Correlation ≠ Causation
Correlation is just a measure of the observed sample. It may suggest that there is a causal relationship within the data, but it does not prove that an increase of one variable results in an increase (or decrease) of another.
Lemonade Sales
Below is a game called Lemonade City. THe object of the game is use data analysis to run a sucessful lemonade business.
Each day, the player is told the weather forecast of the day. As expected the weather has large impact on the amount of lemonade sales. The hotter the day, the higher the demand for lemonade.
It is the player’s job to determine the optimal amount of lemonade that should be sold. Each glass of lemonade costs the player $0.50 and sells for $1.00. The other main cost is the cost of operation. Each lemonade store costs $20/day to operate.
Any lemonade unpurchased at the end of the day is unable to last the night and is discarded.
Over the course of 5 days, try to make as much money as possible.
namespace lemonadeprompt {
const MARGIN: number = 1;
const PADDING: number = 1;
const FONT: image.Font = image.font8;
const SCREEN_BACKGROUND = 15;
const BACKGROUND: number = 13;
const COLOR: number = 15;
const COST_COLOR: number = 2;
const BLINK_COLOR: number = 11;
let currentFunds = 0;
let nextTemp = 0;
let maxQuantity = 0;
let quantity = 0;
let confirm = false;
let inPrompt = false;
export function askForQuantity(temp: number, funds: number): number {
currentFunds = funds;
maxQuantity = ((currentFunds - 60) / 0.5);
quantity = Math.round(maxQuantity / 4) * 2;
nextTemp = temp;
controller._setUserEventsEnabled(false);
game.pushScene()
registerHandlers();
confirm = false;
game.onPaint(function () {
screen.fill(SCREEN_BACKGROUND);
drawTitle();
drawCurrentData();
drawCosts();
drawAmountLeft();
if (inPrompt) {
game.showDialog("Purchase " + quantity + " glasses?", undefined, "A = OK, B = CANCEL");
}
});
pauseUntil(() => confirm);
game.popScene();
controller._setUserEventsEnabled(true);
return quantity;
}
function drawTitle() {
screen.fillRect(MARGIN, MARGIN,
screen.width - (MARGIN * 2),
FONT.charHeight + (PADDING * 2),
BACKGROUND);
screen.printCenter("Purchase Lemonade", MARGIN + PADDING, COLOR, FONT);
}
enum TextLineKind {
Label,
Equation,
Amount
}
interface TextLine {
text: string;
kind: TextLineKind;
lineNumber: number;
cost: boolean;
}
function drawCurrentData() {
let top = 2 * MARGIN + 1 * FONT.charHeight + 2 * PADDING;
let lines: TextLine[] = [];
const NUM_LINES = 4;
lines.push({
text: "Temperature High:",
lineNumber: 0,
kind: TextLineKind.Label,
cost: false
});
lines.push({
text: nextTemp + "°F",
lineNumber: 1,
kind: TextLineKind.Amount,
cost: false
}); lines.push({
text: "Current Funds:",
lineNumber: 2,
kind: TextLineKind.Label,
cost: false
});
lines.push({
text: "$" + currentFunds + "",
lineNumber: 3,
kind: TextLineKind.Amount,
cost: false
});
screen.fillRect(MARGIN, top, screen.width - 2 * MARGIN, PADDING * 2 + (NUM_LINES * FONT.charHeight), BACKGROUND);
printLines(lines, top);
}
function drawCosts() {
let top = 3 * MARGIN + 5 * FONT.charHeight + 4 * PADDING;
let lines: TextLine[] = [];
const NUM_LINES = 6;
lines.push({
text: "Operations:",
lineNumber: 0,
kind: TextLineKind.Label,
cost: false
});
lines.push({
text: "$20 x 3 =",
lineNumber: 1,
kind: TextLineKind.Equation,
cost: false
});
lines.push({
text: "$(60)",
lineNumber: 1,
kind: TextLineKind.Amount,
cost: true
});
lines.push({
text: "Lemonade:",
lineNumber: 2,
kind: TextLineKind.Label,
cost: false
});
lines.push({
text: "$0.50 x " + quantity + " =",
lineNumber: 3,
kind: TextLineKind.Equation,
cost: false
});
lines.push({
text: "$(" + (quantity * 0.5) + ")",
lineNumber: 3,
kind: TextLineKind.Amount,
cost: true
});
lines.push({
text: "Total:",
lineNumber: 4,
kind: TextLineKind.Label,
cost: false
});
lines.push({
text: "$(" + (60 + (quantity * 0.5)) + ")",
lineNumber: 5,
kind: TextLineKind.Amount,
cost: true
});
screen.fillRect(MARGIN, top, screen.width - 2 * MARGIN, PADDING * 2 + (NUM_LINES * FONT.charHeight), BACKGROUND);
if (!inPrompt && Math.round(game.runtime() / 500) % 2 == 0) {
// blink
