Chapter 3 3-6 Nonlinear models

Objectives O Classify scatterplotsO Use scatterplots and a graphing

utility to find models for data and choose the model that best fits a set of data.

Non linear modelsO 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.

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.

ScatterplotsO 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 modelsO 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·bx where a > 0 and either 0 < b < 1 or b> 1. Exponential functions are used to model exponential growth, exponential decay, compound interest, and continuously compounded interest.

O  

Types of modelsO 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.

Example#1O 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 #2O 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#2Minutes, x yield, y 1 1.52 7.43 10.24 13.45 15.86 16.37 18.28 18.3

Discovery Activity O Lets do the discovery activity

HomeworkO DO problems 13-16,30 and 31 from

your book page 238 and 239