1. Line of Best fit, slope and y- intercepts MAP4C

2. Best fit lines 0 A line of best fit is a line drawn through data points that represents a linear relationship between 2 variables. 0 This is also called a trend line or regression line. 0 The line of best fit isn’t just drawn through the middle of the data: it needs to be closest to each point. 0 In a scatter plot, a point that lies off the best fit line is called an outlier. 0 Outliers may be from bad data, an error or is just unusual. (The outliers should be considered in a line of best fit!)

3. The effects of outliers 0 Which graph is the line of best fit? Justify your choice. ABCABC 0 Graph C is the best line of best fit. 0 The two outliers pull the line down slightly, not as much as in Graph B. 0 Graph A ignores outliers.

4. How do you know if the data is linear?? 0 A linear model may be unreliable if: a) There are too few data points. b) The model is based on data clustered together. c) There does not appear to be any correlation. d) There are outliers. e) The data do not appear to be linear.

5. Interpolation and Extrapolation 0 A line of best fit can be used to predict values. 0 Estimating values within a set of data is called interpolation. 0 Estimating values outside a set of data is called extrapolation. (Usually your best fit line needs to be extended)

6. Example and Review! 0 In a grade 12 math class: pre-exam marks and exam marks were collected for some students as shown: a) Graph the data and draw a line of best fit. b) Determine the equation of the line of best fit. c) Use the data to predict the exam mark of a student with a pre-exam mark of 98% and 10% d) Estimate what pre-exam mark would best match an exam mark of 65% Term mark (%)8476709592612555517362 Exam mark (%)8072689690582960537767

7. Example and Review!

8. P.S. 0 Instead of using y and x, other letters may be used to represent equations. 0 We could have used P and E for the last example to give: E = 0.9P + 7 0 We also could have calculated extrapolated or interpolated data by subbing in numbers into our equation: For part c) for P = 10%....... E = 0.9P + 7 = 0.9(10) + 7 = 9 + 7 = 16%

9. Text work 0 Page 453 #1-6, 8, 13, 15