1

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

Objective: 1-6 Modeling Real-World Data with Linear Fucntions

2SAT 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

3

Domain Review

Two conditions to watch for: What is the domain of

362 xy36

12

x

y

Objective: 1-6 Modeling Real-World Data with Linear Fucntions

4

You Try Determine the domain of:

642 xy 183

12

xx

y

Objective: 1-6 Modeling Real-World Data with Linear Fucntions

5

Prediction EquationsWhen 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

6

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

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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

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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

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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

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You Try Determine the correlation coefficient for the following data. If

the data is “highly correlated”, determine the regression equation. Food Carbs CalsCabbage 1.1 9Peas 4.3 41Orange 8.5 35Apple 11.9 46Potatoes 19.7 80Rice 29.6 123White bread 49.7 233Whole wheat 65.8 318

Objective: 1-6 Modeling Real-World Data with Linear Fucntions

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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.