Answer:
build linear model
When modeling scenarios with linear functions and solving problems involving quantities with a constant rate of change, we typically follow the same problem solving strategies that we would use for any type of function.
fitting linear models to data
A professor is attempting to identify trends among final exam scores. His class has a mixture of students, so he wonders if there is any relationship between age and final exam scores. One way for him to analyze the scores is by creating a diagram that relates the age of each student to the exam score received.
distinguish between linear and nonlinear relations
As we saw in the cricket-chirp example, some data exhibit strong linear trends, but other data, like the final exam scores plotted by age, are clearly nonlinear. Most calculators and computer software can also provide us with the correlation coefficient, which is a measure of how closely the line fits the data.
use a linear model to make predictions
Once we determine that a set of data is linear using the correlation coefficient, we can use the regression line to make predictions. As we learned previously, a regression line is a line that is closest to the data in the scatter plot, which means that only one such line is a best fit for the data.
key concepts
1. Scatter plots show the relationship between two sets of data.
2. Scatter plots may represent linear or non-linear models.
3. The line of best fit may be estimated or calculated using a calculator or statistical software.
4. Interpolation can be used to predict values inside the domain and range of the data, whereas extrapolation can be used to predict values outside the domain and range of the data.
glossary
correlation coefficient
1. a value, r, between –1 and 1 that indicates the degree of linear correlation of variables or how closely a regression line fits a data set.
extrapolation
1. predicting a value outside the domain and range of the data
Step-by-step explanation:
