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School
Daytona State College *
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Course
MAT0018C
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
11
Uploaded by ElaineR78 on coursehero.com
Line of Fit
Vocabulary
line of fit:
a line drawn on a scatter plot to estimate the relationship between two sets of data; also known as a trend line
linear equation:
a polynomial equation that contains a term of degree 1, but no term of higher degree
scatter plot:
a graph in the coordinate plane representing a set of bivariate numerical data that is used to observe the relationship between two variables
slope:
the ratio of the change in the vertical direction (y direction) to change in the horizontal direction (
x
direction), often expressed as
y-intercept:
the value of
y
at the point where a line or graph intersects the y-axis; the value of
x
is 0
at this point
What is a
Line of Fit?
page 2
One way to predict other points on a scatter plot is by drawing a line of fit
. This line describes the overall pattern
of the movement in the data set and summarizes the relationship
between the two variables.
Learn to Determin
e the Line of Fit
In the course, three possible lines of fit are drawn for the same scatter plot. Which graph has a line of fit that most appropriately fits the data? Is it graph A, B, or C? Sketch the graphs and explain your choice. Graph A
Graph B
Graph C
A line of fit should show the general direction of a group of points on a scatter plot. It should also have roughly half
of the points above and half of the points below the line. It is not necessarily going to pass through every point,
but it may pass through one or more points.
Learn to Use the “Scatter Plot” interactive in the course to practice sketching a line of fit.
Sketch a Line of Fit
Sketch your drawing here. Please use a separate sheet of paper to complete your practice problems.
The Equation of the Line of Fit
page ____
When a scatter plot shows a linear
pattern, you can sketch a line of fit for the data. This line of fit can be represented with an equation
and can be used to describe the relationship between the two variables. Remember, a line can be written in slope-intercept form
y
= mx
+ b
, where
m
is the slope
and
b
is the y-intercept. The slope,
b, represents the rate of change
that occurs in the problem. The y-intercept tells us the starting value of y
when x
= 0.
Learn to Find the Equation of the Line of Fit
An advertisement agency released a new advertisement on Sunday. The agency was interested in determining if there was an association between the number of days since the advertisement was released and the thousands of consumers who viewed the ad. A scatter plot was created, and a line of fit was drawn. Find the equation for the
line of fit using the scatter plot in the course.
Slope: Y-Intercept: Equation:
Learn to Interpret the Equation of the Line of Fit
Interpret the line of fit using the scatter plot in the course. Interpreting Slope - Identify the slope in the equation and explain what it means in terms of the context. Interpreting Y-Intercept - Identify the y-intercept in the equation and explain what it means in terms of the context. Think Like a Mathema
tician
Interpretations for both the slope and y-intercept in the previous example use the word "
predicted
." What does this mean? The line of fit is not a line that will pass through all of the points on the scatter plot,
so it gives you a line that should best fit the data. Although this line may not be able to tell someone exactly what should happen for any given value of x
in the domain, it will allow you to make a prediction on the value of
y.
Learn More About Interpreti
ng the Equation of the Line of Fit
Damian collected data on the height of Golden Retriever puppies, in inches, from
6
weeks old to
20
weeks old. He graphed the data on the scatter plot and then drew a line of fit through the scatter plot. Use the scatter plot in the course.
What is the y-intercept of the line of fit, and what does it mean for the scenario?
What is the slope of the line of fit, and what does it mean for the scenario?
What is the equation of the line of fit?
A golden retriever puppy that is 15 weeks old is predicted to be how tall? Please use a separate sheet of paper to complete your practice problems.
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