Chapter Nonlinear models

Objectives O Classify scatterplots O Use scatterplots and a graphing utility to find models for data and choose the model that best fits a set of data.

Non linear models O nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations.regression analysis

Scatterplots O What is a scatterplot ?. O scatterplot is a useful summary of a set of bivariate data (two variables), usually drawn before working out a linear correlation coefficient or fitting a regression line. It gives a good visual picture of the relationship between the two variables, and aids the interpretation of the correlation coefficient or regression model.

Scatterplots O A scatter plot can be used to give you and idea of which type of model will best fit a set of data.

Types of models O Linear Models : The simplest mathematical model or equation is the equation of straight line. Form: y=ax+b. O Exponential model: A function of the form y = a·b x where a > 0 and either 0 1. Exponential functions are used to model exponential growth, exponential decay, compound interest, and continuously compounded interest.functionmodel exponential growthexponential decay compound interestcontinuously compounded interest O

Types of models O Logarithmic model:Logarithmic models are useful in several physical applications including the following: magnitude of earthquakes, intensity of sound, and acidity of a solution. A logarithmic model generally has a period of rapid increase followed by a period of slow growth, but the model continues infinitely without bound.acidity of a solution

Example#1 O Decide whether each set of data could be best be modeled by a linear model, exponential model or logarithmic model O A) (2,1),(2.5,1.2),(3,1.3),(3.5,1.5),(4,1.8),(4.5,2 ),(5,2.4),(5.5,2.5),(6,3.1),(6.5,3.8),(7,4.5),(7. 5,5),(8,6.5),(8.5,7.8),(9,9),(9.5,10)

Example #2 O The table show, the yield( ml) of a chemical reaction after x minutes. Use a graphing utility to find a logarithmic model and a linear model for the data and identify the coefficient of determination for each model. O Determine which model fits the data better.

Example#2 Minutes, x yield, y

Discovery Activity O Lets do the discovery activity

Homework O DO problems 13-16,30 and 31 from your book page 238 and 239