LESSON - St. Louis Public Schools



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. _________

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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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