Understanding Regression Coefficients

Very Easy Multiple Regression Analysis Regression Coefficients

In a multiple regression analysis, the estimated regression equation is expressed as:

Y = β₀ + β₁X₁ + β₂X₂ + ... + β_nX_n + ε

Where:

Y is the dependent variable
β₀ is the intercept
β_i (for i = 1 to n) are the regression coefficients
X_i are the independent variables
ε is the error term

Consider a regression coefficient, β₁, which represents the effect of the independent variable X₁ on the dependent variable Y, holding all other variables constant. If, during analysis, the coefficient β₁ is found to be 2.5, what does this indicate?

For every unit increase in X1, Y increases by 2.5 units, holding all other variables constant.

For every unit increase in Y, X1 increases by 2.5 units, holding all other variables constant.

X1 has no effect on Y.

Hint

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