Section 4.1 Transforming Relationships AP Statistics

More on Two-Variable Data Outliers are present Clustered data points AP Statistics, Section 4.1 2

3 Looking at non-linear data Clustered points w/out outliers Linear? Transforming or reexpressing data  x (explanatory), y(response) or both

Transformations Change the scale of original data Linear Transformations(changing units)  Temperature (  C to  F)  Miles to Kilometers Common transformations in Statistics  Linear Cannot straighten a curved relationship between two variables  Positive powers  Negative powers (1/t= )  Logarithms 4

Monotonic Functions Monotonic Functions (moves in one direction as its argument t increases. )  Linear Cannot straighten a curved relationship between two variables  Positive powers  Negative powers (1/t= )  Logarithms Monotonic increasing function  If a>b, then f(a)>f(b) Increasing everywhere Monotonic decreasing function  If a>b, then f(a)<f(b) Decreasing everywhere 5

Monotonic Functions Monotonic Increasing  Linear with positive slope  Square  Log t Monotonic Decreasing  Linear with negative slope  Reciprocal square root  Reciprocal AP Statistics, Section 4.1 6

Transforming the Data Using Log Transform both variables AP Statistics, Section 4.1 7

Homework Exercise 4.1 and 4.2… AP Statistics, Section 4.1 8

Linear Transformations What to do when you have non-linear data.  Step 1: AP Statistics, Section 4.1 9