const BLINK_PADDING = 2;
let x = PADDING + 30 + ("$0.50 x ".length * FONT.charWidth);
let y = 3 * MARGIN + 5 * FONT.charHeight + 4 * PADDING + PADDING + 3 * (FONT.charHeight);
screen.fillRect(x - BLINK_PADDING, y - BLINK_PADDING,
(("" + quantity).length * FONT.charWidth) + (BLINK_PADDING * 2),
FONT.charHeight + (BLINK_PADDING * 2),
BLINK_COLOR);
}
printLines(lines, top);
}
function drawAmountLeft() {
let top = 4 * MARGIN + (11 * FONT.charHeight) + 6 * PADDING;
let lines: TextLine[] = [];
const NUM_LINES = 2;
lines.push({
text: "Funds Left:",
lineNumber: 0,
kind: TextLineKind.Label,
cost: false
});
lines.push({
text: "$" + (currentFunds - 60 - (quantity * 0.5)),
lineNumber: 1,
kind: TextLineKind.Amount,
cost: false
});
screen.fillRect(MARGIN, top, screen.width - 2 * MARGIN, screen.height - top - MARGIN, BACKGROUND);
printLines(lines, top);
}
function printLines(lines: TextLine[], top: number) {
for (let line of lines) {
let x = 0;
let y = 0;
if (line.kind == TextLineKind.Label) {
x = PADDING;
} else if (line.kind == TextLineKind.Equation) {
x = PADDING + 30;
} else if (line.kind == TextLineKind.Amount) {
const MAX_LENGTH = 7;
x = (screen.width - PADDING * 2) - PADDING - (MAX_LENGTH * FONT.charWidth);
}
y = PADDING + line.lineNumber * (FONT.charHeight);
screen.print(line.text, x + MARGIN, y + top, line.cost ? COST_COLOR : COLOR, FONT);
}
}
function adjustQuantity(increase: boolean) {
if (!inPrompt) {
quantity += increase ? 2 : -2;
quantity = Math.max(0, Math.min(maxQuantity, quantity));
}
}
function registerHandlers() {
controller.up.onEvent(SYSTEM_KEY_DOWN, function () {
adjustQuantity(true);
})
controller.up.onEvent(SYSTEM_KEY_REPEAT, function () {
adjustQuantity(true);
})
controller.down.onEvent(SYSTEM_KEY_DOWN, function () {
adjustQuantity(false);
})
controller.down.onEvent(SYSTEM_KEY_REPEAT, function () {
adjustQuantity(false);
})
controller.B.onEvent(SYSTEM_KEY_DOWN, function () {
inPrompt = false;
})
controller.A.onEvent(SYSTEM_KEY_DOWN, function () {
if (!inPrompt) {
inPrompt = true;
} else {
confirm = true;
inPrompt = false;
}
})
}
}
let storeSprites = [sprites.create(img`0`), sprites.create(img`0`), sprites.create(img`0`)];
let customerTimes: number[] = [];
let storeSales: number[] = [0, 0, 0];
storeSprites[0].setPosition(46, 48);
storeSprites[1].setPosition(135, 62);
storeSprites[2].setPosition(65, 80);
info.setLifeImage(img`
. . 1 1 1 1 . .
. 1 . . . . 1 .
. 1 1 1 1 1 1 .
. 1 . . . . 1 .
. 1 5 5 5 5 1 .
. 1 5 5 5 5 1 .
. 1 5 5 5 5 1 .
. 1 5 5 5 5 1 .
`);
info.setBackgroundColor(0x3)
info.setFontColor(0x1)
let waves: Sprite = null
scene.setBackgroundImage(img`
7777777777777bbbbbbbbbbbbbbbbbbb7777777777777777777777777bbbbbbbbbbbbbbbbbbbb7777777777777777777777777777777bbbbbbbbbbbbbbbbbbb777777777777777777777777777777777
777777777777777bbbbbbbbbbbbbbbbbbb777777777777777777777bbbbbbbbbbbbbbbbbbbb77777777777777777777777777777777777bbbbbbbbbbbbbbbbbbb7777777777777777777777777777777
77777777777777777bbbbbbbbbbbbbbbbbbb777777777777777777bbbbbbbbbbbbbbbbbbb777777777777777777777777777777777777777bbbbbbbbbbbbbbbbbbb77777777777777777777777777777
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777777777777777777777bbbbbbbbbbbbbbbbbbb7777fff777bbbbbbbbbbbbbbbbbbb7777777777777777777777777777777ffff777777777777bbbbbbbbbbbbbbbbbbb7777777777777777777777777
77777777777777777777777bbbbbbbbbbbbbbbbbbbfffffffbbbbbbbbbbbbbbbbbb7777777777777777777777777777777ffffffff777777777777bbbbbbbbbbbbbbbbbbb77777777777777777777777
7777777777777777777777777bbbbbbbbbbbbbbbfffff5fffffbbbbbbbbbbbbbb7777777777777777777777777777777fffffcffffff777777777777bbbbbbbbbbbbbbbbbbb777777777777777777777
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77777777777777777777777777fffff5555fffffff555555555555555555fffff77777777777777777fffffcccccccccccccccccccccccccccccffffff777777777777bbbbbbbbbbbbbbbbbbbbbbbbbb
7777777777777777777777777ffff5555fffffff5555555555555555555555fffff777777777777777fffffccccccccccccccccccccccccccccccccfff77777777777777bbbbbbbbbbbbbbbbbbbbbbbb
