Curvilinear Regression – Problems & Solutions
Curvilinear Regression – Problems & Solutions Curvilinear regression is used when the relationship between variables is not linear (not a straight line) . Common forms: Quadratic (Parabolic): Y = a + b X + c X 2 Y = a + bX + cX^2 Y = a + b X + c X 2 Exponential: Y = a b X Y = a b^X Y = a b X Power function: Y = a X b Y = aX^b Y = a X b 🔵 Problem 1: Quadratic (Parabolic) Regression 🔹 Given Data X -2 -1 0 1 2 Y 7 2 1 2 7 Fit equation: Y = a + b X + c X 2 Y = a + bX + cX^2 Y = a + b X + c X 2 ✅ Step 1: Normal Equations For quadratic regression: ∑ Y = n a + b ∑ X + c ∑ X 2 \sum Y = na + b\sum X + c\sum X^2 ∑ Y = na + b ∑ X + c ∑ X 2 ∑ X Y = a ∑ X + b ∑ X 2 + c ∑ X 3 \sum XY = a\sum X + b\sum X^2 + c\sum X^3 ∑ X Y = a ∑ X + b ∑ X 2 + c ∑ X 3 ∑ X 2 Y = a ∑ X 2 + b ∑ X 3 + c ∑ X 4 \sum X^2Y = a\sum X^2 + b\sum X^3 + c\sum X^4 ∑ X 2 Y = a ∑ X 2 + b ∑ X 3 + c ∑ X 4 ✅ Step 2: Compute Required Sums Prepare table: X Y X² X³ X⁴ XY X²Y -2 7 4 -8...