4-5 Scatter Plots and Lines of Best Fit

GOALS:•WRITE A LINEAR EQUATION THAT APPROXIMATES A

SET OF DATA POINTS•DETERMINE IF THERE IS A POSITIVE, NEGATIVE OR

NO CORRELATION BETWEEN DATA POINTS.

ELIGIBLE CONTENT: A1 .1 .2 .1 .1 / A1 .1 .2 .1 .3 / A1 .2 .2 .1 .3 / A1 .2 .2 .2 .1 /

A1 .2 .3 .2 .1 / A1 .2 .3 .2 .2 / A1 .2 .3 .2 .3

4-5 Scatter Plots and Lines of Best Fit

Vocabulary

Data – collection of numbers or pairs of numbers to be analyzed.

Scatterplot - a graph of pairs of numbers that represent a real-life situation.

Scatterplot

Vocabulary

Best Fitting Line - line that is the best approximation of where the points lie.

Other terms for Best Fitting Line: Line of Best Fit Regression Line Trend Line

Vocabulary

Correlation – the relationship between the inputs and the outputs.

Other term for correlation: Trend

Types of correlation: Positive Negative None

Positive Correlation

Line of best fit has a positive slopePoints are increasing from left to right

0 2 4 6 8 10 12 1402468

101214

Negative Correlation

Line of best fit has a negative slopePoints are decreasing from left to right

0 2 4 6 8 10 120

2

4

6

8

10

12

Relatively No Correlation

Line of best fit cannot be drawnPoints are scattered

0 2 4 6 8 10 120123456789

10

Example

The graph shows the average number of students per computer in Maria’s school. Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.

The graph shows a negative correlation. Each year, more computers are in Maria’s school, making the students-per-computer rate smaller.

A. Positive correlation; with each year, the number of mail-order prescriptions has increased.

B. Negative correlation; with each year, the number of mail-order prescriptions has decreased.

C. no correlationD. cannot be determined

The graph shows the number of mail-order prescriptions. Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe it.

How to find the Equation of the Line of Best Fit

Draw the scatter plot of the data.Sketch the line of best fit.Pick 2 points on the line.Find the slope.Find the y-intercept.Write the equation of the line.

Let’s look at an example

Discus Throws

Example

The table shows the amount of sleep a baby needs at each age.

Make a scatter plot of the data and find the equation of the line of best fit.

Age(weeks)

Sleep(hours)

3 15.86 15.114 15.418 15.227 14.439 14.245 13.947 13.149 13.750 13.2

y = -0.05 x + 15.85

Practice

The table shows the largest vertical drops of nine roller coasters in the US and the number of years after 1988 that they were opened. Make a scatterplot and find the equation of the line of best fit.

y = 15x + 120

Years since 1988

1 3 5 8 12 12 12 13 15

Vertical drop (feet)

151

155

225

230

306

300

255

255

400

Homework

Page 250 #1-7for #3 only complete parts a-c.

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