7777777777777777777777777fffff55555fffffff555555555555555555555ffff777777777777777fffffffccccccccccccccccccccccccccccccfff7777777777777777bbbbbbbbbbbbbbbbbbbbbb
7777777777777777777777777fffffff55555fffffff55555555555555555ffffff777777777777777ffccfffffccccccccccccccccccccccccccfffff777777777777777777bbbbbbbbbbbbbbbbbbbb
777777777777777777777777bff55fffff55555fffffff5555555555555fffff5ff777777777777777ffccccfffffccccccccccccccccccccccfffffff777777777777777777bbbbbbbbbbbbbbbbbbbb
7777777777777777777777bbbff5555fffff55555fffffff555555555fffff555ffb77777777777777ffccccccfffffccccccccccccccccccfffffccff7777777777777777bbbbbbbbbbbbbbbbbbbbbb
77777777777777777777bbbbbff555555fffff55555ffff55555555fffff55555ffbbb777777777777ffccccccccfffffccccccccccccccfffffccccff7777777777fff7bbbbbbbbbbbbbbbbbbbbbbbb
777777777777777777bbbbbbbff55555555fffff55555f5555555fffff5555555ffbbbbb7777777777ffccccccccccfffffccccccccccfffffccccccff77777777fffffffbbbbbbbbbbbbbbbbbbbbbbb
7777777777777777bbbbbbbbbff5555555555fffff555555555fffff555555555ffbbbbbbb77777777ffccccccccccccfffffccccccfffffccccccccff777777fffff5fffffbbbbbbbbbbbbbbbbbbbbb
77777777777777bbbbbbbbbbbff555555555555fffff55555fffff55555555555ffbbbbbbbbb777777ffccccccccccccccfffffccfffffccccccccccff7777fffff55555fffffbbbbbbbb777bbbbbbbb
777777777777bbbbbbbbbbbbbff55555555555555fffff5fffff5555555555555ffbbbbbbbbbbb7777ffccccccccccccccccffffffffccccccccccccff77fffff5555ff555fffffbbbb7777777bbbbbb
7777777777bbbbbbbbbbbbbbbff5555555555555555fffffff555555555555555ffbbbbbbbbbbbbb77fffcccccccccccccccccffffccccccccccccccfffffff5555fffff5555fffff77777777777bbbb
77777777bbbbbbbbbbbbbbbbbff555555555555555555fff55555555555555555ffbbbbbbbbbbbbbbbfffffccccccccccccccccffcccccccccccccccfffff5555ffffff5555555fffff77777777777bb
7777777bbbbbbbbbbbbbbbbbbfff55555555555555555ff555555555555555555ffbbbbbbbbbbbbbbbbbfffffccccccccccccccffcccccccccccccfffff5555ffffff55555555555fffff77777777777
77777bbbbbbbbbbbbbbbbbbb7fffff555555555555555ff5555555555555555ffffbbbbbbbbbbbbbbbbbbbfffffccccccccccccffcccccccccccfffff5555ffffff555555555555555fffff777777777
777bbbbbbbbbbbbbbbbbbb77777fffff5555555555555ff55555ffff55555fffff777bbbbbbbbbbbbbbbbbbbfffffccccccccccffcccccccccfffff5555fffffff555555555555555555fffff7777777
7bbbbbbbbbbbbbbbbbbb777777777fffff55555555555ff555ffffffff5fffff7777777bbbbbbbbbbbbbbbbbbbfffffccccccccffccccccccffff5555fffffff5555555555555555555555fffff77777
bbffffbbbbbbbbbbbb7777777777777fffff555555555ff5fffffcffffffff77777777777bbbbbbbbbbbbbbbbbbbfffffccccccffccccccfffffff55555fffffff555555555555555555555ffff77777
ffffffffbbbbbbbb77777777777777777fffff5555555ffffffcccccffffff7777777777777bbbbbbbbbbbbbbbbbbbfffffccccffccccfffffffffff55555fffffff55555555555555555ffffff77777
fffcffffffbbbb777777777777777777777fffff5555fffffcccccccccffffff7777777777777bbbbbbbbbbbbbbbbbbbfffffccffccfffffbff55fffff55555fffffff5555555555555fffff5ff77777
fcccccffffff7777777777777777777777777ffffffffffcccccccccccccffffff7777777777777bbbbbbbbbbbbbbbbbbbffffffffffffbbbff5555fffff55555fffffff555555555fffff555ff77777
ccccccccffffff7777777777777777777777777ffffffcccccccccccccccccffffff7777777777777bbbbbbbbbbbbbbbbbbbffffffffbbbbbff555555fffff55555ffff55555555fffff55555ff77777
ccccccccccffffff7777777777777777777777fffffcccccccccccccccccccccffffff7777777777777bbbbbbbbbbbbbbbbbbbffffbbbbbbbff55555555fffff55555f5555555fffff5555555ff77777
ccccccccccccffffff777777777777777777fffffcccccccccccccccccccccccccffffff7777777777777bbbbbbbbbbbbbbbbbbbbbbbbbbbbff5555555555fffff555555555fffff555555555ff77777
ccccccccccccccffffff77777777777777fffffcccccccccccccccccccccccccccccffffff7777777777777bbbbbbbbbbbbbbbbbbbbbbbbbbff555555555555fffff55555fffff55555555555ff77777
ccccccccccccccccffffff777777777777fffffccccccccccccccccccccccccccccccccfff777777777777777bbbbbbbbbbbbbbbbbbbbbbbbff55555555555555fffff5fffff5555555555555ff77777
ccccccccccccccccccffffff7777777777fffffffccccccccccccccccccccccccccccccfff77777777777777777bbbbbbbbbbbbbbbbbbbbbbff5555555555555555fffffff555555555555555ff77777
cccccccccccccccccccccfff7777777777ffccfffffccccccccccccccccccccccccccfffff7777777777777777777bbbbbbbbbbbbbbbbbbbbff555555555555555555fff55555555555555555ff77777
