May 6 - Day 6 - Line of Best Fit

mpm1d1 ­ 6.6.notebook
May 06, 2015
Day 6: Line of Best Fit and Correlation
Relationships in the “real world” are rarely perfect. So, when we collect and graph data
comparing two variables, we often see that the data does not perfectly lie on a line or curve. We can determine if the relationship is linear or non­linear based on the scatter plot; if the points lie along or close to a line, it is linear, and if they lie along or close to a curve, it is non­linear.
If the relationship is __________, we can determine the equation for the line that represents the data, called the line of best fit. We can use this equation to determine values for data that have not been collected!
If the relationship is linear, a pattern or _________ in a scatter plot is described as either increasing or decreasing.
Ex 1 The following graph represents the height (in cm) and ages of 35 males. Notice that the relationship between age and height is not perfectly linear; this is an indication that changes in height are not 100% dependent on changes in one’s age. Notice that not all 8 year olds are the same height
A point that is ______ away from the rest of the points is called an outlier. Outliers can sometimes indicate that you made a mistake plotting or recording the data, or, they can indicate that there is something unique/exceptional about the individual the point represents.
a) Does there look like there is an outlier in the data above? If so, identify it.
b) Does the relationship appear to be linear or non­linear? Also, what is the trend in the points?
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mpm1d1 ­ 6.6.notebook
May 06, 2015
The Line of Best Fit
To be able to make predictions, we need to model the data with a line of best fit (or curve of best fit, when the points conform to a curve).
Rules for drawing a line of best fit:
1. The line must follow the __________ in the scatter plot.
2. There should be ____________________________ of points above and below the line.
3. The line should _________ through as many points as possible (all along the line, not just at the ends).
To determine the equation of the line of best fit
1. Use the grid to pick two easy points on the line; use them to calculate the ________ (m). 2. Determine the y­intercept, using the ___________ equation.
3. Unless otherwise stated, write the equation in ___________ form.
Note: Since we will all draw slightly different lines of best fit, there will be a range of acceptable answers.
c)
Draw a line of best fit for the data.
d)
Use the line of best fit to predict the height of a 2 year old male. To make this prediction, are you interpolating or extrapolating?
e)
Use the line of best fit to predict the height of an 11 year old male. To make this prediction, are you interpolating or extrapolating?
f)
Determine the equation of the line of best fit representing the relationship between a male’s height in cm, h, and his age in years, a.
g)
Use your equation to predict the height of a male who is 15.5 years old.
h)
Use your equation to predict the height of a male who is 40 years old.
i)
Based on your prediction in h), do you think the linear relationship continues beyond the data collected (for males older than 20)? Explain.
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mpm1d1 ­ 6.6.notebook
May 06, 2015
Ex 2 Julie gathered the following data about her age and height from the markings on the wall
in her house.
Age (years)
1
2
3
4
5
6
7
8
Height (cm)
70
85
95
100
105
120
130
135
a) Graph the data.
b) Describe the relationship between the variables. Also, describe the trend in the points.
c) Draw a line of best fit for the data.
d) Use the line of best fit to predict how tall Julie was when she was 5.5 years old.
e) Use the line of best fit to predict how old Julie was when she was 90 cm tall.
f) Determine the equation of the line of best fit representing the relationship between Julie’s height in cm, h, and her age in years, a.
g) Use your equation to predict how tall Julie will be when she is 12 years old.
h) Use your equation to predict how old Julie will be when she is 150 cm tall.
Correlation
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mpm1d1 ­ 6.6.notebook
May 06, 2015
Strength of the Correlation
If the points nearly form a line, then the correlation is ___________.
If the points are dispersed, but still form a rough line, then the correlation is _________.
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