4Warm up1. 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).
5Objectives Students will be able to : Fit scatter plot data using linear models with and without technology.Use linear models to make predictions
6Curve 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.
7If 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.
8The correlation coefficient r is a measure of how well the data set is fit by a model.
9Steps to put into calculator Identify and list all of the data pointsPut data into calculator – use STAT keySTAT CALC and select LinReg (ax + b) to get the equation
10Example 1Find the equation of best line for the following for the following points :
11Example 2The table shows the U.S. daily oil production y (in thousands of barrels x years) after 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.
12Student PracticeFind the following line of equation for this data on average temperature and rainfall for eight months in Boston, MA