cccccccccccccccccccccfff7777777777ffccccfffffccccccccccccccccccccccfffffff777777777777777777bbbbbbbbbbbbbbbbbbbbbfff55555555555555555ff555555555555555555ff77777
cccccccccccccccccccfffff7777777777ffccccccfffffccccccccccccccccccfffffccff7777777777777777bbbbbbbbbbbbbbbbbbbbbbbfffff555555555555555ff5555555555555555ffff77777
cccccccccccccccccfffffff7777777777ffccccccccfffffccccccccccccccfffffccccff77777777777777bbbbbbbbbbbbbbbbbbbbbbbbbbbfffff5555555555555ff55555555555555fffff777777
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cccccccccccccfffffccccffbbb7777777ffccccccccccccfffffccccccfffffccccccccff7777777777bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbfffff555555555ff5555555555fffff7777777777
fccccccccccfffffccccccffbbbbb77777ffccccccccccccccfffffccfffffccccccccccff77777777bbbbbbbbbbbbbbbbbbbb777bbbbbbbbbbbbbbbbfffff5555555ff55555555fffff777777777777
fffccccccfffffccccccccffbbbbbbb777ffccccccccccccccccffffffffccccccccccccff777777bbbbbbbbbbbbbbbbbbbb7777777bbbbbbbbbbbbbbbbfffff55555ff555555fffff77777777777777
fffffccfffffccccccccccffbbbbbbbbb7fffcccccccccccccccccffffccccccccccccccff7777bbbbbbbbbbbbbbbbbbbb77777777777bbbbbbbbbbbbbbbbfffff555ff5555fffff7777777777777777
ccffffffffccccccccccccffbbbbbbbbbbfffffccccccccccccccccffcccccccccccccccff77bbbbbbbbbbbbbbbbbbbb777777777777777bbbbbbbbbbbbbbbbfffff5ff55fffff777777777777777777
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cccccffcccccccccccccccffbbbbbbbbbbbbbbfffffccccccccccccffccccccccccccfffffbbbbbbbbbbbbbbbbbbb7777777777777777777777bbbbbbbbbbbbbbbbfffffff7777777777777777777777
cccccffccccccccccccccfffbbbbbbbbbbbbbbbbfffffccccccccccffccccccccccfffffbbbbbbbbbbbbbbbbbbb777777777bbbbbbbbb77777777bbbbbbbbbbbbbbbbfff777777777777777777777777
cccccffccccccccccccfffffbbbbbbbbbbbbbbbbbbfffffccccccccffccccccccfffffbbbbbbbbbbbbbbbbbbb77777777bbbbbbbbbbbbbb77777777bbbbbbbbbbbbbbbbbbb7777777777777777777777
cccccffccccccccccfffff7777bbbbbbbbbbbbbbbbbbfffffccccccffccccccfffffbbbbbbbbbbbbbbbbbbb77777777bbbbbbbbbbbbbbbbbbbb777777bbbbbbbbbbbbbbbbbbb77777777777777777777
cccccffccccccccfffff77777777bbbbbbbbbbbbbbbbbbfffffccccffccccfffffbbbbbbbbbbbbbbbbbbb77777777bbbbb8888888888888bbbbbb777777bbbbbbbbbbbbbbbbbbb777777777777777777
cccccffccccccfffff777777777777bbbbbbbbbbbbbbbbbbfffffccffccfffffbbbbbbbbbbbbbbbbbbb777777777bbbbb8888888888888888bbbbb7777777bbbbbbbbbbbbbbbbbbb7777777777777777
fccccffccccffffff777777777777777bbbbbbbbbbbbbbbbbbffffffffffffbbbbbbbbbbbbbbbbbbb777777777bbbbbb888888888888888888bbbbb77777777bbbbbbbbbbbbbbbbbbb77777777777777
fffccffccfffff77777777777777777777bbbbbbbbbbbbbbbbbbffffffffbbbbbbbbbbbbbbbbbbb7777777777bbbbb8888888888888888888888bbbb777777777bbbbbbbbbbbbbbbbbbb777777777777
fffffffffff7777777777777777777777777bbbbbbbbbbbbbbbbbbffffbbbbbbbbbbbbbbbbbbb77777777777bbbbb8888888888888888888888888bbb7777777777bbbbbbbbbbbbbbbbbbb7777777777
77fffffff77777777777777777777777777777bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb777777777777bbbbb8888888888888888888888888888bbb7777777777bbbbbbbbbbbbbbbbbbb77777777
7777ff7777777777777777777777777777777777bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb7777777777777bbbbb888888888888888888888888888888bbbb7777777777bbbbbbbbbbbbbbbbbbb777777
777777777777777777777777777777777777777777bbbbbbbbbbbbbbbbbbbbbbbbbbbbb777777777777777bbbb88888888888888888888888888888888bbbb77777777777bbbbbbbbbbbbbbbbbbb7777
77777777777777777777777777777777777777777777bbbbbbbbbbbbbbbbbbbbbbbbb7777777777777777bbbbb888888888888888888888888888888888bbbb777777777777bbbbbbbbbbbbbbbbbbb77
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777777777777777777777777777777777777777777777bbbbbbbbbbbbbbbbbbbbbb777777777777777777bbbbb88888888888888888888888888888888888bbb777777777777777bbbbbbbbbbbbbbbbb
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77777777777777777777777777777777777777777bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb7777777777777bbbbb88888888888888888888888888888888888888bbb77777777777777777bbbbbbbbbbbbb
