This document discusses how to analyze a dataset by creating a graph. It involves plotting age (months) on the x-axis and height (inches) on the y-axis for various data points. A line of best fit is drawn and its equation is determined to be y = 0.65x + 64.7. This line equation allows predictions to be made, such as a height of 103.7 inches at 5 years (60 months). The document provides a step-by-step guide to graphing data, determining the line of best fit equation, and using that equation to make predictions.

1. CREATING AND
ANALYZING GRAPHS

2. Age
(months)
Height
(inches)
18 76.1
19 77
20 78.1
21
22 78.8
23 79.7
24 79.9
25 81.1
26 81.2
27 82.8
28
29 83.5
Plot the data on a
graph and make a
prediction for the
height at:
• 21 months
• 28 months
• 5 years

3. 1) Identify Dependent and Independent Variables
• Before plotting the graph we must choose which
variable is dependent and which is independent.
• Independent Variable: Influences the dependent
variable and is plotted on the horizontal axis.
• Dependent Variable: Depends on the independent
variable and is plotted on the vertical axis.
• In this case which variable is the dependent variable
and which variable is the independent variable?

4. • Make your graph as large as possible by spreading out
the data on each axis
• Let each space stand for a convenient amount
• In our example, what scale would you choose?
2) Choose your scale carefully

5. 3) Plot the axes and data
• Plot and label (include name of variable and unit) the
independent variable on the horizontal axis (x) and the
dependent variable on the vertical axis (y).
• Plot each data point. These data points are sometimes
referred to as a “scatterplot”
• What does our data look like?

6. 4) Title Your Graph
• Just like you learned for a table, a graph title should be as
descriptive as possible
• Title should clearly state the purpose of the graph and
include the independent and dependent variables
• Choose a descriptive title for the graph we are using as
an example

7. How the Age of a __________Affects Its Height

8. 5) Draw Line of Best Fit
• Definition - A Line of Best is a straight line on a
Scatterplot that comes closest to all of the dots
on the graph.
• A Line of Best Fit does not touch all of the
dots.
• A good technique is to try to get the same
number of points above the line as below.
• A Line of Best Fit is useful because it allows us
to:
• Understand the type and strength of the relationship
between two sets of data.
• Predict missing values.
• Draw the line of best fit for our data

10. Predicting Data with Scatterplots
• Interpretation - Making a prediction for an
unknown value within a range of known data
• Extrapolation - Making a prediction for an
unknown value outside of a range of known data.
We must extend the line of best to do this.
• More accurate: Interpretation
• Less accurate: Extrapolation
• Can you use the graph we made to interpolate
and extrapolate the required data?

12. • Recall that we want to make a prediction of the height
in 5 years.
• Extrapolating the graph to this point would require
drawing the graph with a much larger scale.
• Let’s try determining the equation of the line and using
this to make a prediction.
Predicting Data by Using the Equation of a Line:

13. The Equation of the Line
• The equation of a line comes in the form: y = mx + b
• m is the slope.
• b is the y-intercept, this is the y-value where the line
crosses the y-axis when x = 0.

14. • The slope of a line (m) gives the rate at which our
dependent variable changes with respect to the
independent variable.
• We can find the slope of the line by using any two
points on the line of best fit.
• These points do not have to be from the data.
The Slope of the Line

16. • To calculate the slope we can use the formula:
𝑠𝑙𝑜𝑝𝑒 =
Δ𝑦
Δ𝑥
=
𝑦2 − 𝑦1
𝑥2 − 𝑥1
• The points are: (x1, y1) = (19, 77)
(x2, y2) = (28, 82.9)
𝑠𝑙𝑜𝑝𝑒 =
82.9 − 77
28 − 19
=
5.9
9
= 0.65
The Slope of the Line

17. • What does this slope mean?
• Let’s look at the units …
• y is inches, x is months.
• Therefore this slope means that on average the _____
grows by 0.65 inches per month.
• m = 0.65 inches/month
The Slope of the Line

18. The Equation of the Line
• Since our graph does not start at x = 0 we will use the
equation of the line, and one point from the line to
solve for the y-intercept (b):
𝑦 = 𝑚𝑥 + 𝑏 𝑠𝑙𝑜𝑝𝑒 = 𝑚 = 0.65
𝑦 = 0.65𝑥 + 𝑏
• Now let’s find a point on the line.
𝑥, 𝑦 = (22, 79)
𝑦 = 0.65𝑥 + 𝑏
79 = 0.65 22 + 𝑏
79 = 14.3 + 𝑏
79 − 14.3 = 𝑏
64.7 = 𝑏
• Therefore 𝑦 = 0.65𝑥 + 64.7

20. • We can now use this equation to determine the height
in 5 years.
• 𝑦 = 0.65𝑥 + 64.7
• What is 𝑥?
The age in months.
• What is 𝑦?
The height in inches.
Therefore 5 years in months would be:
𝑥 = 12 5 = 60
The Equation of the Line

21. • Since 𝑥 = 12 5 = 60
• Plugging into our equation of the line:
𝑦 = 0.65𝑥 + 64.7
𝑦 = 0.65 60 + 64.7
𝑦 = 39 + 64.7
𝑦 = 103.7 𝑖𝑛𝑐ℎ𝑒𝑠
• Therefore the height in 5 years would be 103.7 inches.
The Equation of the Line

22. Practice Questions
1. Please read page 18 w/b
2. w/b page 19 & 20, 21, 23
3. Hand – in work sheet