Analyze the relationship between two sets of data points. This calculator helps you compute key statistical measures used to describe a scatterplot and the linear relationship between two variables.
Data Input
Results
Enter your data points above to see the analysis.
Understanding Scatterplots and Their Analysis
A scatterplot is a type of data visualization that uses dots to represent the values for two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point. Scatterplots are used to observe relationships between variables.
Key Statistical Measures for Scatterplots
To quantify the relationship shown in a scatterplot, several statistical measures are computed. This calculator focuses on the Pearson correlation coefficient (r) and the coefficients for a simple linear regression line (y = mx + b).
1. Pearson Correlation Coefficient (r)
The Pearson correlation coefficient measures the strength and direction of a linear relationship between two variables. It ranges from -1 to +1:
r = 1: Perfect positive linear correlation.
r = -1: Perfect negative linear correlation.
r = 0: No linear correlation.
Values close to 1 or -1 indicate a strong linear relationship.
Values close to 0 indicate a weak or no linear relationship.
x̄ and ȳ are the means of the x and y values, respectively.
Σ denotes summation.
2. Linear Regression Line (y = mx + b)
A simple linear regression line is the "best fit" line through the data points on a scatterplot. It can be used to predict the value of one variable based on the value of another.
The slope (m) and y-intercept (b) are calculated as follows:
m = Σ[(xi - x̄)(yi - ȳ)] / Σ(xi - x̄)²
b = ȳ - m * x̄
Note that the numerator for m is the same as the numerator for r, and the denominator for m is related to the denominator for r.
Use Cases
Science & Engineering: Analyzing relationships between experimental measurements (e.g., temperature vs. pressure).
Economics: Studying the correlation between economic indicators (e.g., inflation rate vs. unemployment).
Finance: Examining how one stock's performance relates to another or to a market index.
Social Sciences: Investigating relationships between social or demographic variables (e.g., education level vs. income).
Quality Control: Identifying potential relationships between manufacturing process parameters and product defects.
This calculator provides basic statistical measures. For complex analyses or visualization, dedicated statistical software is recommended.
function calculateScatterplotStats() {
var xValuesStr = document.getElementById("xValues").value.trim();
var yValuesStr = document.getElementById("yValues").value.trim();
var xValues = xValuesStr.split(',').map(function(val) { return parseFloat(val.trim()); });
var yValues = yValuesStr.split(',').map(function(val) { return parseFloat(val.trim()); });
if (xValues.length === 0 || yValues.length === 0) {
document.getElementById("scatterResultOutput").innerHTML = "Please enter data for both X and Y values.";
return;
}
if (xValues.length !== yValues.length) {
document.getElementById("scatterResultOutput").innerHTML = "The number of X values must match the number of Y values.";
return;
}
var n = xValues.length;
var sumX = 0, sumY = 0, sumXY = 0, sumX2 = 0, sumY2 = 0;
for (var i = 0; i < n; i++) {
var x = xValues[i];
var y = yValues[i];
if (isNaN(x) || isNaN(y)) {
document.getElementById("scatterResultOutput").innerHTML = "Invalid number format detected. Please ensure all values are valid numbers.";
return;
}
sumX += x;
sumY += y;
sumXY += x * y;
sumX2 += x * x;
sumY2 += y * y;
}
var meanX = sumX / n;
var meanY = sumY / n;
var numerator_r = 0;
var denominator_x = 0;
var denominator_y = 0;
for (var i = 0; i 0 && denominator_y > 0) {
correlation_r = numerator_r / Math.sqrt(denominator_x * denominator_y);
} else if (numerator_r === 0) {
correlation_r = 0; // Handle cases where all x or all y are the same, but no variation implies no linear relationship
} else {
correlation_r = 0; // Default to 0 if denominators are zero or negative due to floating point issues
}
var slope_m = 0;
if (denominator_x > 0) {
slope_m = numerator_r / denominator_x;
}
var intercept_b = meanY – slope_m * meanX;
var resultHTML = "";
resultHTML += "
Descriptive Statistics
";
resultHTML += "Number of Data Points (n): " + n + "";
resultHTML += "Mean of X (x̄): " + meanX.toFixed(4) + "";
resultHTML += "Mean of Y (ȳ): " + meanY.toFixed(4) + "";
resultHTML += "