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7777777777777777777777777777777777fffffffffffbbbbbbbbbb777bbbbbbbbbbbbbbbbbbb777777777bbbb88888888888888888888888888888888888888bbb77777777777777777777bbbbbbbbb
77777777777777777777777777777777fffffccccffffffbbbbbb7777777bbbbbbbbbbbbbbbbbbb77777777bbbb88888888888888bbbbb888888888888888888bbb777777777777777777bbbbbbbbbbb
777777777777777777777777777777fffffccccccccffffffbb77777777777bbbbbbbbbbbbbbbbbbb7777777bbbbb88888888888bbbbbbbbb88888888888888bbbb7777777777777777bbbbbbbbbbbbb
7777777777777777777777777777fffffccccccccccccffffff7777777777777bbbbbbbbbbbbbbbbbbb777777bbbbbbbbbbbbbbbbb777bbbbbbbb888888888bbbb777777777777777bbbbbbbbbbbbbbb
7777777777777777777777777ffffffccccccccccccccccffffff7777777777777bbbbbbbbbbbbbbbbbbb777777bbbbbbbbbbbbbb777777bbbbbbbbbbbbbbbbbb77777777777777bffffbbbbbbbbbbbb
77777777777777777777777ffffffccccccccccccccccccccffffff7777777777777bbbbbbbbbbbbbbbbbbb777777bbbbbbbbbb7777777777bbbbbbbbbbbbbbb7777777777777bffffffffbbbbbbbbbb
777777777777777777777ffffffccccccccccccccccccccccccffffff7777777777777bbbbbbbbbbbbbbbbbbb77777777777777777777777777777777bbbb77777777777777bfffffcffffffbbbbbbbb
7777777777777777777ffffffccccccccccccccccccccccccccccffffff7777777777777bbbbbbbbbbbbbbbbbbb7777777777777777777777777777777777777777777777bfffffcccccffffffbbbbbb
7777777777777777777fffffccccccccccccccccccccccccccccccccfff777777777777777bbbbbbbbbbbbbbbbbbb777777777777777777777777777777777777777777bfffffcccccccccffffffbb77
777777777777777777bfffffffccccccccccccccccccccccccccccccfff777777fff77777777bbbbbbbbbbbbbbbbbbb77777777777777777777777777777777777777bfffffcccccccccccccffffff77
bb77777777777777bbbffccfffffccccccccccccccccccccccccccfffff7777fffffff77777777bbbbbbbbbbbbbbbbbbb7777777777777777777777777777777777bfffffcccccccccccccccccffffff
bbbb7777777777bbbbbffccccfffffccccccccccccccccccccccfffffff77fffff5fffff77777777bbbbbbbbbbbbbbbbbbb777777777777777777777777777777bfffffcccccccccccccccccccccffff
bbbbbb777777bbbbbbbffccccccfffffccccccccccccccccccfffffccfffffff55555fffff77777777bbbbbbbbbbbbbbbbbbb77777777777777777777777777bfffffcccccccccccccccccccccccccff
bbbbbbbb77bbbbbbbbbffccccccccfffffccccccccccccccfffffccccfffff5555ff555fffff77777777bbbbbbbbbbbbbbbbbbb7777777777777777777777bfffffccccccccccccccccccccccccccccc
bbbbbbbbbbbbbbbbbbbffccccccccccfffffccccccccccfffffccccfffff5555fffff5555fffff77777777bbbbbbbbbbbbbbbbbbb777777777777777777bbbfffffccccccccccccccccccccccccccccc
bbbbbbbbbbbbbbbbbbbffccccccccccccfffffccccccfffffccccfffff5555ffffff5555555fffff77777777bbbbbbbbbbbbbbbbbbb77777777777777bbbbbfffffffccccccccccccccccccccccccccc
bbbbbbbbbbbbbbbbbbbffccccccccccccccfffffccfffffccccfffff5555ffffff55555555555fffff77777777bbbbbbbbbbbbbbbbbbb7777777777bbbbbbbffccfffffccccccccccccccccccccccccc
bbbbbbbbbbbbbbbbbbbffccccccccccccccccffffffffccccfffff5555ffffff555555555555555fffff77777777bbbbbbbbbbbbbbbbbbb777777ffffbbbbbffccccfffffccccccccccccccccccccccf
bbbbbbbbbbbbbbbbbbbfffcccccccccccccccccffffccccfffff5555fffffff555555555555555555fffff77777777bbbbbbbbbbbbbbbbbbb77ffffffffbbbffccccccfffffccccccccccccccccccfff
dbbbbbbbbbbbbbbbbbbfffffccccccccccccccccffccccffff5555fffffff5555555555555555555555fffff77777777bbbbbbbbbbbbbbbbbfffffcffffffbffccccccccfffffccccccccccccccfffff
dddbbbbbbbbbbbbbbbbbbfffffccccccccccccccffccccfffff55555fffffff555555555555555555555ffff7777777777bbbbbbbbbbbbbfffffcccccfffffffccccccccccfffffccccccccccfffffcc
dddddbbbbbbbbbbbbbbbbbbfffffccccccccccccffccccfffffff55555fffffff55555555555555555ffffff777777777777bbbbbbbbbfffffcccccccccffffffcccccccccccfffffccccccfffffcccc
dddddddbbbbbbbbbbbbbbbbbbfffffccccccccccffccccff55fffff55555fffffff5555555555555fffff5ff77777777777777bbbbbfffffcccccccccccccffffffcccccccccccfffffccfffffcccccc
dddddddddbbbbbbbbbbbbbbbbbbfffffccccccccffccccff5555fffff55555fffffff555555555fffff555ff7777777777777777bfffffcccccccccccccccccffffffcccccccccccffffffffcccccccc
dddddddddddbbbbbbbbbbbbbbbbbbfffffccccccffccccff555555fffff55555ffff55555555fffff55555ff777777777777777fffffcccccccccccccccccccccffffffcccccccccccffffcccccccccc
dddddddddddddbbbbbbbbbbbbbbbbbbfffffccccffccccff55555555fffff55555f5555555fffff5555555ff7777777777777fffffcccccccccccccccccccccccccffffffccccccccccffccccccccccc
