Toggle points on and off in altair

Question

I'd like to be able to toggle the display of the points on and off in the below chart. The 2 lines are the means of the points in groups 1 and 2. I thought there would be a way to do this using interactive but cannot find any examples. Any help is much appreciated.

import math
import numpy as np
import pandas as pd
import altair as alt

x = np.arange(0,math.pi,0.1);
y = np.sin(x); 
a, b = -0.2, 0.2

summary_df=[]

for i in range(0,2):
    for j in range(0,5):
        rand_y = (b - a)*np.random.rand(len(y)) + a
        df = pd.DataFrame({
            'group': i,
            'batch': j,
            'x': x,
            'y': y+rand_y
        })
        summary_df.append(df)
summary_df = pd.concat(summary_df)

base = alt.Chart(
    summary_df
).properties(
    width=200,
    height=400
)

mean_selection = alt.selection_multi(fields=['group'], bind='legend')
mean_line = base.mark_line(size=2).encode(
    x=alt.X('x:Q'),
    y=alt.Y('y:Q', aggregate='mean', axis=alt.Axis(title='y')),
    color='group:N',
    opacity=alt.condition(mean_selection, alt.value(1), alt.value(0.2))
).add_selection(
    mean_selection
).interactive()

all_selection = alt.selection_multi(fields=['group'], bind='legend')
all_points = base.mark_square(size=10).encode(
    y=alt.Y('y:Q', axis=alt.Axis(title='y')),
    x=alt.X('x:Q',),
    color='group:N',
    tooltip='batch:N',
    opacity=alt.condition(all_selection, alt.value(1), alt.value(0.2))
).add_selection(
    all_selection
).interactive()


(mean_line+all_points)