• How do I draw scatter plots and find equations of best-fitting lines?

7.1 Draw Scatter Plots and Best-Fitting Lines

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 = _____.

7.1 Draw Scatter Plots and Best-Fitting Lines

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

7.1 Draw Scatter Plots and Best-Fitting Lines

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.

7.1 Draw Scatter Plots and Best-Fitting Lines

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.

7.1 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 (2, ___).722 7504. Write an equation of the line. The line passes through

the two points has a slope of:___

m 722750

12 28

7.1 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

Use the point-slope form to write the equation.

11 xxmyy _________ y 722 28 1x______y 69428 x

An approximation of the best-fitting line is______y 69428 x

7.1 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

_________ y 863

4 3x

86y x3

44 xy

3

4 82

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

7.1 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

8293

4y 94

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

7.1 Draw Scatter Plots and Best-Fitting Lines

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