Learning Objectives

By the end of this lesson, learners should be able to:

  • Explain correlation.
  • Interpret correlation coefficients.
  • Explain simple linear regression.
  • Conduct basic hypothesis testing.
  • Use statistical evidence in business decisions.

Correlation

Correlation measures the strength and direction of relationship between two variables.

  • +1 = perfect positive relationship,
  • 0 = no relationship,
  • -1 = perfect negative relationship.

Example: Advertising expenditure and sales often have a positive correlation.

Correlation Does Not Imply Causation

Two variables may move together without one causing the other.

Simple Linear Regression

Regression predicts one variable from another.

Equation:

Y = a + bX

Where:

  • Y = dependent variable,
  • X = independent variable,
  • a = intercept,
  • b = slope.

Example: Predict sales based on advertising spending.

Interpreting The Slope

If b = 2.5, each additional KES 1,000 spent on advertising is associated with KES 2,500 increase in sales on average.

Hypothesis Testing

Steps

  1. State null hypothesis (H₀).
  2. State alternative hypothesis (H₁).
  3. Choose significance level.
  4. Calculate test statistic.
  5. Make decision.
  6. Interpret business meaning.

Business Example

A company tests whether a new training program increases employee productivity. Statistical evidence determines whether observed improvement is likely genuine or due to chance.

Type I And Type II Errors

Error Type

Meaning

Type I

Reject true H₀

Type II

Fail to reject false H₀

Managers should understand the cost of each error.

Practical Business Uses

  • Marketing effectiveness,
  • Pricing analysis,
  • Productivity analysis,
  • Financial forecasting,
  • Quality improvement.

Learning Materials / Reference Materials

  • Anderson et al. Statistics for Business and Economics.
  • Montgomery & Runger. Applied Statistics and Probability for Engineers.
  • StatQuest Regression and Hypothesis Testing Videos.

Lesson Summary

Correlation identifies relationships, regression predicts outcomes, and hypothesis testing evaluates business assumptions using statistical evidence.

PreviousNext