm’s monthly sales revenues.
Simple Linear Regression Model
statistical techniques used to determine the apparent relationship between two variables, such as marketing expenditure and sales revenue or seasonal impacts on the demand for certain goods and services
Line of best fit
a linear line used to represent the best approximation of a scatter graph of different data points. It is used to study the nature of the relationship between two variables.
Negative correlation exists if
the values of one variable in a data set increases whilst the values of another variable in the data set decreases.
Positive correlation exists if
the values of both variables in a data set move in the same direction.
Scatter diagram
a visual statistical tool used to show the relationship or correlation between two variables, such as marketing expenditure and sales revenues.
4.3 bmt-15---simple-linear-regression-infographic.pdfLine of Best Fit
Line of Best Fit
Scatter Diagram with Line of Best Fit
- Also known as the regression line
- Represents the overall trend in the data
To draw a line of best fit:
Find the coordinates of the mean point,
Plot the mean point on the graph with all of the other data values.
Draw a single-ruled straight line through the mean point. It must extend across the full data set.
Extrapolation:
✅ Advantages of Simple Linear Regression
Predictive Analytics – Helps businesses forecast future trends and prepare for risks and opportunities.
Enhances Decision-Making – Provides data-driven insights that improve strategic business decisions.
Reveals New Business Opportunities – Identifies correlations that may uncover untapped market potential.
Reduces Errors and Risks – Tests business strategies and hypotheses to minimize decision-making risks.
Improves Business Management – Aids in budgeting, resource allocation, and performance tracking.
Easy to Use and Cost-Effective – Simple to apply and interpret, requiring minimal computational resources.
❌ Limitations of Simple Linear Regression
Correlation vs. Causation – A relationship between two variables does not necessarily mean one causes the other.
Time-Consuming and Costly – Requires a large and representative dataset for meaningful results.
Sensitive to Outliers – Extreme data points can distort the regression line and affect accuracy.
Over-Simplification – Assumes a single independent variable influences the outcome, which is often unrealistic.
Past Trends May Not Predict the Future – Unexpected events (e.g., economic crises, pandemics) can disrupt historical patterns.
Case Study 1 - The Price of Starbucks Coffee
The range of prices of a Tall Latte from Starbucks in different parts of the world is quite remarkable. The scatter diagram below shows there is a positive correlation between the price of a Starbucks Tall Latte and a country’s gross domestic product (GDP) per capita.
Countries that appear above the line of best fit get relatively bad value for money at Starbucks, while countries placed below the line can afford more lattes with their average income. Countries with a high GDP per capita (or GDP per person), such as Luxembourg and Switzerland, tend to have higher prices. However, the data is not perfect. Cambodia and India, for example, need to pay relatively high prices despite their low GDP per capita.
Read more about the reasons for these findings from The Visual Capitalist.
Case Study 2 - Less in more?
This chart shows that workers in Mexico tend to have the highest average working hours per week and the lowest weekly wage. By contrast, those in Luxembourg and Iceland tend to earn significant more yet work fewer hours per week. The chart suggests there is a strong negative correlation between the average working hours per week and the average weekly wage.
Whilst the chart might provide some valuable insights, it also suggest that people work less to earn more or work more to earn less. But is this really the full picture?
Cause versus Effect
Tyler Vigen, a former student at Harvard University, shared the following examples on his website as a reminder to us to look carefully at statistics.
Margarine consumption has a 99.26% correlation with divorce rates in Maine, US.
Total revenue generated by arcades has a 98.51% correlation with Computer Science doctorates awarded in the US.
Worldwide non-commercial space launches has a 78.92% correlation with Sociology doctorates awarded in the US.
The consumption of mozzarella cheese has a 95.82% correlation with Civil Engineering doctorates awarded in the US.
The per capita consumption of chicken has a 89.99% correlation with total US crude oil imports.
There is a 95.4% correlation between consumption of cheese in the US and the stock price of Alphabet (Google).
There is an even stronger correlation of 96.7% for Mater's degrees awarded in Education and Google searches for "Gangam Style"!
There is also a 97.6% correlation between butter consumption in the US and ticket prices at movies theatres (cinemas) in North America.
Source: TylerVigen.com
4.3 Simple Linear Regression - Cases IB Biz 2024.pdfPage updated
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