Name:_______________________________ Date:_____________________
Statistics – Line of Best Fit
Do Now:
Determine if the given relationship is correlated or causal.
1) The amount of exposure to the sun and the chances of sunburn.
2) The summer months and the amount of water related accidents.
Vocabulary
Line of Best Fit (Line of Regression, Trend Line, Least Squares Line) – is a straight
line that is used to represent the data on a scatter plot. This line can pass through
all of the points, none of the points, or some of the points.
Example
1) The scatter plot below shoes the money (y) Christina has after x days of holiday
shopping.
a) According the least squares line, when the number of days increases by 2, how
much does Christina’s money decrease?
Name:_______________________________ Date:_____________________
Statistics – Line of Best Fit
b) Using the least squares line, predict how much money Christina has after 6
days.
c) How would you describe the slope of this line?
d) How much money did Christina have when she started shopping?
2) Every year since 2000, the minimum wage has been raised.
Year since 2000
4
5
6
7
8
9
10
Minimum Wage $
4.20
4.25
4.30
5.25
5.30
5.30
5.75
a) Label the axes with words.
b) Label the axes with numbers.
c) Plot the points on the graph.
d) Use your graphing calculator to find the equation of the line of best fit for this
data. Write the equation here. (Round values to the nearest 100th)
e) Use your equation to predict the minimum wage in the year 2020 (20 years
since 2000).
Name:_______________________________ Date:_____________________
Statistics – Line of Best Fit
3) Look at the table of data below.
x
y
-3
-8
-1
-6
0
1
5
4
8
5
12
7
Use the graphing calculator to find the equation for the line of best fit (Round
values to the nearest hundredth). Then make the following predictions:
a) What is y when x = 10?
b) What is x when y = 30?
You Try
In a math class of 10 students, the teacher wanted to determine how a homework
grade influenced a student’s performance on a subsequent test. The homework
grade and the subsequent test grade for each student are given in the following
table.
a) Give the equation for the linear
regression line for this set of data.
b) A new student comes to class and earns a
homework grade of 78. Based on the
equation in part a, what grade would the
teacher predict the student would receive
on the subsequent test, to the nearest
integer?
Name:_______________________________ Date:_____________________
Statistics – Line of Best Fit
Homework
1) Two different tests were designed to measure understanding of a topic. The
two tests were given to ten students with the following results.
a) Construct a scatter plot for these scores, and then write an equation for the line
of best fit (round slope and y – intercept to the nearest hundredth).
b) Find the correlation
coefficient.
c) Predict the score, to the
nearest integer, on test y for
a student who score 87 on
test x.