Algebra 2/Trig
Name: __________________________________
Section 1.5 Notes: Scatter Plots and Least-Squares Lines (Line of Best Fit)
p. 37
Goals: Create a scatter plot, understand correlations, use a graphing calculator to find an equation for the line of
best fit for a set of data and use it to make predictions or estimates
You can view the relationship between two variables with a scatter plot.
Outliers: A value that is much greater or much less than most of the other values in a data set. Typically,
statisticians throw out the outliers when analyzing data.
Correlation coefficient: A measure, denoted by r where -1 ≤r ≤1, of how well a line fits a set of data.
Scatter Plot: a graph of a set of data pairs (x, y)
Positive Correlation – y tends to ___________________ as x ___________________.
Negative Correlation – y tends to __________________ as x ___________________.
Approximately No Correlation – if points show no obvious pattern
If r = ______ points lie near or on the line with a negative slope.
If r = ______ points do not lie on or near any line.
If r = ______ points lie near or on the line with a positive slope.
Draw a Scatter Plot: plot the (x, y) pair as one point.
Example 1:
Create a scatter plot of the given data.
x
1
2
3
4
5
6
7
8
9
10
y
4
5
4
3
3
2
3
2
1
1
1
Line of Best Fit:
Once we have made a scatter plot of our data, we try to draw in a “Line of Best Fit”. We can use this line to make
predictions or estimate unknown outcomes.
Step 1: Draw a scatter plot of the data.
Step 2: Sketch the line that appears to follow most closely the trend given by the data points. There should be
about as many points ________________ the line as __________________ it.
Step 3: Choose two points on the line, and estimate the coordinates of each point. These points do NOT have to be
original data points.
Step 4: Write an equation of the line that passes through the two points from Step 3. This equation is a model for
the data.
Example 2:
Estimate the Line of Best Fit for the scatter plots in Example 1.
If our correlation is close to 1 or -1, we can use the line of best fit to predict the grades of future students by the
number of hours they study.
Turn to page 38 in your book. We will do Example 2 using our Graphing Calculators.
CALCULATORS:
Follow along, please do not get ahead of me. First clear the calculator by pressing 2nd, MEM
(+ key), #7, #1, #2. The screen should say “RAM cleared”.
In your calculator:
STAT (2nd button to the right of the green ALPHA key)
EDIT
Under the L1 column, enter the x coordinates. (0, 2, 4, etc.)
Under L2, enter the y coordinates. (-3.2, 1.2, 5, etc.)
Go to 2nd STAT PLOT (y=)
ENTER
Make sure Plot 1 is “ON” by hitting ENTER
Now press STAT again.
Arrow Right to TESTS.
Scroll down to Linear Regression (LinRegTTest)(F), press Enter.
Scroll down to “Calculate” and hit ENTER.
2
Scroll down and find the values for a and b,write them here:
a = ________, b = _______. (2 decimal places please).
Scroll down until you find the value for r, write the value for r here: r = ________. (2 decimals)
This is the correlation. We can make predictions with _______% accuracy.
Go to “y =”
Write the equation for the Line of Best Fit using the values for a and b. y = _______________.
Now GRAPH. You should see your plotted points as well as your line of best fit.
Using your equation, estimate the time for the year 1940.
Go to 2ND CALC
Go to Value and hit ENTER
Type in the value of x you are using for your predictions
(you may have to adjust your window with the ZOOM button)
HW: Page 42 - 43. # 22, 23, 25
For #22, Type the age in L1, and the CD’s in L2.
For #23, Changes the heights to inches and place them in L1 and the shoe size in L2.
For #25, follow directions in book.
Remember the on-line graphing calculator: desmos.com
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