How do I find the equation of a line of best fit for a scatter plot? How do I find and interpret the...

• How do I find the equation of a line of best fit for a scatter plot? How do I find and interpret the correlation coefficient, r?

S.ID.8 Interpreting Correlation

Example 1 Describe and estimate correlation coefficientsDescribe and estimate correlation coefficients

Describe the data as having a Describe the data as having a positive correlationpositive correlation, a , a negative negative correlationcorrelation, or , or approximately no correlationapproximately no correlation. Tell whether the . Tell whether the correlation coefficient for the data is closest to correlation coefficient for the data is closest to orora.

Solutiona. The scatter plot shows a strong _________ correlation.negative

So, the best estimate given is r = ____.1

So, r is between ___ and ___, but not too close to either one. The best estimate given is r = _____.


Example 1 Describe and estimate correlation coefficientsDescribe and estimate correlation coefficients

Describe the data as having a Describe the data as having a positive correlationpositive correlation, a , a negative negative correlationcorrelation, or , or approximately no correlationapproximately no correlation. Tell whether the . Tell whether the correlation coefficient for the data is closest to correlation coefficient for the data is closest to ororb.

Solutionb. The scatter plot shows a weak _________ correlation.positive

0 15.0


Checkpoint. For the scatter plot, (a) tell whether the Checkpoint. For the scatter plot, (a) tell whether the data has a data has a positive correlationpositive correlation, a , a negative correlationnegative correlation, or , or approximately no correlationapproximately no correlation, and (b) tell whether the , and (b) tell whether the correlation coefficient for the data is closest to correlation coefficient for the data is closest to or 1.or 1.

a. positive correlation

b. 1

1.


Checkpoint. For the scatter plot, (a) tell whether the Checkpoint. For the scatter plot, (a) tell whether the data has a data has a positive correlationpositive correlation, a , a negative correlationnegative correlation, or , or approximately no correlationapproximately no correlation, and (b) tell whether the , and (b) tell whether the correlation coefficient for the data is closest to correlation coefficient for the data is closest to or 1.or 1.

a. approximately no correlation

b. 0

2.

S.ID.6 Draw Scatter Plots and Best-Fitting Lines

Example 2 Approximate the best-fitting lineApproximate the best-fitting line

The table below gives the number of people The table below gives the number of people yy who attended each of who attended each of the first seven football games the first seven football games xx of the season. Approximate the of the season. Approximate the best-fitting line for the data.best-fitting line for the data.

x 1 2 3 4 5 6 7

y 722 763 772 826 815 857 897

01 2 3 4 5 6 7

650

700750800850

900

1. Draw a __________.scatter plot

2. Sketch a best-fitting line.3. Choose two points on the line. For the scatter plot

shown, you might choose (1, ___) and (3, ___).722 7724. Write an equation of the line. The line passes through

the two points has a slope of:___

m 722772

13 25




x 1 2 3 4 5 6 7

y 722 763 772 826 815 857 897

01 2 3 4 5 6 7

650

700750800850

900

Use the slope-intercept form to write the equation.

Choose a point from the table to substitute in for x and y.

m = 25 ; Use (1, 722).

722 = 25(1) + b

722 = 25 + b

697 = b

bmxy

An approximation of the best-fitting line is ______y 69725 x




x 1 2 3 4 5 6 7

y 722 763 772 826 815 857 897

01 2 3 4 5 6 7

650

700750800850

900

You can enter the data in your calculator to get the

equation for the line of best fit also. Enter the x data in L1

and the y data in L2. Run 2-VAR STATS. a = slope and b = y-int.

bmxy An approximation of the best-fitting line

from the calculator is______y 4.69927 x




x 1 2 3 4 5 6 7

y 722 763 772 826 815 857 897

01 2 3 4 5 6 7

650

700750800850

900

In addition, the correlation coefficient, r, can be

found on the calculator. Scroll down past a and b,

and you will find that the correlation coefficient for

this example is r = 0.976. This indicates that the line

y = 27x + 699.4 fits the data well since r is close to 1.

S.ID.6 & 8 Draw Scatter Plots and Best-Fitting Lines

Checkpoint. Complete the following exercise.Checkpoint. Complete the following exercise.3. The table gives the average class score y on each

chapter test for the first six chapters x of the textbook.

x 1 2 3 4 5 6

y 84 83 86 88 87 90

01 2 3 4 5 6 7

82

84868890

92

_______

m 8690

36 3

4

a. Approximate the best-fitting line for the data by hand.

So, the equation describing

this data is y = 4/3x + 82.y = mx + b 86 = 4/3(3) + b 86 = 4 + b 82 = b

S.ID.6 & 8 Draw Scatter Plots and Best-Fitting Lines



x 1 2 3 4 5 6

y 84 83 86 88 87 90

01 2 3 4 5 6 7

82

84868890

92

b. Approximate the best-fitting line using your calculator.

c. Find the correlation coefficient, r.

From the calculator, a = 1.26 and b = 81.93.So, the equation describing this data is y = 1.26x + 81.93.

From the calculator, r = 0.91, which suggests that the equation fits the data well since r is close to 1.




x 1 2 3 4 5 6

y 84 83 86 88 87 90

01 2 3 4 5 6 7

82

84868890

92

8293

4y 94

d. Use your equation from part (a) to predict the average class score on the chapter 9 test.

The average class score on the chapter 9 test is predicted to be a 94.

How do I find the equation of a line of best fit for a scatter plot? How do I find and interpret the...

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