# 2.2 Linear And Nonlinear Relationsmr. Mac's Page

## Topics

• Linear and non-linear relationships demonstrate the relationships between two quantities. The graph of a linear equation forms a straight line, whereas the graph for a non-linear relationship is curved. A non-linear relationship reflects that each unit change in the x variable will not always bring about the same change in the y variable.
• Linear or nonlinear. A second order ODE is said to be linear if it can be written in the form a(t) d2y dt2 +b(t) dy dt +c(t)y = f(t), (1.8) where the coeﬃcients a(t), b(t) & c(t) can, in general, be functions of t. An equation that is not linear is said to be nonlinear. Note that linear ODEs are characterised by two properties. Represent data using multiple representations, recognize and use linear and non linear (inverse variation) models, use residual analysis, use scatter plots, two way tables, correlation coefficients, and standard deviation

Note that the Melissa RGB profile I'm providing here has the real sRGB gamma curve. The sRGB gamma is close to a 2.2 gamma, but is linear at low values. So, if you take a readout of the darkest patch of the GretagMacBeth chart, there is is about a 1.5% difference between the reading using ProPhoto at a 2.2 gamma and a true Melissa RGB profile.

## Overview of Changes

Significant changes The CCSS standards for statistics are addressed in this unit.

## Description of Changes

The first three investigations of this unit have changed very little from the preceding edition. A few changes involve problem context and giving more attention to residual analysis as a technique for measuring the goodness-of-fit of a function model to given data. There is some additional coverage of slope, connecting with ideas from seventh grade units. The fourth and fifth investigations present new material that addresses the Common Core State Standards requirements regarding correlation and 2-way table analysis

### Investigation 4 (NEW) - Variability and Association in Numeric Data

The problems of this investigation review and enhance student understanding and skill in data analysis by focusing on two key statistical concepts—correlation and standard deviation. Students explore positive and negative correlations shown in scatter plots of bivariate data, use of the correlation coefficient as a measure of linearity for scatter plots, and the standard deviation as a measure of spread in single variable distributions. ### Investigation 5 (NEW) - Variability and Association in Categorical Data

The problems in this investigation review and enhance student understanding and skill in data analysis by focusing on use of 2-way tables to test the strength of association between categorical variables. Quicktimeapple inc..

### 2.2 Linear And Nonlinear Relationsmr. Mac's Page Key

New InvestigationChanges in CMP2 Investigation
Investigation 1 Exploring Data PatternsInvestigation 1 similar to Investigation 1 in CMP2
Investigation 2 Linear Models and EquationsInvestigation 1 similar to Investigation 1 in CMP2
Investigation 3 Inverse VariationInvestigation 1 similar to Investigation 1 in CMP2
Investigation 4 Variability and Associations in Numerical DataInvestigation 4 is new. See description above.
Investigation 5 Variability and Associations in Categorical DataInvestigation 5 is new. See description above.