1. 1.5 Linear Models Warm-up Page 41 #53 How are linear models created to represent real-world situations?

2. 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. Year19931994199519961997 Expenses per share ($)1.241.451.661.882.09 How are linear models created to represent real-world situations?

3. Calculator Tips for Finite Differences Type “Output variable” into List 1 At top of List 2, select 2 nd Stat, Ops #7 Type 2 nd 1 for L1. Try these steps with the last example Year19931994199519961997 Expenses per share ($)1.241.451.661.882.09 How are linear models created to represent real-world situations?

4. Residual: A. Another word for error B. error = observed y – predicted y C. 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?

5. 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, 2 nd Stat #7 RESID enter The list of the residuals for each point will appear. How are linear models created to represent real-world situations?

6. Example: Find the linear model & sum of the squares of the residuals. Number of sides 345678 Radius0.2890.5000.6880.8661.0381.207 How are linear models created to represent real-world situations?

7. Calculator Tips for Graphing Residuals These steps will produce a graph of residuals Select 2 nd 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?

8. Example: Find the linear model & determine if the model is appropriate. Year190019201940196019851995 Farms (in millions) 5.7406.5186.3503.9392.2932.196 How are linear models created to represent real-world situations?

9. Practice: Page 53 #4-8 all Homework Pages 53-57 #12,18,20,22 How are linear models created to represent real-world situations?

10. Answer the LEQ: How are linear models created to represent real- world situations?