dddddddddddddddbbbbbbbbbbbbbbbbbbfffffccffccffff5555555555fffff555555555fffff555555555ff77777777777fffffcccccccccccccccccccccccccccccffffffccccccccffccccccccccc
dddddddddddddddddbbbbbbbbbbbbbbbbbbfffffffffffff555555555555fffff55555fffff55555555555ff7777777777bfffffccccccccccccccccccccccccccccccccfffccccccccffccccccccccc
dddddddddddddddddddbbbbbbbbbbbbbbbbbbffffffff7ff55555555555555fffff5fffff5555555555555ff77777777bbbfffffffccccccccccccccccccccccccccccccfffccccccccffccccccccccf
dddddddddddddddddddddbbbbbbbbbbbbbbbbbbffff777ff5555555555555555fffffff555555555555555ff777777bbbbbffccfffffccccccccccccccccccccccccccfffffccccccccffccccccccfff
dddddddddddddddddddddddbbbbbbbbbbbbbbbbbbb7777ff555555555555555555fff55555555555555555ff7777bbbbbbbffccccfffffccccccccccccccccccccccfffffffffccccccffccccccfffff
dddddddddddddddddddddddddbbbbbbbbbbbbbbbbbbb77fff55555555555555555ff555555555555555555ff77bbbbbbbbbffccccccfffffccccccccccccccccccfffffccffffffccccffccccfffff77
ddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbbfffff555555555555555ff5555555555555555ffffbbbbbbbbbbbffccccccccfffffccccccccccccccfffffccccffbfffffccffccfffff7777
ddddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbbfffff5555555555555ff55555555555555fffffbbbbbbbbbbbbffccccccccccfffffccccccccccfffffccccccffbbbffffffffffff777777
ddddddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbbfffff55555555555ff555555555555fffffbbbbbbbbbbbbbbffccccccccccccfffffccccccfffffccccccccffbbbbbffffffff77777777
ddddddddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbbfffff555555555ff5555555555fffffbbbbbbbbbbbbbbbbffccccccccccccccfffffccfffffccccccccccffbbbbbbbb7777777777777
ddddddddddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbbfffff5555555ff55555555fffffbbbbbbbbbbbbbbbbbbffccccccccccccccccffffffffccccccccccccffbbbbbbbbbb77777777777
ddddddddddddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbbfffff55555ff555555fffffbbbbbbbbbbbbbbbbbbbbfffcccccccccccccccccffffccccccccccccccffbbbbbbbbbbbb777777777
ddddddddddddddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbbfffff555ff5555fffffbbbbbbbbbbbbbbbbbbbbb7fffffccccccccccccccccffcccccccccccccccffbbbbbbbbbbbbbb7777777
ddddddddddddddddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbbfffff5ff55fffffbbbbbbbbbbbbbbbbbbbbb77777fffffccccccccccccccffccccccccccccccfffbbbbbbbbbbbbbbbb77777
ddddddddddddddddddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbbfffffffffffbbbbbbbbbbbbbbbbbbbbb777777777fffffccccccccccccffccccccccccccfffffbbbbbbbbbbbbbbbbbb777
ddddddddddddddddddddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbbfffffffbbbbbbbbbbbbbbbbbbbbb7777777777777fffffccccccccccffccccccccccfffff777bbbbbbbbbbbbbbbbbbb7
ddddddddddddddddddddddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbbfffbbbbbbbbbbbbbbbbbbbbb77777777777777777fffffccccccccffccccccccfffff7777777bbbbbbbbbbbbbbbbbb
ddddddddddddddddddddddddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb777777777777777777777fffffccccccffccccccfffff77777777777bbbbbbbbbbbbbbbb
ddddddddddddddddddddddddddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb7777777777777777777777777fffffccccffccccfffff777777777777777bbbbbbbbbbbbbb
ddddddddddddddddddddddddddddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb77777777777777777777777777777fffffccffccfffff7777777777777777777bbbbbbbbbbbb
ddddddddddddddddddddddddddddddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbbbbbbbb77777777777777777777777777777777777ffffffffffff77777777777777777777777bbbbbbbbbb
ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbbbb777777777777777777777777777777777777777ffffffff777777777777777777777777777bbbbbbbb
ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbb77777777777777777777777777777777777777777ffff7777777777777777777777777777777bbbbbb
ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddbbbbbbbbbbbbbbbbbb7777777777777777777777777777777777777777777777777777777777777777777777777777bbbb
`)
waves = sprites.create(img`
.......................................................
