# Understanding By Design Template

```Capital Area Career Center
Lesson 2: Regression Lines in AutoTech
Content Standard (s): What relevant goals will this design address?
S2.2.1, S2.2.2
Stage 1: Desired Results
What are the “big ideas”? What specific understandings about them are desired?
What misunderstandings are predictable?
Students will understand:
 Least Squares Regression Line
 Appropriate Predictions
 Interpret Slope

Essential Question(s): What arguable, recurring, and thought-provoking questions will
guide inquiry and point toward the big ideas of the unit?
How do you use a least square regression line to make a future prediction with past data?
Knowledge &amp; Skill
 What is the key knowledge and skill needed to develop the desired
understandings? Students will know …
How to determine the regression equation by estimating and through calculation; working
knowledge of slope and y-intercept:
 What knowledge and skill relates to the content standards on which the unit is
focused? Students will be able to…
Construct a Least Squares Regression Line; discuss the differences in slope of two
different lines; take known bivariate data and make predictions (extrapolation and
interpolation.
Stage 2: Assessment Evidence
1
What evidence will be collected to determine whether or not the understandings have
been developed, the knowledge and skill attained, and the state standards met?
[Anchor the work in performance tasks that involve application, supplemented as
needed by prompted work, quizzes, observations, etc.]
Summary in G.R.A.S.P.S. form
Rubric Titles (Key Criteria)
Regression Line: Determine using “best fit”
criteria, calculate using graphing calculator,
Excel, etc.
Students will use collected data (in the
form of a scatterplot) related to a realworld situation, construct a linear
regression line from the scatterplot,
analyze the regression line and prepare a
report to an audience appropriate for the
situation.
Slope and y-intercept: Appropriate for the
data. Slope and y-intercept calculated from
the graph and interpreted in the problem
context.
Predictions: Are they reasonable given
contextual situation?
Formative Assessment
Summative Assessment
Presentation, Authentic, Program
Contextual
End of Unit/Course, Standardized, CACCwide
2
Stage 3: Learning Activities
What sequence of learning activities and teaching will enable students to perform well
at the understandings in Stage 2 and thus display evidence of the desired results in
stage one? Learning Activities: Consider the W.H.E.R.E.T.O elements:
Activity 1:
Data Set
Points
0
0
0
1
1
2
2
3
3
4
4
5
5
5
6
6
6
Cost
229
420
580
450
575
300
720
654
520
620
700
935
650
875
850
570
1100
Using the above data, create a scatterplot.
3
1200
1000
Costs
800
600
400
200
0
0
1
2
3
4
5
6
7
Points
1. Draw the best fit line (Least Regression Line).
2. Estimate the Least Squares Regression Line:
Use the form y = mx + b,
where “m” is the slope and “b” is the y-intercept
m = 70, b = 400, y = 70x + 400
3. Using a graphing calculator or Excel, determine the Least Squares
Regression Line.
Y = 74.308x + 400.57
4
1200
1000
y = 74.308x + 400.57
Costs
800
600
400
200
0
0
1
2
3
4
5
6
7
Points
4. a. Using the above Regression Line Equation, what is the y-value (cost)
when the x-value (number of points) is 2? (interpolation)
74.308(2) + 400.57 = \$549
b. What is the y-value when the x-value is 8? (extrapolation)
74.308(8) + 400.57 = \$995
5. Does this Regression Line work for points beyond 8? Beyond 12?
5
Activity 2: Using the information from Lesson 1, Activity 2 or the
information below, generate a scatter plot and line of best fit (least
squares regression line).
RPM
Oil Pressure (psi)
500
38
750
37
1000
40
1250
42
1500
41
1750
52
2000
49
2250
55
2500
58
2750
56
3000
64
1. Determine the oil pressure at 1900 rpm.
2. Determine the oil pressure at 3400 rpm.
3. Is there a practical limit to rpm range? What is it?
6
GLOSSARY OF TERMS
Least Squares Regression Line: The linear fit that matches the pattern of a set
of paired data as closely as possible. Out of all possible linear fits, the least
squares regression line is the one that has the smallest possible value for the
sum of the squares of the residuals.
Slope: Slope is commonly used to describe the measurement of the steepness,
incline, gradient, or grade of a straight line. A higher slope value indicates a
steeper incline. The slope is defined as the ratio of the &quot;rise&quot; divided by the
&quot;run&quot; between two points on a line, in other words, the ratio of the altitude
change to the horizontal distance between any two points on the line. It is also
always the same thing as how many rises in one run.
Carpenters and builders call this ratio the &quot;rise over the run.&quot; Using any two
points on a line, you can calculate its slope using this formula.
Y-intercept: The y-intercept is the point where the graph of a function or relation
intercepts the y-axis of the coordinate system. For example, in linear equations
that are in the &quot;slope-intercept&quot; form of y = mx + b, the value of b is the yintercept and m is the slope.
Interpolation: Interpolation is the process of constructing new points between
known points, but its results are often less meaningful, and are subject to
greater uncertainty.
Extrapolation: Extrapolation is the process of constructing new data points
outside a discrete set of known data points.
Goal
Role
Audience
Situation
Product/Performance/Purpose
Standards &amp; Criteria for Success
Consider the W.H.E.R.E.T.O. elements for structuring learning activities:
7
Where – Help the students know where the unit is going and what is expected. Help the teacher
know where the students are coming from (prior knowledge, interests).
Hook – Hook all students and hold their interest.
Equip – Equip students, help them experience the key ideas, and explore the issues.
Provide – Provide opportunities to rethink and revise their understanding and work.
Evaluate – Allow students to evaluate their work and its implications.
Tailored – Tailored (personalized) to the different needs, interests, abilities of learners.
Organized – Organized to maximize initial and sustained engagement as well as effective
learning.
8
```