1.6 Modeling Real-World Data with Linear Functions Objectives: Draw and analyze scatterplots, write a prediction equation and draw best-fit lines, use a graphing calculator to compute correlation coefficients to determine goodness of fit, and solve problems using prediction equation models.

Scatterplot: Prediction Equation: Best-fit-line: See page 38 A visual representation of data Prediction Equation: An equation suggested by the points of a scatterplot used to predict other points. Best-fit-line: The graph of a prediction equation. See page 38

The table summarizes the total U. S The table summarizes the total U.S. personal income from the years 1986 to 1997. Predict personal income in the year 2001 Ex. 1) Personal Income Year Income ($ billion) 1986 3658.4 1987 3888.7 1988 4184.6 1989 4501.0 1990 4804.2 1991 4981.6 1992 5277.2 1993 5519.2 1994 5757.9 1995 6072.1 1996 6425.2 1997 6784.0

The degree to which data fits a regression line. Goodness to fit: The degree to which data fits a regression line. Correlation Coefficient: A value that describes the nature of a set of data. The more closely the data fit a line, the closer the correlation coefficient, r, approaches 1 or -1. See pg. 40 Regression Line: A best-fit line

Food Carbohydrates (g) calories The table contains the carbohydrate and calorie content of 8 foods, ranked according to carbohydrate content. Ex. 2) Food Carbohydrates (g) calories Cabbage 1.1 9 Peas 4.3 41 Orange 8.5 35 Apple 11.9 46 Potatoes 19.7 80 Rice 29.6 123 White bread 49.7 233 Whole wheat flour 65.8 318 a.) Find an equation with a calculator b.) Predict the number of calories in a food with 75.9 grams of carbohydrates.