1. 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:
A / A / A / A / A / A / A

2. 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.

3. Scatterplot

4. 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

5. Vocabulary
Correlation – the relationship between the inputs and the outputs.
Other term for correlation:
Trend
Types of correlation:
Positive
Negative
No Correlation

6. Positive Correlation Line of best fit has a positive slope
Points are increasing from left to right

7. Negative Correlation Line of best fit has a negative slope
Points are decreasing from left to right

8. Relatively No Correlation
Line of best fit cannot be drawn
Points are scattered

9. 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.

10. The graph shows the number of mail-order prescriptions
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.
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 correlation
D. cannot be determined

11. 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.

12. Write an equation of your line.
Approximating a Best-Fitting Line
Years since 1900
Distance (ft) 8 16 24 32 40 48 56 64 72 80 88 96
104
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
DISCUS THROWS
The winning Olympic discus throws from 1908 to 1996 are plotted in the graph. Approximate the best-fitting line for these throws.
Write an equation of your line.

13. Approximating a Best-Fitting Line
Years since 1900
Distance (ft) 8 16 24 32 40 48 56 64 72 80 88 96
104
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
SOLUTION
(96, 230).
(96, 230)
Find two points that lie on the best-fitting line, such as (8, 140) and (96, 230).
(8, 140)
Find the slope of the line through these points.

14. m = y = m x + b y = m x + b 140 = (1.02) (8) + b 140 for y.
Approximating a Best-Fitting Line
Years since 1900
Distance (ft) 8 16 24 32 40 48 56 64 72 80 88 96
104
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
(96, 230)
(8, 138)
y2 – y1
x2 – x1
m =
230 – 140
96 – 8 = 90 88
1.02
230 – 138
96 – 8 =
y = m x + b
Write slope intercept form.
Substitute 1.05 for m, 8 for x,
140 for y.
140 = (1.02) (8) + b 92 88 =
1.05
y = m x + b
140 = b
Simplify.
= b
Solve for b.
An equation of the best-fitting line is y = 1.02 x
In most years, the winner of the discus throw was able to throw the discus farther than the previous winner.

15. 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
15.8 6
15.1 14
15.4 18
15.2 27
14.4 39
14.2 45
13.9 47
13.1 49
13.7 50
13.2
y = x

16. 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 13 15
Vertical drop (feet)
151
155
225
230
306
300
255
400

17. Homework
Pages #1-7
for #3 only complete parts a-c.