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2-7
Curve Fitting with Linear Models
LEARNING GOALS FOR LESSON 2.7
1. Fit scatter plot data using linear models with technology.
2. Use linear models to make predictions.
Scatter plot:
Their main purpose is to analyze a relationship between 2 variables.:
• Form
• Direction
• Strength:
Regression line or line of best fit:
Helpful Hint
Try to have about
the same number of
points above and
below the line of
best fit.
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2-7
Curve Fitting with Linear Models
The correlation coefficient r is a measure of how strongly the
data set is fit by a model.
Find the regression line and the correlation coefficient using the data below.
2-7
Curve Fitting with Linear Models
Example 2 Using Technology to Model Linear Data
LG 2.7.1
The gas mileage for randomly selected cars based upon engine horsepower is
given in the table.
a. Make a scatter plot of the data with
horsepower as the independent
variable.
b. Find the correlation coefficient r
and the line of best fit. Interpret the
slope of the line of best fit in the
context of the problem.
To graph a scatter plot
on your calculator; press
2nd, Y=, 1:Plot1…On,
Make sure that On is
highlighted, that the
scatterplot is
highlighted, that the Xlist
says L1 and the Ylist
says L2.
Hit ZOOM 9:ZoomStat
2-7
Curve Fitting with Linear Models
Example 3: Anthropology Application
LG 2.7.1
Anthropologists can use the femur,
or thighbone, to estimate the height
of a human being. The table shows
the results of a randomly selected
sample.
a. Make a scatter plot of the data with
femur length as the independent variable.
b. Find the correlation coefficient r and
the line of best fit. Interpret the slope of
the line of best fit in the context of the
problem.
LG 2.7.2
c. Use the Linear Regression equation you found to answer the
question by plugging in.
A man’s femur is 41 cm long. Predict the man’s height.