{
"$schema": "https://vega.github.io/schema/vega-lite/v5.json",
"description": "Regression with error bands.",
"data": {
"sequence": {
"start": 1,
"stop": 1001,
"step": 1,
"as": "x"
}
},
"transform": [
{
"calculate": "50 + 0.05 * datum.x + sampleNormal(0, 10)",
"as": "y"
}
],
"hconcat": [
{
"layer": [
{
"mark": "point",
"encoding": {
"x": {
"field": "x",
"type": "quantitative",
"title": "Variable X"
},
"y": {
"field": "y",
"type": "quantitative",
"title": "Variable Y"
}
}
}
],
"title": "Stochastic Process with Drift"
},
{
"layer": [
{
"mark": "point",
"encoding": {
"x": {
"field": "x",
"type": "quantitative",
"title": "Variable X"
},
"y": {
"field": "y",
"type": "quantitative",
"title": "Variable Y"
}
}
},
{
"transform": [
{
"regression": "y",
"on": "x",
"method": "linear",
"as": [
"x",
"y"
]
}
],
"mark": {
"type": "line",
"color": "blue"
},
"encoding": {
"x": {
"field": "x",
"type": "quantitative"
},
"y": {
"field": "y",
"type": "quantitative"
}
}
}
],
"title": "Linear Regression Line"
},
{
"layer": [
{
"mark": "point",
"encoding": {
"x": {
"field": "x",
"type": "quantitative",
"title": "Variable X"
},
"y": {
"field": "y",
"type": "quantitative",
"title": "Variable Y"
}
}
},
{
"transform": [
{
"regression": "y",
"on": "x",
"method": "linear",
"as": [
"x_hat",
"y_hat"
]
},
{
"calculate": "datum.y_hat - datum.y",
"as": "errors"
},
{
"calculate": "datum.y_hat + 1.96 * 5",
"as": "ci_upper"
},
{
"calculate": "datum.y_hat - 1.96 * 5",
"as": "ci_lower"
}
],
"layer": [
{
"mark": {
"type": "line",
"color": "blue"
},
"encoding": {
"x": {
"field": "x_hat",
"type": "quantitative"
},
"y": {
"field": "y_hat",
"type": "quantitative"
}
}
},
{
"mark": {
"type": "errorband",
"opacity": 0.6
},
"encoding": {
"x": {
"field": "x_hat",
"type": "quantitative"
},
"y": {
"field": "ci_upper",
"type": "quantitative"
},
"y2": {
"field": "ci_lower"
},
"color": {
"value": "green"
}
}
}
]
}
],
"title": "80%-ile Confident Intervals"
}
]
}