Our online prediction interval calculator determines the confidence interval for the value of the dependent and independent variable of a given value.
Concept of Prediction Interval:
"A prediction interval is the range of values which is likely to have a future observation that gives the specified setting of predictors"
The estimated range of values that have a single new observation based on previous data has two main sources of uncertainty that influence the prediction interval. These include:

Estimated mean

Random Variance of new observance
Steps To Use Prediction Interval Calculator:
A prediction interval is used in the regression analysis for the determination of an interval with a fall of future observation. Our best predicted value calculator is a valuable tool for anyone who needs to make predictions about the future.
What To Enter?

Independent and dependent variables

Confidence Interval

X value for prediction X0
Result Summary:

Predicted Value: Get the value that your model predicts for given values

Prediction Interval: Range of values that is likely to have an actual value of dependent variables.

Confidence Level: Probability of the dependent variables on which the actual value will fall within the prediction interval.
How to Calculate Prediction Interval?
Our Prediction Interval Calculator online helps you make better decisions by quantifying the uncertainty in your predictions. It uses the below formula to pursue instant calculations:
Prediction Interval = Predicted value ± Standard error × tmultiplier
Where:
 Prediction Value = Predicted value by the regression model
 Standard Error = the measure of the variability of individual observations around the mean.
 Tmultiplier = The value from tdistribution determined by the desired level of confidence and degree of freedom.
Practical Example:
Given Data:
 Independent variables = 6, 11, 9, 8, 12, 14, 6, 16, 24, 19
 Dependent variable = 9, 11, 15, 17, 23, 7, 16, 14, 11, 8
 Confidence Level = 0.70
 X value for prediction X0 = 3
Solution:
So, the predicted value of the given data that is available for the determination of regression coefficients with the help of the sample value of the predictor and the response variable:
Obs.  X  Y  X^{2}_{i}  Y^{2}_{i}  X_{i} . Y_{i} 
1  6  9  36  81  54 
2  11  11  121  121  121 
3  9  15  81  225  135 
4  8  17  64  289  136 
5  12  23  144  529  276 
6  14  7  196  49  98 
7  6  16  36  256  96 
8  16  14  256  196  224 
9  24  11  576  121  264 
10  19  8  361  64  152 
Sum =  125  131  1871  1931  1556 
Step # 1 _ Get a sum of squares:
$$ SS_{XX} = \sum^n_{i=1}X_i^2  \dfrac{1}{n} \left(\sum^n_{i=1}X_i \right)^2 $$
$$ = 1871  \dfrac{1}{10} (125)^2 $$
$$ = 308.5 $$
$$ SS_{YY} = \sum^n_{i=1}Y_i^2  \dfrac{1}{n} \left(\sum^n_{i=1}Y_i \right)^2 $$
$$ = 1931  \dfrac{1}{10} (131)^2 $$
$$ = 214.9 $$
$$ SS_{XY} = \sum^n_{i=1}{X_iY_i}  \dfrac{1}{n} \left(\sum^n_{i=1}X_i \right) \left(\sum^n_{i=1}Y_i \right) $$
$$ = 1556  \dfrac{1}{10} (125) (131) $$
$$ = 81.5 $$
Step # 2 _ Find slope and yintercept:
$$ \hat{\beta_1} = \dfrac{SS_{XY}}{SS_{XX}} $$
$$ = \dfrac{81.5}{308.5} $$
$$ = 0.2642 $$
$$ \hat{\beta_0} = \bar{Y}  \hat{\beta_1} \times \bar{X} $$
$$ = 13.1  0.2642 \times 12.5 $$
$$ = 16.4025 $$
Regression equation is here:
$$ \hat{Y} = \hat{\beta_0} + \hat{\beta_1} \times X $$
Now that we have the regression equation, we can compute the predicted value for X=3, by simply plugging in the value of X=3 in the regression equation found above:
$$ \hat{Y} = 16.4025 + 0.2642 \times 3 $$
$$ = 15.6099 $$
Step # 3 _ Calculate the 7% of the value:
Y = 15.6099 is the 7% predicted interval. To find the standard error of the calculations we need to calculate sum of squared errors and the regression sum of the squares.
As we realize sum of square is:
$$ SS_{Total} = SS_{YY} = 214.9 $$
Regression sum of square is figure out by the following way:
$$ SS_{Regression} = \hat{\beta_1} \times SS_{XY} $$
$$ = 0.2642 \times 81.5 $$
$$ = 21.5323 $$
Since we know that:
$$ SS_{Total} = SS_{Regression} + SS_{Error} $$
Step # 4 _ Evaluate the sum of the squared error:
$$ SS_{Error} = SS_{Total}  SS_{Regression} $$
$$ = 214.9  21.5323 $$
$$ = 193.3677 $$
So, mean squared error is:
$$ MSE = \dfrac{SS_{Error}}{n  2} $$
$$ = \dfrac{193.3677}{10  2} $$
$$ = 24.171 $$
Step # 5 _ Find the standard error:
$$ \hat{\sigma} = \sqrt{MSE} $$
$$ = \sqrt{24.171} $$
$$ = 4.9164 $$
As, we figured a 7% prediction intervel for the predicted value that is 15.6099, the level that is used equals to 0.3. The critical tvalue for df = n − 2 = 10  2 = 8 degrees of freedom, and α = 0.3 is t = 2.16.
Now, we are organized to determine the margin error for the prediction interval with this all given information.
$$ E = t_\sigma/2;n2 \times \sqrt{{\sigma}^2 \left(1 + \dfrac{1}{n} + \dfrac{\left( X_0  \bar{X} \right)^2} {SS_{XX}} \right)} $$
$$ = 2.16 \times \sqrt{24.171 \left(1 + \dfrac{1}{10} + \dfrac{\left( 3  12.5 \right)^2} {308.5} \right)} $$
$$ = 12.5316 $$
Final Answer:
So, the predicted value of the 7% prediction interval is Y = 15.6099
$$ PI = \left(\hat{Y} + E , \hat{Y}  E \right) $$
$$ PI = \left(15.6099 + 12.5316 , 15.6099  12.5316 \right) $$
$$ PI = \left(3.0783 , 28.1415 \right) $$
FAQs:
Why Prediction Interval is Less Certain Than Confidence Interval?
The prediction interval is less certain than the confidence interval because both terms are used to quantify the level of uncertainty in the given set of data. The reason behind the priority of Prediction intervals over the confidence interval is that it focuses on future events and the confidence interval focuses on past events.
What is the Effect of Sample Size on Prediction Interval?
As the sample size increases, the prediction interval becomes narrower. This is because a sample size provides information about the population that allows us to make more precise predictions.
References:
From the source Wikipedia: Prediction interval, Normal distribution, Nonparametric methods, Contrast with other intervals, Bayesian statistics.
From the source study.com: What is a Prediction Interval? How do you make a prediction interval? Prediction Interval vs Confidence Interval, Prediction Interval Formula.