2. Essential Understanding: Sometimes it is possible
to model data from a real-world situation with a
linear equation. You can then use the equation to
draw conclusions about the situation.
Objectives:
Students will be able to
write linear equations that model real world data
make predictions from linear models of data
define and identify various types of correlation
3. Algebra
A-CED.2. Create equations in two or more variables to represent
relationships between quantities; graph equations on coordinate
axes with labels and scales.
Functions
F-IF.4. For a function that models a relationship between two
quantities, interpret key features of graphs and tables in terms of
the quantities, and sketch graphs showing key features given a
verbal description of the relationship★
F-IF.6. Calculate and interpret the average rate of change of a
function (presented symbolically or as a table) over a specified
interval. Estimate the rate of change from a graph.★
F-BF.1. Write a function that describes a relationship between two
quantities.★
4. What is a scatter plot?
A graph that relates two sets of data by
plotting the data as ordered pairs.
Can be used to determine strength of a
relationship. The closer the points fall
together the stronger the
correlation(Correlation does not mean
causation)
6. The following table shows the number of
hours students spent online the day before a
test and the scores on the test. Make a
Scatter Plot and describe the correlation.
What would you predict the test score to be
of someone who was online for 2.5 hours?
Computer Use and Test Scores
# of 0 0 1 1 1.5 1.75 2 2 3 4 4.5 5
Hours
Online
Test 100 94 98 88 92 89 75 70 78 72 57 60
Scores
7. Trend Line: a line that approximates the
relationship between the variables, or data
sets, of a scatter plot.
You can use a trend line to make predictions
from the data
You can pick to two points in the scatter plot
to represent the equation of a trend line
8. The table shows median home prices in
California. What is the equation for a trend
line that models the relationship between
time and home prices?
California Median Home Prices
Year 1940 1950 1960 1970 1980 1990 2000
Median 36,700 57,900 74,400 88,700 167,300 249,800 211,500
Price ($)
9. Line of Best Fit: trend line that gives the
most accurate model of related data
This is the linear regression (LinReg) function
on your calculator
Correlation Coefficient: r, indicates the
strength of the correlation. The closer the
data is to 1 or -1, the more closely the data
resembles a line and the more accurate your
model is.
10. The table lists the cost of 2% milk. Use a
scatter plot to find the equation of the line of
best fit. Based on your linear model, how
much would you expect to pay for a gallon of
2% milk in 2025?
Cost of 2% Milk
Year 1998 2000 2002 2004 2006 2008
Avg Cost for 1 gal 2.57 2.83 2.93 2.93 3.10 3.71
($)
