1.5 Linear Models

Warm-upPage 41 #53

How are linear models created to represent real-world situations?

Finite Differences The difference between each value in the

range is the same.Linear models have first differences that

are the same. Example: Find the finite first differences and

determine if a linear model is appropriate.Year 1993 1994 1995 1996 1997

Expenses per share ($) 1.24 1.45 1.66 1.88 2.09

How are linear models created to represent real-world situations?

Calculator Tips for Finite Differences

Type “Output variable” into List 1 At top of List 2, select 2nd Stat, Ops #7 Type 2nd 1 for L1.

Try these steps with the last example

List

Year 1993 1994 1995 1996 1997Expenses per share ($) 1.24 1.45 1.66 1.88 2.09

How are linear models created to represent real-world situations?

Residual:

A. Another word for errorB. error = observed y – predicted yC. Used to determine if a model fits the data

Graphing the model can help decide which type of equation is best.

How are linear models created to represent real-world situations?

Calculator Tips for Linear Model

These steps will produce a linear model Type data into List 1 & List 2 Stat > Calc #4 LinReg L1, L2 enter Correlation coefficient “r” tells type of correlation

(closer to 1 is positive, closer to -1 is negative). To get the list of Residuals

Go to top of List 3, 2nd Stat #7 RESID enter The list of the residuals for each point will appear.

How are linear models created to represent real-world situations?

Example:Find the linear model & sum of the squares of the residuals.Number of

sides3 4 5 6 7 8

Radius 0.289 0.500 0.688 0.866 1.038 1.207

How are linear models created to represent real-world situations?

Calculator Tips for Graphing Residuals

These steps will produce a graph of residuals Select 2nd Y=, enter for plot 1 Hit enter for On to become dark, select the first type of

graph for scatterplot Leave Xlist L1 and make Ylist RESID Select zoom 9 for zoom stat

The more scattered the plot the better the model.

How are linear models created to represent real-world situations?

Example:Find the linear model & determine if the model is appropriate.

Year 1900 1920 1940 1960 1985 1995

Farms (in millions)

5.740 6.518 6.350 3.939 2.293 2.196

How are linear models created to represent real-world situations?

Practice: Page 53 #4-8 all

HomeworkPages 53-57 #12,18,20,22

How are linear models created to represent real-world situations?

Answer the LEQ:

How are linear models created to represent real-world situations?