1. Dependent Variable (placed on vertical axis: y) A dependent variable is a variable dependent on the value of another variable Independent Variable (placed on horizontal axis: x) The independent variable causes an apparent change in, or affects the dependent variable

2. independent variable (x) dependent variable (y) Examples: 1)In a call centre, the number of customers serviced depends on the number of agents 2)At ski resort, the amount of sales, in $, depends on the amount of snow 3)The amount of bacteria on your hands depends on how often frequently you use hand sanitizer.

4. ExperimentIndependent VariableDependent Variable Is there a relationship between tv viewing and classroom grades? TV viewingClassroom Grades Does a person's height depend on their foot length? Foot Length (could go either way) Height What is the relationship between the world’s population and time? TimePopulation Is there a relationship between the likelihood of cancer and the amount of red meat consumed? Amount of Red Meat Consumed Likelihood of Cancer Is there a relationship between the number of words on a page versus the area of a book cover? Area of Book CoverNumber of Words on a Page Is there a relationship in babies between crying and being held? Time Being HeldAmount of Crying

5. A scatter plot shows a ____________ correlation when the pattern rises up to the right. This means that the two quantities increase together. A scatter plot shows a ____________ correlation when the pattern falls down to the right. This means that as one quantity increases the other decreases. A scatter plot shows _____ correlation when no pattern appears. Hint: If the points are roughly enclosed by a circle, then there is no correlation. positive negative no

6. Strong or Weak Correlation? Hint: To visualize this, enclose the plotted points in an oval. If the oval is thin, then the correlation is strong. If the oval is fat, then the correlation is weak. If the points nearly form a line, then the correlation is ___________________. If the points are dispersed more widely, but still form a rough line, then the correlation is _______________________. strong weak

8. a)Does age have a strong positive correlation with height? Explain. b)Do you think the variables are placed appropriately on the axes? c) Would weight vs. age show a strong positive correlation? d) Can you think of a variable that does have a strong positive correlation with age? e) Can you think of a variable that has a strong negative correlation with age?

9. …affectionately known as LOBF

10. All about the LOBF… What is it? shows a trend or pattern on a scatterplot used to make predictions How do I draw it? models the trend/pattern through as many points as possible equal points above and below the line models the trend/pattern

11. Line of Best Fit To be able to make predictions, we need to model the data with a line or a curve of best fit. Guide for drawing a line of best fit: 1. The line must follow the ______________. 2. The line should __________ through as many points as possible. 3. There should be ____________________________ of points above and below the line. 4. The line should pass through points all along the line, not just at the ends. trend pass equal

12. Which one of these is the best LOBF? And what is wrong with the others? #1 #3 #2 #4 Doesn’t model trend Line not in middle of points Wrong for all kinds of reasons!

13. Return to front side of hand out and make lines of best fit on each of the given 6 graphs.

14. You can use LOBF’s to make predictions for values that are not actually recorded or plotted. Interpolation prediction involving a point within the set of data Extrapolation prediction involving a point outside the set of data (line needs to be extended)

15. Fill in blanks on handout

16. Using our height and humerus data… How tall would a person be that had a humerus of 44 cm? Is this interpolation or extrapolation? Extend the line! 181 cm tall exptrapolation

17. Using our height and humerus data… How long would a person’s humerus be that was 163 cm tall? Is this interpolation or extrapolation? 28 cm long interpolation

18. Makin’ sure you get it! See bottom of handout