Prediction intervals are used to predict the range of values within which a new observation will fall with a certain degree of confidence. To calculate the prediction interval, one must first calculate the standard error of the regression, the mean of the dependent variable, and the values of the independent variables in the new observation. From these values, the prediction interval can be calculated by adding and subtracting a multiple of the standard error to the mean of the dependent variable.
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This calculator creates a prediction interval for a given value in a regression analysis.
Simply enter a list of values for a predictor variable, a response variable, an individual value to create a prediction interval for, and a confidence level, then click the “Calculate” button:
Predictor values:
Response values:
X value for prediction:
Confidence Level:
90% Prediction Interval: (74.643, 86.903)
function calc() {
//get input data
var x = document.getElementById(‘x’).value.split(‘,’).map(Number);
var y = document.getElementById(‘y’).value.split(‘,’).map(Number);
var xpred = +document.getElementById(‘xpred’).value;
var CI = +document.getElementById(‘CI’).value;
//check that both lists are equal length
if (x.length – y.length == 0) {
document.getElementById(‘error_msg’).innerHTML = ”;
function linearRegression(y,x){
var lr = {};
var n = y.length;
var sum_x = 0;
var sum_y = 0;
var sum_xy = 0;
var sum_xx = 0;
var sum_yy = 0;
for (var i = 0; i < y.length; i++) {
sum_x += x[i];
sum_y += y[i];
sum_xy += (x[i]*y[i]);
sum_xx += (x[i]*x[i]);
sum_yy += (y[i]*y[i]);
}
lr['slope'] = (n * sum_xy – sum_x * sum_y) / (n*sum_xx – sum_x * sum_x);
lr['intercept'] = (sum_y – lr.slope * sum_x)/n;
lr['r2'] = Math.pow((n*sum_xy – sum_x*sum_y)/Math.sqrt((n*sum_xx-sum_x*sum_x)*(n*sum_yy-sum_y*sum_y)),2);
lr['sum_y'] = sum_y;
lr['sum_xx'] = sum_xx;
return lr;
}
//create regression variables
var lr = linearRegression(y, x);
var a = lr.slope;
var b = lr.intercept;
var r2 = lr.r2;
var r2p = r2*100;
var sxx = lr.sum_xx;
//create sse variable
var my = lr.sum_y / y.length;
let sst = 0;
for (let i = 0; i < y.length; i++) {
sst += Math.pow((y[i] – my), 2);
}
var CI_out = CI*100
var sse = sst – r2*sst;
var n = y.length;
var var2 = sse/(n-2);
var xbar = math.mean(x);
var ypred = b – (-1*a*xpred);
var df = n-2;
var tcrit = -1*jStat.studentt.inv((1-CI)/2, df);
//calculate lower and upper bounds of prediction interval
var lowCI = ypred-tcrit*Math.sqrt(var2*(1-(-1*(1/n))-(-1*Math.pow(xpred-xbar,2)/sxx)));
var highCI = ypred-(-1*(tcrit*Math.sqrt(var2*(1-(-1*(1/n))-(-1*Math.pow(xpred-xbar,2)/sxx)))));
//output results
document.getElementById('lowCI').innerHTML = lowCI.toFixed(3);
document.getElementById('highCI').innerHTML = highCI.toFixed(3);
document.getElementById('CI_out').innerHTML = CI_out.toFixed(0);
}
//output error message if boths lists are not equal
else {
document.getElementById('error_msg').innerHTML = 'The two lists must be of equal length.';
}
} //end calc function