WEEK 20-FITTING-AND-INTERPRETING-SCATTER-PLOTS

Objectives

Start

Fitting and Interpreting Scatter Plots

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Story

Fitting a Line to Data

Real-World Contexts

Summary

Interpretation and Predictions

Story

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Fitting a Line to Data

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What is a Linear Association?

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A linear association occurs when the data points in a scatter plot tend to cluster around a straight line.

Example 1: Distance over time of a car shows an increasing pattern

Points tend to be around a certain middle line (red)

Method 1: A "Good Fit" can be found by the line equation between two data points

Example 2: Given the scatter plot below, find a best fitting line through the points.

y=2x+1

Step 3

Step 2

Step 1

Step 4

y=mx+b y=(2)x+(1)

1. Trace on a paper (or just mentally) lines that changes y-intercept, until you get the line in the middle of the points.

2.Calculate the slope using the formula.

3. Find the intercept of the line by replacing a point in the equation y=mx+b

4. Replace values of m and b obtained:

Method 2: A "Good Fit" can be found graphically drawing the line in the middle of all points

Example 2: Given the scatter plot below, find a best fitting line through the points.

y=x+1

Step 3

Step 2

Step 1

1. Trace on a paper (or just mentally) lines that changes y-intercept, until you get the line in the middle of the points.

2.Draw lines varying their slope (inclination) until you get the best inclination.

3. Find slope and intercept of the line. Note that: m=1 as y increases 1 as x run 1. b=1 as y intercept is y=1.

Interpretation and Predictions

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Example 3: Given the fitting line of example 2, let's determine:

• + association
• y(5)=6
• y(10)=11

Step 2

Step 1

Let's see some examples:

• The kind of association
• values of y if x=5 and if x=10

From data points, there is a positive association.

It goes in accordance to positive slope

m=+1

y=x+1

• For x=5:

• For x=10:

y=5+1y=6y=10+1y=11

1. Trace on a paper (or just mentally) lines that changes y-intercept, until you get the line in the middle of the points.

2.Draw lines varying their slope (inclination) until you get the best inclination.

Real-World Contexts

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Medical Staff Wage

The table below shows the years of job experience of eight physicians who are employed at the May Hospital and the hourly rate of pay that each physician earns.

Plot data in the scatter plot and determine the line of best fitting.

Click here to draw >

Solution

table

m=

65-23 10-1

14 3

m=

=4.6...

23=14(1)/3+b

b=55/3=18.3...

y=4.6x+18.3

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Data follows a positive association.

Data follows a positive association.

Height of a Student

07:00

Height of a person was measured at different ages. The results are found in the table:

Plot data in the scatter plot and find the best line of fitting.

Click here to draw >

y=4.6x+18.3

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Try it by yourself:

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Try it by yourself:

Summary:Finding The Best Fitting Line

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Line in the "middle" of all points

Line through two points

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Welcome 6th graders!

A journey soon begin through Social Science experiences!

Great job!

See you next time

8TH-FITTING-AND-INTERPRETING-SCATTER-PLOTS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

Write the fitting line

In the form y=mx+b

It is highly advised to have:

MATERIAL

• Grid paper.
• Pencils of different colors.
• Eraser.
• A rule.
• A compass.
• A Protactor.
• A calculator.
• Geogebra installed on your phone/tablet/computer (or use online version).

"MA.8.DP.1 Represent and investigate numerical bivariate data."MA.8.DP.1.3 Given a scatter plot with a linear association, informally fit a straight line.MA.8.DP.1.2 Given a scatter plot within a real-world context, describe patterns of association.MA.K12.MTR.7.1 Apply mathematics to real-world contexts.

On a Cartesian plane

Plot the given points

For the cartesian plane.

Select appropiate proportions and labels

Selecting one of the methods seen

Draw the best line of fitting

Interpret and find other values

Find the slope and intercept

Of the line drawn among the points.

Solution

Step 3

Step 2

Step 1

Answer

Step 4

b)

a)

a) 2.5x+65≤500b) 174 months

Step 5

c)

Write each sentence in mathematical terms. x is the unknown, what is asked. Note: In addition, x≥0 because there are no negative cost.

Divide both sides by 2.5.

Subtract from both sides 65.

Write the givens in a list/table.

Plot the result.