1 6 Modeling RealWorld Data with Linear Functions

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: 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. 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 1992 5277. 2 1987 3888. 7 1993 5519. 2 1988 4184. 6 1994 5757. 9 1989 4501. 0 1995 6072. 1 1990 4804. 2 1996 6425. 2 1991 4981. 6 1997 6784. 0

Goodness to fit: Correlation Coefficient: The degree to which data fits a regression line. 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

Ex. 2) The table contains the carbohydrate and calorie content of 8 foods, ranked according to carbohydrate content. 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.