4-5 scatter plots and lines of best fit
DESCRIPTION
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. Vocabulary. Data – collection of numbers or pairs of numbers to be analyzed. - PowerPoint PPT PresentationTRANSCRIPT
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.
Get progress report signed!