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Indicate goodness of fit of regression line

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The goodness of fit of a regression line is the percentage
of the variance of the y values that is explained by the
dependence on the x values.

Set the alpha value of the regression line to this goodness
of fit.

Further, set the width of the regression line to a standard
deviation of the values from the regression line valies.

Signed-off-by: Robert C. Helling <helling@atdotde.de>
This commit is contained in:
Robert C. Helling 2021-01-10 00:12:41 +01:00
parent 622e5aab69
commit d83c9b5246
2 changed files with 50 additions and 32 deletions
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74
stats/statsview.cpp
View file

@ -723,13 +723,14 @@ void StatsView::QuartileMarker::updatePosition()
x + quartileMarkerSize / 2.0, y); x + quartileMarkerSize / 2.0, y);
} }
StatsView::RegressionLine::RegressionLine(double a, double b, QPen pen, QGraphicsScene *scene, StatsAxis *xAxis, StatsAxis *yAxis) : StatsView::RegressionLine::RegressionLine(double a, double b, double width, QBrush brush, QGraphicsScene *scene, StatsAxis *xAxis, StatsAxis *yAxis) :
item(createItemPtr<QGraphicsLineItem>(scene)), item(createItemPtr<QGraphicsPolygonItem>(scene)),
xAxis(xAxis), yAxis(yAxis), xAxis(xAxis), yAxis(yAxis),
a(a), b(b) a(a), b(b), width(width)
{ {
item->setZValue(ZValues::chartFeatures); item->setZValue(ZValues::chartFeatures);
item->setPen(pen); item->setPen(Qt::NoPen);
item->setBrush(brush);
} }
void StatsView::RegressionLine::updatePosition() void StatsView::RegressionLine::updatePosition()
@ -738,21 +739,16 @@ void StatsView::RegressionLine::updatePosition()
return; return;
auto [minX, maxX] = xAxis->minMax(); auto [minX, maxX] = xAxis->minMax();
auto [minY, maxY] = yAxis->minMax(); auto [minY, maxY] = yAxis->minMax();
double y1 = a * minX + b;
double y2 = a * maxX + b;
// If not fully inside drawing region, do clipping. QPolygonF poly;
if ((y1 < minY || y1 > maxY || y2 < minY || y2 > maxY) && fabs(a) > 0.0001) { poly << QPointF(xAxis->toScreen(minX), yAxis->toScreen(a * minX + b + width))
// Intersections with y = minY and y = maxY lines << QPointF(xAxis->toScreen(maxX), yAxis->toScreen(a * maxX + b + width))
double intersect_x1 = (minY - b) / a; << QPointF(xAxis->toScreen(maxX), yAxis->toScreen(a * maxX + b - width))
double intersect_x2 = (maxY - b) / a; << QPointF(xAxis->toScreen(minX), yAxis->toScreen(a * minX + b - width))
if (intersect_x1 > intersect_x2) << QPointF(xAxis->toScreen(minX), yAxis->toScreen(a * minX + b + width));
std::swap(intersect_x1, intersect_x2); QRectF box(QPoint(xAxis->toScreen(minX), yAxis->toScreen(minY)), QPoint(xAxis->toScreen(maxX), yAxis->toScreen(maxY)));
minX = std::max(minX, intersect_x1);
maxX = std::min(maxX, intersect_x2); item->setPolygon(poly.intersected(box));
}
item->setLine(xAxis->toScreen(minX), yAxis->toScreen(a * minX + b),
xAxis->toScreen(maxX), yAxis->toScreen(a * maxX + b));
} }
StatsView::HistogramMarker::HistogramMarker(double val, bool horizontal, QPen pen, QGraphicsScene *scene, StatsAxis *xAxis, StatsAxis *yAxis) : StatsView::HistogramMarker::HistogramMarker(double val, bool horizontal, QPen pen, QGraphicsScene *scene, StatsAxis *xAxis, StatsAxis *yAxis) :
@ -784,9 +780,15 @@ void StatsView::addHistogramMarker(double pos, const QPen &pen, bool isHorizonta
histogramMarkers.emplace_back(pos, isHorizontal, pen, &scene, xAxis, yAxis); histogramMarkers.emplace_back(pos, isHorizontal, pen, &scene, xAxis, yAxis);
} }
void StatsView::addLinearRegression(double a, double b, double minX, double maxX, double minY, double maxY, StatsAxis *xAxis, StatsAxis *yAxis) void StatsView::addLinearRegression(double a, double b, double res2, double r2, double minX, double maxX, double minY, double maxY, StatsAxis *xAxis, StatsAxis *yAxis)
{ {
regressionLines.emplace_back(a, b, QPen(Qt::red), &scene, xAxis, yAxis); QColor red = QColor(Qt::red);
red.setAlphaF(r2);
QPen pen(red);
QBrush brush(red);
brush.setStyle(Qt::SolidPattern);
regressionLines.emplace_back(a, b, sqrt(res2), brush, &scene, xAxis, yAxis);
} }
// Yikes, we get our data in different kinds of (bin, value) pairs. // Yikes, we get our data in different kinds of (bin, value) pairs.
@ -1025,12 +1027,21 @@ static bool is_linear_regression(int sample_size, double cov, double sx2, double
return true; // can't happen, as we tested for sample_size above. return true; // can't happen, as we tested for sample_size above.
} }
// Returns the coefficients [a,b] of the line y = ax + b struct regression_data {
// If case of an undetermined regression or one with infinite slope, returns [nan, nan] double a,b;
static std::pair<double, double> linear_regression(const std::vector<StatsScatterItem> &v) double res2, r2;
};
// Returns the coefficients a,b of the line y = ax + b
// as well as the variance of the residuals (averaged residual squared) as res2
// and r^2 = 1.0 - variance of data / res2 which is the fraction of the variance of
// the data that is explained by the linear regression.
// If case of an undetermined regression or one with infinite slope, returns {nan, nan, 0.0, 0.0}
static struct regression_data linear_regression(const std::vector<StatsScatterItem> &v)
{ {
if (v.size() < 2) if (v.size() < 2)
return { NaN, NaN }; return { .a = NaN, .b = NaN, .res2 = 0.0, .r2 = 0.0};
// First, calculate the x and y average // First, calculate the x and y average
double avg_x = 0.0, avg_y = 0.0; double avg_x = 0.0, avg_y = 0.0;
@ -1051,10 +1062,15 @@ static std::pair<double, double> linear_regression(const std::vector<StatsScatte
bool is_linear = is_linear_regression((int)v.size(), cov, sx2, sy2); bool is_linear = is_linear_regression((int)v.size(), cov, sx2, sy2);
if (fabs(sx2) < 1e-10 || !is_linear) // If t is not statistically significant, do not plot the regression line. if (fabs(sx2) < 1e-10 || !is_linear) // If t is not statistically significant, do not plot the regression line.
return { NaN, NaN }; return { .a = NaN, .b = NaN, .res2 = 0.0, .r2 = 0.0};
double a = cov / sx2; double a = cov / sx2;
double b = avg_y - a * avg_x; double b = avg_y - a * avg_x;
return { a, b };
double res2 = 0.0;
for (auto [x, y, d]: v)
res2 += (y - a * x - b) * (y - a * x - b);
double r2 = sy2 > 0.0 ? 1.0 - res2 / sy2 : 1.0;
return { .a = a, .b = b, .res2 = res2 / v.size(), .r2 = r2 };
} }
void StatsView::plotScatter(const std::vector<dive *> &dives, const StatsVariable *categoryVariable, const StatsVariable *valueVariable) void StatsView::plotScatter(const std::vector<dive *> &dives, const StatsVariable *categoryVariable, const StatsVariable *valueVariable)
@ -1084,10 +1100,10 @@ void StatsView::plotScatter(const std::vector<dive *> &dives, const StatsVariabl
series->append(dive, x, y); series->append(dive, x, y);
// y = ax + b // y = ax + b
auto [a, b] = linear_regression(points); struct regression_data reg = linear_regression(points);
if (!std::isnan(a)) { if (!std::isnan(reg.a)) {
auto [minx, maxx] = axisX->minMax(); auto [minx, maxx] = axisX->minMax();
auto [miny, maxy] = axisY->minMax(); auto [miny, maxy] = axisY->minMax();
addLinearRegression(a, b, minx, maxx, miny, maxy, xAxis, yAxis); addLinearRegression(reg.a, reg.b, reg.res2, reg.r2, minx, maxx, miny, maxy, xAxis, yAxis);
} }
} }