.......................................................
88.....................................................
888....................................................
88888..................................................
888888.................................................
88888888...............................................
6668888888.............................................
888688888888...........................................
8888666888888..........................................
88888886888888888......................................
888888886888888888.....................................
8888888886888888888....................................
88888888888888888888...................................
888888888888888888888..................................
88888888888888888888888888.............................
888888888888888888888888888............................
86668888888888888888888888888..........................
888868888888888888888888888888.........................
888886888888888888888888888888.........................
8888886888888888888888888886888........................
888888868888886666668888888866888888...................
88888886888888888888688888888868888888.................
888888888888888888888688888888868888888................
8888888888888888888888688888888866888888...............
88888888888888888888886888888888886688888.88...........
888888888888888888888886888888888888688888888888.......
88888888888888888888888868888888888888888888888888.....
`)
waves.setPosition(15, 111);
const lengthOfDay = 20000;
let time = 0;
const interval = 100;
const initialInvestment = 150;
info.setScore(initialInvestment);
showIntroDialog();
let dayNumber = 0;
newDay();
game.onUpdateInterval(interval, function () {
waves.setPosition(15 + 6 * Math.sin(game.runtime() / 1000), 111 - 3 * Math.sin(game.runtime() / 1000))
let newPallet = control.createBuffer(48);
let lightFactor = 0.6 + 0.4 * ((1 - Math.cos(2 * Math.PI * time / lengthOfDay)) / 2);
for (let i = 0; i < newPallet.length; i++) {
let value = origPalette.getNumber(NumberFormat.UInt8BE, i);
newPallet.setNumber(NumberFormat.UInt8BE, i, Math.round(value * lightFactor));
}
while (customerTimes.length > 0 && customerTimes[0] <= time) {
customerBuy();
customerTimes.splice(0, 1);
}
updateSales();
image.setPalette(newPallet);
if (time == lengthOfDay) {
dayEnd();
} else {
time += interval;
}
})
function showIntroDialog() {
game.showLongText("Welcome to the wonderful Lemonade City!", DialogLayout.Top);
game.showLongText("You are in charge of determining how much lemonade to sell to customers.", DialogLayout.Full);
game.showLongText("Each day, you will be given the weather forecast and will have to estimate how many people will want lemonade.", DialogLayout.Full);
game.showLongText("The hotter the day, the more people want lemonade. You can buy lemonade for $0.50 and can sell it for $1.00", DialogLayout.Full);
game.showLongText("Buy too much lemonade and it will expire overnight and not be sold. Buy too little and you won't make enough to cover the costs of the stores. ($20 per store per day)", DialogLayout.Full);
game.showLongText("Good Luck! You will have 5 days to make as much money as you can!", DialogLayout.Full);
}
function dayEnd() {
image.setPalette(origPalette);
displayDayEndScreen();
if (dayNumber < 5) {
newDay();
} else {
game.splash("After subtracting the $" + initialInvestment + " initial investment");
info.changeScoreBy(-initialInvestment);
if (info.score() >= 0) {
game.splash("Congrats! You made $" + (info.score()));
game.over(true);
} else {
game.splash("Oh no! You lost $" + (-info.score()));
game.over(false);
}
}
}
function displayDayEndScreen() {
let sum = 0;
for (let val of storeSales) {
sum += val;
}
game.splash("You sold " + sum + " glasses");
}
function newDay() {
if (info.score() <= 60) {
game.splash("Oh no! You don't have enough money to sell lemonade!");
game.over(false);
}
time = 0;
dayNumber++;
storeSales = [0, 0, 0];
let temp = Math.round(calculateNorm(76, 8));
displayNewDayScreen(temp);
let numberOfCustomers = calculateCustomers(temp);
customerTimes = [];
for (let i = 0; i < numberOfCustomers; i++) {
customerTimes.push(interval * randint(1, (lengthOfDay / interval) - 1));
}
sortCustomers();
}
function displayNewDayScreen(temp: number) {
let order: number = lemonadeprompt.askForQuantity(temp, info.score());
info.setScore(info.score() - (order * 0.5) - (20 * 3));
info.setLife(order);
}
function sortCustomers() {
// simple selection sort.
