# Least Squares Equation (Change in Estimated Value)

The specified Least Square regression line is Price=5.2+2.5*Value

If I was told that the estimated Value had changed from $1.4 to $1.7, How would this effect the Price?

Im guessing substituting 1.7 with value will give me the right answer?, or am I looking for calculating the input change here of Y=mΔx? ## 1 Answer \begin{align} P&=5.2+2.5V\\ \dfrac{\partial P}{\partial V}&=2.5\\ \dfrac{\Delta P}{\Delta V}&=2.5\\ \Delta P &=2.5\times \Delta V\\ \Delta P &=2.5\times 0.3\\ &=\\;0.75 \end{align}

• Thanks @Inquest, but what happened to the 5.2 in the second step? – I AM L Mar 3 '13 at 12:43
• The derivative of a constant is zero. – preferred_anon Mar 3 '13 at 12:47
• Why cant I use the Following calculation, how is what was calculated different to the below.. So an increase in the input from x to x+Δx induces a change in output of mΔx. For an estimated regression equation we estimate this change by mΔx. – I AM L Mar 3 '13 at 12:51
• I actually got the same result by calculating mΔx, I just want to figure out how though.... Thanks Guys! – I AM L Mar 3 '13 at 12:57
• @IAML, Partial derivatives is a way of generalizing what you did. Since the equation is linear, it doesn't matter which approach you take. – Inquest Mar 3 '13 at 13:57