Fitting of Data
Objectives
Start
Story
Linear Functions
Quadratic Functions
Practice
Summary
Story
Linear Functions
Fitting a Line by Tracing a Line
You can find a fitting line of data by tracing a line in the middle of the points.
Example:
Given a set of data points, trace a line that approximately passes through the middle of the data set.
best=8
mest=-1
ŷ=8-x
Least Square Method
Least Square Method finds the line which minimizes the total square distance of line with data points.
Square error:
Sum of square errors:
Our objective is to:
Minimize S
Fitting a Line by the Least Square Method
A pot heats heats water as time passes as shown in the table. Let's see how to find the best fitting line the table data using Geogebra.
Quadratic Functions
For any three points , there's only one parabola passing through them.
Parabola Equation:
Example:
Given points (0,1), (1,4), (2,9), find a,b,c:
f(x)=x²+2x+1
Practice
Try it by yourself:
Measures of resistance of a circuit changes with temperature as shown on Geogebra. Follow steps to find the best fitting line.
Try it by yourself:
Try it by yourself:
Move the sliders a, b and c until you find the parabola that best fit the data. (Hint: Take c=0)
Try it by yourself:
Summary: Fitting Data
Least squares method
by "EYE" METHODS
LINE
PARABOLA
Great job!
See you next time
Welcome 6th graders!
A journey soon begin through Social Science experiences!
6TH-INTRODUCTIONTORATIONALNUMBERS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0
MA.912.DP.2 Solve problems involving univariate and bivariate numerical data. MA.912.DP.2.4 Fit a linear function to bivariate numerical data that suggests a linear association and interpret the slope and y-intercept of the model. Use the model to solve real-world problems in terms of the context of the data. MA.912.DP.2.5 Given a scatter plot that represents bivariate numerical data, assess the fit of a given linear function by plotting and analyzing residuals. MA.912.DP.2.6 Given a scatter plot with a line of fit and residuals, determine the strength and direction of the correlation. Interpret strength and direction within a real-world context. ELD.K12.ELL.MA: Language of Mathematics ELD.K12.ELL.MA.1 English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. MA.K12.MTR.7: Apply mathematics to real-world contexts. MA.K12.MTR.7.1 Apply mathematics to real-world contexts.
MATERIAL
It is highly advised to have:
- Grid paper.
- Pencils of different colors.
- Eraser.
- A rule.
- A calculator.
- Geogebra installed on your phone/tablet/computer (or use online version).
WEEK 30-FITTING-OF-DATA
VIMSCHOOL
Created on October 12, 2025
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Transcript
Fitting of Data
Objectives
Start
Story
Linear Functions
Quadratic Functions
Practice
Summary
Story
Linear Functions
Fitting a Line by Tracing a Line
You can find a fitting line of data by tracing a line in the middle of the points.
Example: Given a set of data points, trace a line that approximately passes through the middle of the data set.
best=8
mest=-1
ŷ=8-x
Least Square Method
Least Square Method finds the line which minimizes the total square distance of line with data points.
Square error:
Sum of square errors:
Our objective is to:
Minimize S
Fitting a Line by the Least Square Method
A pot heats heats water as time passes as shown in the table. Let's see how to find the best fitting line the table data using Geogebra.
Quadratic Functions
For any three points , there's only one parabola passing through them.
Parabola Equation:
Example: Given points (0,1), (1,4), (2,9), find a,b,c:
f(x)=x²+2x+1
Practice
Try it by yourself:
Measures of resistance of a circuit changes with temperature as shown on Geogebra. Follow steps to find the best fitting line.
Try it by yourself:
Try it by yourself:
Move the sliders a, b and c until you find the parabola that best fit the data. (Hint: Take c=0)
Try it by yourself:
Summary: Fitting Data
Least squares method
by "EYE" METHODS
LINE
PARABOLA
Great job!
See you next time
Welcome 6th graders!
A journey soon begin through Social Science experiences!
6TH-INTRODUCTIONTORATIONALNUMBERS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0
MA.912.DP.2 Solve problems involving univariate and bivariate numerical data. MA.912.DP.2.4 Fit a linear function to bivariate numerical data that suggests a linear association and interpret the slope and y-intercept of the model. Use the model to solve real-world problems in terms of the context of the data. MA.912.DP.2.5 Given a scatter plot that represents bivariate numerical data, assess the fit of a given linear function by plotting and analyzing residuals. MA.912.DP.2.6 Given a scatter plot with a line of fit and residuals, determine the strength and direction of the correlation. Interpret strength and direction within a real-world context. ELD.K12.ELL.MA: Language of Mathematics ELD.K12.ELL.MA.1 English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. MA.K12.MTR.7: Apply mathematics to real-world contexts. MA.K12.MTR.7.1 Apply mathematics to real-world contexts.
MATERIAL
It is highly advised to have: