What you will learn How to draw and analyze a scatter plot How to write a prediction equation and draw a line of best-fit How to use a graphing calculator to compute a correlation coefficient How to use a prediction equation

SAT Prep 1. A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 100 seniors, 150 juniors, and 200 sophomores who applied. Each senior's name is placed in the lottery 3 times; each junior's name, 2 times; and each sophomore's name, 1 time. What is the probability that a senior's name will be chosen? 2. ( √2 - √3 )² = Objective: 1-6 Modeling Real-World Data with Linear Fucntions

Domain Review Two conditions to watch for: What is the domain of Objective: 1-6 Modeling Real-World Data with Linear Fucntions

You Try Determine the domain of: Objective: 1-6 Modeling Real-World Data with Linear Fucntions

Prediction Equations When real-life data is plotted, it may not form a perfectly straight line. An example of a perfectly straight line relationship might be the gallons of gas you put in the car and the cost. Objective: 1-6 Modeling Real-World Data with Linear Fucntions

Prediction Equations (continued) If the data doesn’t form a perfectly straight line, the data may approximate a line. When this is the case, a best-fit line can be drawn. From that we can come up with a prediction equation. Data that has been plotted will form a scatter plot. Examples of linear relationships (or not). Objective: 1-6 Modeling Real-World Data with Linear Fucntions

Example 1 on page 39 Steps for determining a prediction equation. 1. Plot the data 2. Rough in a straight line that comes closest to as many “dots” as possible. 3. Get the slope using two of the points that lie closest to the line. 4. Use the point-slope equation to get the equation of the line. Objective: 1-6 Modeling Real-World Data with Linear Fucntions

Goodness of Fit or Correlation Data that are linear in nature will have varying degrees of “goodness of fit” to the line that approximates the linear equation. You can determine how closely the data are related by finding a correlation coefficient. The closer the data fit a line, the closer the correlation coefficient will be to 1 or negative 1. The “best fit” line is also called a regression line. Objective: 1-6 Modeling Real-World Data with Linear Fucntions

Example 2, Page 40 We can use a graphing calculator to find the correlation coefficient and to develop the “line of best fit” or regression line. Objective: 1-6 Modeling Real-World Data with Linear Fucntions

You Try Determine the correlation coefficient for the following data. If the data is “highly correlated”, determine the regression equation. Food Carbs Cals 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 65.8 318 Objective: 1-6 Modeling Real-World Data with Linear Fucntions

Homework Do a REALLY good job of the following problems (use graph paper and graph accurately) Page 42, problem 6, do steps a through d. Objective: 1-6 Modeling Real-World Data with Linear Fucntions