How To Calculate Residual On TI 84 (Step-by-Step Guide with Example)

Many use graph calculators, such as the TI 84 calculator online and its other variations like TI 84 Plus and TI-84 Plus CE, to perform complex statistical analyses in both academia and the workforce. The TI-84 is an excellent calculator for a variety of statistical functions, including regression in high school and data analysis in the real world. Remains are an essential component of regression analysis.

Using this blog post, you can learn about how to calculate Residual on TI 84, leftovers, their significance, and how to calculate them. Additionally, we will provide you with a practical case to investigate.

What Are Residuals & How To Find Residual?

In the context of regression analysis, there is a distinction between the forecasted value (the predicted value of the regression line) and the observed value (a real data point).

Here’s the formula:

Residual = y – ŷ

Where:

y = the actual observed value
ŷ = the predicted value from the regression line.

Residuals are crucial for evaluating how well your regression model fits the data.

When residuals are small, it means the line fits the data well.
On the other hand, large residuals indicate that the line isn’t a good fit.

Why Are Residuals Important?

Residuals provide insight into the reliability of your regression model. They help with:

Measuring Accuracy – Residuals indicate how closely your predicted values align with the actual values.
Evaluating Model Fit – Patterns in residuals can tell you if a linear model is appropriate.
Identifying Outliers – Large residuals can point out data points that don’t follow the trend.
Statistical Testing – Many hypothesis tests and confidence intervals rely on analyzing residuals.

Residuals are often a topic in AP Statistics, IB Math, or college-level regression courses for students.

How Do You Calculate a Residuals on TI 84?

The TI 84, TI 84 Plus and TI 84 Plus CE comes equipped with features for regression analysis. After you run a regression analysis, you can instruct the calculator to save the residuals in a specific list. This allows you to:

Access residual values directly.
Start by creating a residual plot, which is a simple graph that displays residuals in relation to the independent variable.
Next, examine the patterns to determine if linear regression is a suitable fit.

Step-by-Step: How to Calculate Residuals on TI 84

Let’s break it down step by step how to calculate residual on TI 84

Step 1: Input the Data

Hit STAT → 1:Edit
Enter your x-values (the independent variable) into L1.
Then, put your y-values (the dependent variable) into L2.

Here’s a sample data set:

X	Y
1	2
2	4
3	5
4	4
5	6

Step 2: Execute Linear Regression

Press STAT on TI 84 Keyboard→ arrow to CALC
Choose 4: LinReg(ax + b).
Input: L1, L2, Y1.

To find Y1, go to VARS → Y-VARS → Function → Y1.

This will calculate the regression equation and save it in Y1 for future predictions.

In our example, the calculator might show:

ŷ = 0.9x + 1.4
y = 0.9x + 1.4

Step 3: Compile Residuals in a List

Select STAT → go to CALC → pick 4:LinReg(ax+b) again.
Scroll down to the Store Residuals section.
Press 2nd → LIST → NAMES → L3.

Now, your residuals will be stored in L3.

Step 4: Examine Residuals

Press STAT → 1: Edit

L1 will show the X-values.
L2 contains the Actual Y-values.
L3 holds the residuals.

Example Calculation

If x is 2 and y is 4, using the regression equation:

ŷ = 0.9(2) + 1.4 = 3.2
Now, calculate the remaining:
y – ŷ = 4 – 3.2 = 0.8

Upon examining L3, you will see 0.8 recorded there.

Step 5: Create Residual Plot (Optional)

A residual plot is a handy tool for checking if a linear model is a good fit for your data.

Start by pressing 2nd → Y= (STAT PLOT).
Turn Plot 1 ON
Set Xlist to L1 and Ylist to L3.
Next, hit the GRAPH button on the graphing calculator.

If the residuals are scattered randomly, it means your linear model is a good match. However, if you notice any patterns, such as curves, it may be time to consider a different model.

Another Example with Uneven Data

How to calculate Residual on TI 84, suppose if you have these values:

X	Y
1	3
2	6
3	7
4	9
5	11

By adhering to the same procedures, the TI-84 may provide a regression equation: ŷ =2x+1

Residuals:

For (1,3): Residual = 3 – (2 * 1 + 1) = 0
For (2,6): Residual = 6 – (2 * 2 + 1) = 1
For (3,7): Residual = 7 – (2 * 3 + 1) = 0
For (4,9): Residual = 9 – (2 * 4 + 1) = 0
For (5,11): Residual = 11 – (2 * 5 + 1) = 0

In L3, the data is displayed as {0, 1, 0, 0, 0}.

This indicates that the regression line provides a good fit to the data.

Common Mistakes to Avoid

Forgetting to Store Residuals: It’s crucial to save residuals in a list, like L3.
Mixing Up Lists: Ensure that your x-values are in L1 and your y-values are in L2.
Not Turning Off Plots: If your graphs appear strange, verify that the residual plots are properly activated or deactivated.
Misinterpreting Residuals: Large residuals indicate a poor fit, but they don’t automatically mean your data is wrong.

Conclusion

This guide elaborates how to calculate residual on TI 84 in full details. Getting the hang of calculating residuals on a TI-84 Plus is key to understanding regression analysis. Residuals help you evaluate how well your model fits, spot outliers, and check if linear regression is appropriate.

By following a few simple steps—inputting your data, running the regression, and saving the residuals—you can efficiently compute and visualize them. With practice,

FAQs for How To Calculate Residual On TI 84

A remaining is the amount remaining after deducting the value (y) from the predicted value (ŷ).

It is possible to store residues in a list (eg L3) after regression.

Select L3 after running LinReg(ax+b) → scroll, then go down to save the residues.

They determine the accuracy of the model, highlight any deviations and assess the fitness of linear regression.

Use STAT PLOT, set Xlist = L1 and Ylist = L3, then press GRAPH.

The results suggest that linear regression models work well with the given data.

How To Calculate Residual On TI 84 (Step-by-Step Guide with Example)

What Are Residuals & How To Find Residual?

Why Are Residuals Important?

How Do You Calculate a Residuals on TI 84?