CHAPTER 11-4 curve fitting with linear functions

Warm up • 1. Let g(x) be a vertical compression of f(x) = 3x - 2 by a

factor of 1/2 . Write the rule for g(x).

• 2. Let g(x) be a horizontal shift 3 units to the left of f(x)=7x-5 followed by a horizontal compression by a factor of 3. Let h(x) be the horizontal shift and g(x) be the horizontal compression. Write the rule for g(x).

Objectives

Students will be able to :• Fit scatter plot data using linear models with and without

technology.• Use linear models to make predictions

Curve Fitting with linear models• What is regression?• Answer: The statistical study of the relationship between variables is called regression.

• What is a scatterplot?• Answer: Is a graph with points plotted to show a possible relationship between two sets of data.

A scatter plot is helpful in understanding the form, direction, and strength of the relationship between two variables. Correlation is the strength and direction of the linear relationship between the two variables.

If there is a strong linear relationship between two variables, a line of best fit, or a line that best fits the data, can be used to make predictions.

• The correlation coefficient r is a measure of how well the data set is fit by a model.

Best Line Fit • What is a line of best fit?• Answer: A line of best fit  (or "trend" line) is a straight line

that best represents the data on a scatter plot.  This line may pass through some of the points, none of the points, or all of the points.

Steps to put into calculator

1. Identify and list all of the data points

2. Put data into calculator – use STAT key

3. STAT CALC and select LinReg (ax + b) to get the equation

Example 1• Find the equation of best line for the following for the

following points :

Example 2

The table shows the U.S. daily oil production y (in thousands of barrels x years) after 1994.

a) Use the graphing calculator to find and graph the equation of the best-fitting line.

b) Use the equation from part (a) to predict the daily oil production in 2009.

Student Practice • Find the following line of equation for this data on average temperature and rainfall for eight months in Boston, MA

Worksheet • Please work on worksheet

Homework• Please do problems 2 to 4 from page 26

Closure• Today we saw about how to find the line of best fit

tomorrow we are going to continue with chapter 1