SWBAT: Use technology to find lines of best fit
Lesson 7A-2
Do Now:
1)
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SWBAT: Use technology to find lines of best fit
Lesson 7A-2
Finding a Line of Best Fit Using Technology
1)
 Use a graphing calculator to find an equation of the line of best fit.
 Then plot the data and graph the equation in the same viewing window.
 Identify and interpret the correlation coefficient.
 Interpret the slope and y-intercept of the line of best fit.
The table shows the durations x (in minutes) of several eruptions of the geyser Old Faithful and
the times y (in minutes) until the next eruption.
Using a graph or its equation to approximate a value between two known values is called
interpolation. Using a graph or its equation to predict a value outside the range of known
values is called extrapolation. In general, the farther removed a value is from the known
values, the less confidence you can have in the accuracy of the prediction.
a. Approximate the duration before a time of 77 minutes.
b. Predict the time after an eruption lasting 5.0 minutes.
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SWBAT: Use technology to find lines of best fit
Lesson 7A-2
2)




Use a graphing calculator to find an equation of the line of best fit.
Then plot the data and graph the equation in the same viewing window.
Identify and interpret the correlation coefficient.
Interpret the slope and y-intercept of the line of best fit.
The table shows the attendances y (in thousands) at an amusement park from 2005 to 2014,
where x = 0 represents the year 2005.
a) Use the equation of the line of best fi t to predict the attendance at the amusement park in
2017.
3)
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SWBAT: Use technology to find lines of best fit
Lesson 7A-2
You Try!!
4)
Multiple Choice Practice
5)
What is the line of best fit for this data?
a. y = 11.83x – 1. 11; r = –0.9760964904
b. y = –1.11x + 11.83; r = –0.9760964904
c. y = 11.83x – 1. 11; r = 0.9527643586
d. y = –1.11x + 11.83; r = 0.9527643586
Average Speed
(mi/h)
Time (hours)
8.5
2.5
7.5
3.75
6.5
4.5
6.0
5.0
5.5
5.5
5.0
6.25
4.0
6.75
3.5
8.75
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SWBAT: Use technology to find lines of best fit
Lesson 7A-2
6)
Which of the following equations best fits the data shown in the scatterplot below?
a. y = -2x + 8
b.
y=
x+8
c. y = -x + 8
d. y = 2x + 8
7)
Which of the following best describe the data shown in the scatterplot below?
a.
b.
c.
d.
It cannot be determined if there is a correlation.
There is a weak correlation.
There is a strong negative correlation.
There is a strong positive correlation.
Number of Weeks
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SWBAT: Use technology to find lines of best fit
Lesson 7A-2
REFERENCE SHEET FOR REGRESSION
Step 1. Enter the data into
Step 2. C reate a scatter plot Step 3. C hoose Linear
the lists.
of the data.
Regression Model.
Go to STATPLOT (2nd Y=) and
choose the first plot.
Turn the plot ON, set the icon
to Scatter Plot (the first one),
set Xlist to L1 and Ylist to L2
Press STAT,
Press CALC,
Enter #4: LinReg (ax+b).
Hit ENTER. When LinReg
appears on the home screen,
type the parameters L1, L2,
Y1. The Y1 will put the
equation into Y= for you.
(Y 1 comes from VARS →
YVARS, #Function, Y1)
The
linear regression equation is
y = 25.3x + 353.2
Step 4. Graph the Linear
Regression Equation from Y1.
Step 5. Is this model a "good
fit"?
ZOOM #9 ZoomStat to see the 0.8 or greater is a "strong"
graph.
correlation
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SWBAT: Use technology to find lines of best fit
Lesson 7A-2
Definition Residuals
•
•
A residual is the difference in the observed value of the response variable and the value
predicted by the regression line.
(how far the data falls from the regression line).
Residual = observed y – predicted y
•
•
•
A Residual Plot is a scatterplot of the regression residuals against the explanatory variable.
The Residual helps us assess the fit of a regression line.
If the regression line captures the overall relationship between x and y, the residuals
should have no systematic pattern.
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SWBAT: Use technology to find lines of best fit
Lesson 7A-2
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SWBAT: Use technology to find lines of best fit
Lesson 7A-2
Analyzing Different Residual Plots
Things to look out for with
residual plots
The uniform scatter of points
indicates that the regression line
fits the data well, so the line is a
good model.
• Increasing or decreasing
spread about the line. The
response variable y has more spread
for larger values of the explanatory
variable x, so the prediction will be
less accurate when x is large.
• A curved pattern shows that
the relationship is not linear.
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SWBAT: Use technology to find lines of best fit
Lesson 7A-2
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