LESSON
Reteach
Curve Fitting with Linear Models
Use a scatter plot to identify a correlation. If the variables appear
correlated, then find a line of fit.
The table shows the relationship between two variables. Identify the
correlation, sketch a line of fit, and find its equation.
Step 1 Make a scatter plot of the data.
As x increases, y decreases.
The data is negatively correlated.
Step 2 Use a straightedge to draw a line.
There will be some points above and below the line.
Step 3 Choose two points on the line to find the equation:
(1, 16) and (7, 2).
Step 4 Use the points to find the slope:
[pic]
Step 5 Use the point-slope form to find the equation of a
line that models the data.
y − y1 ’ m (x − x1)
y − 2 ’ −[pic] (x − 7)
[pic]
Use the scatter plot of the data to solve.
1. The correlation is _____________.
2. Choose two points on the line and find the slope.
3. Find the equation of a line that models the data.
Reteach
Curve Fitting with Linear Models (continued)
A line of best fit can be used to predict data.
Use the correlation coefficient, r, to measure how well the data fits.
−1 ≤ r ≤ 1
Use a graphing calculator to find the correlation coefficient of the data and the line of best fit. Use STAT EDIT to enter the data.
Use the linear regression model to predict y when x ’ 3.5.
y ( −2.2x + 17.79
y ≈ −2.2 (3.5) + 17.79
y ≈ 10.09
Use a calculator and the scatter plot of the data to solve.
4. Find the correlation coefficient, r. __________
5. Find the equation of the line of best fit.
6. Predict y when x ’ 2.6. __________
7. Predict y when x ’ 5.3. _________
-----------------------
LESSON
2-7
|Positive correlation |Negative correlation |No correlation |
|[pic] |[pic] |[pic] |
|x |1 |2 |3 |4 |5 |6 |7 |8 |
|y |16 |14 |11 |10 |5 |2 |3 |2 |
LESSON
2-7
If r is near 1, data is modeled
by a line with a positive slope.
If r is near −1, data is modeled by a line with a negative slope.
If r is near 0, data
has no correlation.
|x |1 |2 |3 |4 |5 |6 |7 |8 |
|y |16 |14 |11 |10 |5 |2 |3 |2 |
Use LinReg from the STAT CALC menu to find the line of best fit and the correlation coefficient.
LinReg
y ’ ax + b
a ’ −2.202
b ’ 17.786
r 2 ’ .9308
r ’ −.9648
The correlation coefficient is −0.9648. The data is very close
to linear with a negative slope.
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