Does age have a strong positive correlation with height? Explain. 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?

Line of Best Fit …affectionately known as LOBF

All about the LOBF… What is it? How do I draw it? shows a trend or pattern on a scatterplot used to make predictions How do I draw it? models the trend/pattern models the trend/pattern through as many points as possible equal points above and below the line Line should pass through points all along the line not just at the ends.

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

Time to Practice Refer to the six graphs you were given on the “What am I” worksheet. Add a line to the graphs we identified as being linear. Add a curve to the graph we identified as being nonlinear. If no correlation exists, we would not draw a line or curve of best fit.

Strong positive linear Strong negative linear No correlation Strong nonlinear Weak negative linear Weak positive linear

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

Another humerus experiment… How tall would a person be that had a humerus of 44 cm? 181 cm tall Extend the line! Is this interpolation or extrapolation? exptrapolation

Another humerus experiment… How long would a person’s humerus be that was 163 cm tall? 28 cm long Is this interpolation or extrapolation? interpolation

Makin’ sure you get it! See bottom of handout

Estimate the number of absences for a student with 50%. Estimate the mark for a student with 25 absences.

Independent Practice: Shots 25 32 24 15 34 67 19 10 30 50 Points 40 54 36 60 108 20 45 85 A basketball team recorded the number of points each player scored vs. the number of shots they took. Identify the independent variable and the dependent variable. Explain. Draw a scatter plot by hand on graph paper and find the line of best fit. Describe the correlation and the relationship between the variables. If a person shot 40 times, how many points would they receive? Is this interpolating or extrapolating? If a person got 90 points, how many shots did they take? Is this interpolating or extrapolating? If a person shot 80 times, how many points would they receive? Is this interpolating or extrapolating?