1. Linear Functions and Models Section 1.4

2. Linear Functions and Models Revenue Output from workers Price by volume

3. Linear Functions and Models

4. Linear Functions and Models

5. Linear Functions and Models

6. Linear Functions and Models • Model estimation • Use functions to approximate the relationship between two variables • Determine what function to use • Linear • Exponential • Logarithmic • Logistic • Polynomial

7. Linear Functions and Models • Linear Function

8. Linear Functions and Models

9. Linear Functions and Models Y-intercept Value of output when input = 0

10. Linear Functions and Models Slope Increase in output for a 1 unit increase in input +5 +1 +5 +5 +1 +1

11. Linear Functions and Models • Linear Function Adds a constant amount (equal to the slope) to the output “Constant rate of change”

12. Linear Functions and Models

13. Linear Functions and Models

14. Linear Functions and Models • Estimating a linear model • Enter data STAT 1: Edit

15. Linear Functions and Models

16. Linear Functions and Models • Estimating a linear model • Find line of “best fit” • Ordinary Least Squares (OLS) STAT CALC 4: LinReg (ax+b)

17. Linear Functions and Models

18. Linear Functions and Models • After estimation • Inference • Prediction • Interpolation • Extrapolation

19. Linear Functions and Models • Interpolation • Predict the output variable for a value of the input variable within the observed range

20. Linear Functions and Models 50 Sales for 50 hours?

21. Linear Functions and Models 222.4 50

22. Linear Functions and Models • Extrapolation • Predict the output variable for a value of the input variable outside of the observed range

23. Linear Functions and Models 100 Sales for 100 hours?

24. Linear Functions and Models 347.4

25. Linear Functions and Models • In-Class