1. Chapter 5 Linear Models Linear Models are studied intensively because: Easiest to understand and analyze Relationships are often linear Variables with non-linear relationship can often be transformed into linear relationship through an appropriate transformation Even when a relationship is non-linear, a linear model may provide an accurate approximation for a limited range of values.

2. 5 Linear Models Least Square Line: Let X and Y be two quantitative variables. Let (x1, y1), (x2, y2), …, (xn, yn) be data points collected on n individuals Goal: Find a linear model in the form Y = a + b X that represents the given data set

3. 5 Linear Models

6. Formulas for computing b and a b = Sxy/Sxx a = average(y) – b average(x) Sxy = Sum(xy) –Sum(x)Sum(y)/n Sxx = Sum(x^2) –(Sum(x))^2/n

7. 5 Linear Models Remarks: 1. Use linear regression if the scatter plot looks reasonably straight 2. Check for outliers which could drastically influence regression lines 3. If data seem to cluster in scatter plot, look data more carefully 4. Large magnitude of slope indicates steeper line 5. Negative slope shows negative association 6. Positive slope shows positive association