What is the process called when transforming a variable into deviations around a fixed point, usually the mean?

What is the process called when transforming a variable into deviations around a fixed point, usually the mean?

• A. Centring
• B. Normalizing
• C. Standardization
• D. Scaling

Answer: (A)

Centring involves transforming a variable by subtracting a fixed value, usually the mean, so each observation becomes its deviation from that point. After centring, the new variable has a mean of zero, because the average deviation from the mean is zero. This is particularly handy in regression, especially with interaction terms, because it makes the interpretation of the main effects clearer and can reduce multicollinearity between predictors and interactions. For example, if a variable X has values 2, 5, and 9 with a mean of 5, centring yields -3, 0, and 4. The key idea is subtracting the fixed point to focus on how far each value lies from that reference, rather than on its absolute level.

Centring involves transforming a variable by subtracting a fixed value, usually the mean, so each observation becomes its deviation from that point. After centring, the new variable has a mean of zero, because the average deviation from the mean is zero. This is particularly handy in regression, especially with interaction terms, because it makes the interpretation of the main effects clearer and can reduce multicollinearity between predictors and interactions. For example, if a variable X has values 2, 5, and 9 with a mean of 5, centring yields -3, 0, and 4. The key idea is subtracting the fixed point to focus on how far each value lies from that reference, rather than on its absolute level.