Regression Analysis in Research

 

Definition:

Regression Analysis is a statistical technique used to examine the relationship between a dependent variable and one or more independent variables.

It helps predict outcomes, test hypotheses, and measure the strength and direction of relationships.

✅ Types of Regression:

TypeDescription
Simple Linear RegressionOne independent variable predicting one dependent variable
Multiple Linear RegressionMore than one independent variable
Logistic RegressionDependent variable is binary (yes/no)
Time Series RegressionUsed when data is observed over time

📊 Use of Regression in Finance Research

Common Applications:

  • Stock price prediction

  • Impact of interest rates on investment

  • Relationship between GDP and stock market returns

  • Determinants of firm value or profitability

🧮 Solved Example: Simple Linear Regression

🔢 Research Problem:

Does advertising expenditure impact sales revenue of a financial services firm?

Given Data:

Advertising Expense (₹ in lakhs) (X)Sales Revenue (₹ in lakhs) (Y)
230
450
670
890
10100

Step 1: Calculate Means

Xˉ=2+4+6+8+105=6,Yˉ=30+50+70+90+1005=68\bar{X} = \frac{2+4+6+8+10}{5} = 6, \quad \bar{Y} = \frac{30+50+70+90+100}{5} = 68

Step 2: Calculate Slope (b₁)

b1=∑(Xi−Xˉ)(Yi−Yˉ)∑(Xi−Xˉ)2b_1 = \frac{\sum{(X_i - \bar{X})(Y_i - \bar{Y})}}{\sum{(X_i - \bar{X})^2}}
XYX−6Y−68(X−6)(Y−68)(X−6)²
230-4-3815216
450-2-18364
6700200
890222444
1010043212816
b1=152+36+0+44+12816+4+0+4+16=36040=9b_1 = \frac{152 + 36 + 0 + 44 + 128}{16 + 4 + 0 + 4 + 16} = \frac{360}{40} = 9

Step 3: Calculate Intercept (b₀)

b0=Yˉ−b1Xˉ=68−(9×6)=68−54=14b_0 = \bar{Y} - b_1 \bar{X} = 68 - (9 \times 6) = 68 - 54 = 14

📈 Regression Equation:

Sales Revenue (Y)=14+9×Advertising Expense (X)\text{Sales Revenue (Y)} = 14 + 9 \times \text{Advertising Expense (X)}

✅ Interpretation:

  • The model predicts that for every ₹1 lakh increase in advertising, sales revenue increases by ₹9 lakhs.

  • Even with zero ad expense, the baseline revenue is ₹14 lakhs.

🧠 How It Helps in Research:

  • Helps test cause-effect hypotheses (e.g., "Advertising causes increase in sales").

  • Provides quantitative prediction models.

  • Supports decision-making in budgeting and investment planning.

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