4,12 Stats Interpolation and Extrapolation**
Statistical Models: Interpolation and Extrapolation
When we create a scatterplot between two variables, we describe the highest and lowest x-variables as the upper and lower poles respectively. If a line of best fit has been drawn, then predictions can be made for one variable given the other.
If we predict a value that occurs in between the lower and upper poles, then we say we are interpolating between the poles. If we predict a value that occurs outside of either the lower or upper pole, then we say we are extrapolating outside the poles.
The accuracy of the predictions in either situation depends on how strong the correlation of the original data was to begin with. However, the extrapolation of data assumes that the correlation is going to continue outside of the poles. The validity of this assumption depends greatly on the situation we are looking at.
5,7.09 Linear Regressions and Residual Plots | Algebra I Math
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Linear Regression is a statistical method used to find the best-fitting line for a set of data points. The line of best fit is determined by minimizing the sum of the squared residuals, which are the differences between each data point and the line.
How to Find Line of Best Fit on TI-84 Calculator – Statology
A line of best fit is the line that best “fits” the trend of a dataset. This tutorial provides a step-by-step example of how to calculate the line of best fit for the following dataset on a TI-84 calculator:
Step 1: Enter the Data
First, we will enter the data values. Press STAT, then press EDIT. Then enter the x-values of the dataset in column L1 and the y-values in column L2:
[Image]
Step 2: Find the Line of Best Fit
Next, we will find the line of best fit.
Press Stat, then scroll over to CALC. Then scroll down to LinReg(ax+b) and press ENTER.
Then press 2nd and 1 and comma , then press 2nd and 2 and comma , then press VARS and scroll over to to Y-VARS and press ENTER.
Your screen should look like this:
[Image]
Press ENTER once more and the following line of best fit will be displayed:
The line of best fit is: y = 5.493 + 1.14x
Step 3: Plot the Line of Best Fit
Lastly, we will plot the line of best fit.
Press ZOOM and then scroll down to ZOOMSTAT and press ENTER.
The following scatterplot with the line of best fit will be shown:
[Image]
Additional Resources
- How to Perform Linear Regression on a TI-84 Calculator
- How to Perform Quadratic Regression on a TI-84 Calculator
- How to Create a Residual Plot on a TI-84 Calculator
About the Author
Hey there. My name is Zach Bobbitt. I have a Masters of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike.
My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations.
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