Scatter Plots: Colour, Size & Fits

The problem, from first principles

A scatter plot is the honest way to look at two numbers per observation: one dot per row, no line implying that neighbouring dots are connected. Its power is that a dot has more than a position. Its size can carry a third number (population, revenue), its colour can carry a fourth (a score, a temperature), and a line drawn over the dots can summarise the trend. A reader should be able to tell what each encoding means, which is why a colour scale needs a colourbar and a fitted line needs a label.

This question builds the three layers of a typical scatter figure: the dots with size and colour, a least-squares trend line, and a second layer that marks the points that sit unusually far from the average.

From theory to code

Implement scatter_chart(x, y, sizes, values, label), fit_line(ax, x, y) and highlight_outliers(ax, x, y, k). The signatures and docstrings are already in the editor.

Constraints

• scatter_chart returns (fig, ax, points): a new figure with one scatter of (x, y), marker areas sizes, coloured by values with the viridis colormap, and a colourbar whose label is label. points is the scatter's collection.
• fit_line(ax, x, y) computes the ordinary least-squares line y = slope * x + intercept through the points and draws it on ax as one line segment from the smallest x to the largest x, colour "red", label "fit". It returns (slope, intercept) as Python floats.
• highlight_outliers(ax, x, y, k) draws, as a second scatter on ax, the points whose y differs from the mean of y by more than k times the (population) standard deviation of y. They are red, with marker area 80. It returns the number of outliers as an int. If there are none it draws nothing.
• x, y, sizes, values are equal-length sequences of numbers. Do not call plt.show().

Hints