41. The regression coefficients are affected by the change of: A) Origin B) Scale C) Origin and Scale D) None of these

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The regression coefficients in a linear regression model are influenced by both the **origin** and the **scale** of the variables involved. Here's how:

1. **Change of Origin:**
   - **Intercept (β₀):** Shifting the origin (e.g., replacing $$ x $$ with $$ x - a $$) directly affects the intercept. The slope ($$ β₁ $$) remains unchanged because it represents the rate of change in $$ y $$ for a unit change in $$ x $$.
   
2. **Change of Scale:**
   - **Slope (β₁):** Scaling a variable (e.g., replacing $$ x $$ with $$ cx $$) affects the slope. If $$ x $$ is scaled by a factor of $$ c $$, the slope becomes $$ β₁/c $$.
   - **Intercept (β₀):** If the dependent variable $$ y $$ is also scaled, the intercept will be affected accordingly.

Since both altering the origin and changing the scale of variables modify the regression coefficients, the correct answer is:

**C) Origin and Scale**
The regression coefficients are affected by both the **origin** and the **scale** of the variables.

41. The regression coefficients are affected by the change of: A) Origin B) Scale C) Origin and Scale D) None of these

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