MBS 1st Semester Statistical Methods (MSC514) Notes

TU MBS First Semester (MSC 514)
Unit 5: Correlation and Regression Analysis

These notes are specially prepared for Tribhuvan University (TU) MBS First Semester students. The content is exam-oriented and covers important concepts, formulas, interpretations, assumptions, and frequently asked examination questions.

Table of Contents

• 1. Correlation Analysis
• 2. Partial Correlation
• 3. Multiple Correlation
• 4. Coefficient of Determination
• 5. Regression Analysis
• 6. Linear Regression
• 7. Non-linear Regression
• 8. Multiple Regression
• 9. Standard Error of Estimate
• 10. Test of Regression Model
• 11. Test of Regression Coefficients
• 12. Autocorrelation
• 13. Multicollinearity
• 14. Residual Analysis

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1. Correlation Analysis

Correlation measures the degree and direction of relationship between two or more variables. It indicates whether changes in one variable are associated with changes in another variable.

Examples

• Income and expenditure (Positive correlation)
• Price and demand (Negative correlation)
• Height and intelligence (No significant correlation)

-1 ≤ r ≤ +1

Types of Correlation

• Positive Correlation
• Negative Correlation
• Zero Correlation
• Perfect Positive Correlation
• Perfect Negative Correlation

Correlation Coefficient (r)	Interpretation
+1.00	Perfect Positive Correlation
+0.80	Strong Positive Correlation
+0.50	Moderate Positive Correlation
0	No Correlation
-0.50	Moderate Negative Correlation
-1.00	Perfect Negative Correlation

Exam Tip: The value of the correlation coefficient always lies between -1 and +1.

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2. Partial Correlation

Partial correlation measures the relationship between two variables after removing the effect of one or more additional variables.

Example

• X = Sales
• Y = Profit
• Z = Advertisement

Partial correlation measures the relationship between Sales and Profit while controlling the effect of Advertisement.

r_xy.z

Use of Partial Correlation

• Removes the influence of third variables.
• Shows the actual relationship between two variables.
• Widely used in business and social science research.

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3. Multiple Correlation

Multiple correlation measures the relationship between one dependent variable and two or more independent variables simultaneously.

Example

• Dependent Variable = Sales
• Independent Variables = Advertisement, Price

0 ≤ R ≤ 1

A higher value of R indicates a stronger combined relationship between the dependent variable and all independent variables.

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4. Coefficient of Determination (R²)

The coefficient of determination measures the proportion of variation in the dependent variable explained by the independent variable(s).

R² = r²

Interpretation

Suppose R² = 0.81

• 81% variation is explained by the regression model.
• 19% variation remains unexplained due to other factors.

Coefficient of Non-Determination

1 − R²

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5. Regression Analysis

Regression analysis is a statistical technique used to estimate the functional relationship between dependent and independent variables and to predict future values.

Main Objectives

• Measure relationship between variables.
• Predict future values.
• Estimate the effect of independent variables.
• Support business decision-making.

Dependent Variable (Y) → Variable to be predicted.

Independent Variable (X) → Predictor variable.

TU Examination Focus Students should clearly distinguish between:

• Correlation
• Regression
• Partial Correlation
• Multiple Correlation
• Coefficient of Determination

These are among the most frequently asked theoretical questions in TU examinations.