for (let i = 0; i < customerTimes.length - 1; ++i) {
for (let j = i + 1; j < customerTimes.length; ++j) {
if (customerTimes[i] > customerTimes[j]) {
let temp: number = customerTimes[i];
customerTimes[i] = customerTimes[j];
customerTimes[j] = temp;
}
}
}
}
function customerBuy() {
if (info.hasLife() && info.life() > 0) {
const storeIndex = randint(0, 2);
storeSales[storeIndex]++;
info.changeScoreBy(1);
info.changeLifeBy(-1);
}
}
info.onLifeZero(function () {
});
function updateSales() {
storeSprites.forEach(function (value: Sprite, index: number) {
value.say("" + storeSales[index]);
})
}
function calculateCustomers(temp: number) {
return calculateNorm(5 * temp - 200, 8);
}
function calculateNorm(mean: number, std: number) {
// Uses a Box-Muller Transform to generate a normally distributed sampling
let v1: number = Math.random();
let v2: number = Math.random();
return std * (Math.sqrt(-2 * Math.log(v2)) * Math.cos(2 * Math.PI * v1)) + mean;
}
const origPalette = hex`
000000
ffffff
ff2121
ff93c4
ff8135
fff609
249ca3
78dc52
003fad
87f2ff
8e2ec4
a4839f
5c406c
e5cdc4
91463d
000000`Example #1a: Plotting Data
The extension pxt-arcade-graphing extension has many helpful functions for displaying data. The first one to look at display.plotSeries.
let xValues: number[] = [1, 2, 3, 4, 5, 6];
let yValues: number[] = [6, 5, 4, 3, 2, 1];
display.plotSeries(xValues, yValues);This function takes 2 arrays: an array of x values and an array of y values and plots them on a graph. Each data point on the chart corresponds with an index. Looking at the example above, the first data point will have an x value of the xValues[0] which is 1 and a y value of yValues[0] which is 6.
Example #1b: Importing Data
For this Data Analysis section, there are a few data sets provided. Importing these data sets is done by importing the extension pxt-arcade-datasets. Once imported, there will be namespaces with functions to access the specific data for that lesson.
This lesson will use the data set with the namespace lemonadedata. This is a data set that contains data about the temperature and customer demand for lemonade on different days.
lemonadedata has the following functions and constants.
| Name | Description |
|---|---|
lemonadedata.NUMBER_OF_DAYS: number |
Returns the number of days recorded in the data set |
lemonadedata.getTemperature(day: number): number |
Returns the temperature recorded for the day specified |
lemonadedata.getSales(day: number): number |
Returns the amount of lemonade sold (in glasses) on the day specified |
let temperatures: number[] = [];
let sales: number[] = [];
for (let i = 0; i < lemonadedata.NUMBER_OF_DAYS; i++) {
temperatures.push(lemonadedata.getTemperature(i));
sales.push(lemonadedata.getSales(i));
}
game.splash("Temperature Mean: " + stats.mean(temperatures));
game.splash("Sales Mean: " + stats.mean(sales));Student Task #1: Graphing Lemonade Data
- Observe Example #1a and how it plots data using certain x and y values
- Observe Example #1b and how it gets the data about sales and temperature
- Build 2 arrays of data: One that is the temperature data and another that is the sales data
- Plot the data using the temperature as the x values and sales as the y values
Example #2: Correlation
The correlation of two arrays is the measure of how well the increase of one results in an increase in the other. For example, it’s expected that data points with higher temperatures also have higher lemonade sales.
The correlation of data falls between -1 and 1. If the correlation is 0, then the two variables seem to be completely independent. A positive correlation means that as one variable increases, so does the other. A negative correlation means that if one variable increases, the other decreases. The father away from 0, the more true this trend is.
Correlation can be calculated the following way:
let xValues: number[] = [10, 20, 30, 40, 50, 60];
let yValues: number[] = [70, 50, 50, 20, 30, 0];
game.splash("Correlation = " + stats.correlation(xValues, yValues));Student Task #2: Correlated Lemonade
- Import the data as shown in Example 1b
- Calculate the correlation between temperature and sales
Example #3: Line of Best Fit
For every data sets with x and y values that contains at least 2 data points, there exists what is known as the Line of Best Fit. This is a line that best approximates the data. It’s not guaranteed to go through every point, but it will at least be the closest to all the points in general.
Calculating the line of best fit is beyond the scope of this course, but the extensions used for this section contain functions that will calculate it.
Use the following functions when using the line of best fit
| Name | Description |
|---|---|
display.graphBestFit(xValues: number[], yValues: number[]) |
Graphs the line of best fit for the given data |
stats.slope(xValues: number[], yValues: number[]): number |
Returns the slope of the line of best fit for the given data |
stats.intercept(xValues: number[], yValues: number[]): number |
Returns the intercept of the line of best fit for the given data |
stats.lineOfBestFit(xValues: number[], yValues: number[]): number[] |
Returns a 2 element array consisting of the form [slope, intercept] for the line of best fit |
let xValues: number[] = [10, 20, 30, 40, 50, 60];
let yValues: number[] = [70, 50, 50, 20, 30, 0];
display.plotSeries(xValues, yValues);
display.graphBestFit(xValues, yValues);
game.splash("Slope = " + stats.slope(xValues, yValues));
game.splash("Intercept = " + stats.intercept(xValues, yValues));Student Task #3: Line of Best Lemonade
- Import the data as shown in Example 1b
- Plot the data on the display
- Graphs the line of best fit for the data to the display
- Observe whether or not this line approximates the data well
- Splash the slope of the line of best fit
- Splash the intercept of the line of best fit
- Challenge: Go back and play Lemonade City, but use data analysis to estimate customer sales