Maximum and Minimum Slopes Wilfrid Laurier University

Transcription

1 Maximum and Minimum Slopes Wilfrid Laurier University Wilfrid Laurier University December 12, 2014

2

3 In this document, you ll learn:

4 In this document, you ll learn: how to determine the uncertainties in the slope and y-intercept when graphs have big error bars;

5 In this document, you ll learn: how to determine the uncertainties in the slope and y-intercept when graphs have big error bars; how this depends on whether the slope is positive or negative

6

7 When you have points on a linear graph, sometimes they will line up pretty well.

8 When you have points on a linear graph, sometimes they will line up pretty well. In this case, the uncertainties in the slope and y-intercept will be determined by the error bars on the graph.

9 Following is an example of a graph with a positive slope.

10 Here s a simple graph with error bars.

11 The line of best fit would look something like this.

12 Note that the line of best fit crosses all of the error bars.

13 This is the steepest line that crosses all of the error bars.

14 (Actually it touches each of the error bar rectangles, which is the important thing.)

15 It s called the line of maximum slope.

16 Since it has a positive slope, it will have a minimum y -intercept.

17 This is the least steep line that crosses all of the error bars.

18 It s called the line of minimum slope.

19 Since it has a positive slope, it will have a maximum y -intercept.

20 Here s another set of points, with a similar line of best fit.

21 A line drawn from the corners of the first and last points like before looks like this.

22 It s the line of maximum slope, as before.

23 Here s an attempt to draw the line of minimum slope as before.

24 It misses the two middle points, so it doesn t work.

25 This line is the line of minimum slope, since it crosses all of the error bars.

26 In general, which points give the lines of maximum and minimum slope will depend on the data.

27 Also, the same points won t be used for both lines.

28 In cases like this, there are no lines which cross all error bars.

29 Uncertainties have to be determined using standard errors.

30 For a graph with a negative slope, things change slightly.

31 Here s a graph with a negative slope.

32 Using the same corners as before to get the line of maximum (negative) slope doesn t work.

33 You need to use different corners for maximum and minimum negative slopes.

34

35 If you can draw lines which cross all of the error bars on a graph, then you use maximum and minimum slopes to determine the uncertainties in the slope and y-intercept;

36 If you can draw lines which cross all of the error bars on a graph, then you use maximum and minimum slopes to determine the uncertainties in the slope and y-intercept; If you can t draw lines which cross all of the error bars on a graph, then you use standard errors to determine the uncertainties in the slope and y-intercept.

37 If you can draw lines which cross all of the error bars on a graph, then you use maximum and minimum slopes to determine the uncertainties in the slope and y-intercept; If you can t draw lines which cross all of the error bars on a graph, then you use standard errors to determine the uncertainties in the slope and y-intercept. In general, which points give the lines of maximum and minimum slope will depend on the data.

38 If you can draw lines which cross all of the error bars on a graph, then you use maximum and minimum slopes to determine the uncertainties in the slope and y-intercept; If you can t draw lines which cross all of the error bars on a graph, then you use standard errors to determine the uncertainties in the slope and y-intercept. In general, which points give the lines of maximum and minimum slope will depend on the data. In general, the same points won t be used for both the maximum and minimum slope lines.

39 If you can draw lines which cross all of the error bars on a graph, then you use maximum and minimum slopes to determine the uncertainties in the slope and y-intercept; If you can t draw lines which cross all of the error bars on a graph, then you use standard errors to determine the uncertainties in the slope and y-intercept. In general, which points give the lines of maximum and minimum slope will depend on the data. In general, the same points won t be used for both the maximum and minimum slope lines. You need to use different corners for maximum and minimum slope lines, depending on whether the slope is positive or negative.