8
stats/statsview.h
View file

@ -9,6 +9,7 @@
#include <QImage> #include <QImage>
#include <QPainter> #include <QPainter>
#include <QQuickItem> #include <QQuickItem>
#include <QGraphicsPolygonItem>
struct dive; struct dive;
struct StatsBinner; struct StatsBinner;
@ -117,11 +118,12 @@ private:
// A regression line // A regression line
struct RegressionLine { struct RegressionLine {
std::unique_ptr<QGraphicsLineItem> item; std::unique_ptr<QGraphicsPolygonItem> item;
StatsAxis *xAxis, *yAxis; StatsAxis *xAxis, *yAxis;
double a, b; // y = ax + b double a, b; // y = ax + b
double width;
void updatePosition(); void updatePosition();
RegressionLine(double a, double b, QPen pen, QGraphicsScene *scene, StatsAxis *xAxis, StatsAxis *yAxis); RegressionLine(double a, double b, double width, QBrush brush, QGraphicsScene *scene, StatsAxis *xAxis, StatsAxis *yAxis);
}; };
// A line marking median or mean in histograms // A line marking median or mean in histograms
@ -134,7 +136,7 @@ private:
HistogramMarker(double val, bool horizontal, QPen pen, QGraphicsScene *scene, StatsAxis *xAxis, StatsAxis *yAxis); HistogramMarker(double val, bool horizontal, QPen pen, QGraphicsScene *scene, StatsAxis *xAxis, StatsAxis *yAxis);
}; };
void addLinearRegression(double a, double b, double minX, double maxX, double minY, double maxY, StatsAxis *xAxis, StatsAxis *yAxis); void addLinearRegression(double a, double b, double res2, double r2, double minX, double maxX, double minY, double maxY, StatsAxis *xAxis, StatsAxis *yAxis);
void addHistogramMarker(double pos, const QPen &pen, bool isHorizontal, StatsAxis *xAxis, StatsAxis *yAxis); void addHistogramMarker(double pos, const QPen &pen, bool isHorizontal, StatsAxis *xAxis, StatsAxis *yAxis);
StatsState state; StatsState state;