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Table to Scatter Plot: Identifying Variable Relationships and Trend Lines

Table to Scatter Plot: Identifying Variable Relationships and Trend Lines
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2023-12-21 11:32
Coordinate GeometryProbability & StatisticsGraphing
This example demonstrates how to convert a data table into a scatter plot, teaching students to identify dependent and independent variables and determine whether the relationship is positive, negative, or shows no correlation. Key mathematical concepts include labeling scatter plot axes correctly, plotting data points, approximating trend lines, and interpreting correlations. Construction highlights: Uses TableText to render tabular data, Sample and RandomUniform to generate random sample data points, Zip and Sequence to construct coordinate pairs, and Polygon to visualize data regions with interactive draggable elements for exploring different data distributions. Designed for grades 6-8 students in statistics and probability units, developing data analysis and visualization skills.

GeoGebra Commands & Parameters

  1. RandomUniform(0, 0.99, 400) → allRandoms, {0.9294057287478594, 0.1321211127431961, 0.18473602354721605, 0.5213883994300303, 0.15089809311475713, 0.07616616444182976, 0.2985144370369922, 0.9482838448925606, 0.2895301751186992, 0.8104704639559568, 0.1523234706420959, 0.03211053171545286, 0.682209760787389, 0.02994822610885676, 0.6420335038325583, 0.5673648207265708, 0.13826791083611198, 0.33261095678209524, 0.8046651450789795, 0.514335246868874, 0.11812430123907386, 0.2081922831318171, 0.5843989670267391, 0.9804859763553179, 0.7005928839634215, 0.4734234158747672, 0.7623590270764886, 0.44930650362578767, 0.7983014543436712, 0.3910280545637683, 0.3184867485537182, 0.2896880590178682, 0.6161189585295899, 0.7135970971971709, 0.9384599575821412, 0.250946841325868, 0.3188407628151292, 0.4210333501005215, 0.23418846707747173, 0.7491129208462396, 0.2216784867608295, 0.6512224874804419, 0.39293099346989036, 0.7990388079532917, 0.8803321220919423, 0.39799173281037936, 0.19752932798265974, 0.2942550052226635, 0.9865929171030268, 0.7882587037667782, 0.3986446658060227, 0.8123101922016317, 0.9305323169546066, 0.4415524112050654, 0.6392068201635177, 0.7175818277309987, 0.6713779904778084, 0.17980573403153483, 0.5115509237484405, 0.026228496945048023, 0.47615932467506566, 0.6134719322667911, 0.2589173801995958, 0.969078381978881, 0.8581256088343231, 0.571610701411292, 0.3851293026920084, 0.5378087232356357, 0.20579714182704884, 0.8486176342903383, 0.24933824720383888, 0.737769504374108, 0.18830436048180646, 0.1687382676383623, 0.5267421951139596, 0.9072394080116404, 0.5534028186673166, 0.0014122467532378402, 0.4411315140342831, 0.11777587311540204, 0.35122126570986506, 0.025834395089116523, 0.39100662258662316, 0.6236316263549101, 0.1494082000541014, 0.2918995444403963, 0.7378379005739288, 0.21995721078833483, 0.6338864837710819, 0.7569137969527615, 0.3728016308219327, 0.11969574658472563, 0.2839084182404234, 0.9131106126859725, 0.6670270703681977, 0.927698417459083, 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0.5617435576030244, 0.2074054200374425, 0.7835092122521287, 0.4029271462469255, 0.08368089751513501, 0.7640832492664408, 0.60523871046076, 0.7299566609025295, 0.24305532915391834, 0.7114748017609486, 0.9652196051263823, 0.04194575510277668, 0.8616205616494008, 0.07015916170903752, 0.26235359075118886, 0.7371443072846346, 0.8030159190266957, 0.8054476849372211, 0.6599013772577399, 0.33817428731238114, 0.2055146238004397, 0.9521065465121716, 0.5766993563552256, 0.05476880742086677, 0.8674809163061352, 0.8583549052252779, 0.15789704568294838, 0.29971687595303, 0.7755346855020537, 0.1650722861183215, 0.7380800904851047, 0.15239920896108713, 0.11326368434658599, 0.43453711462564526, 0.42545416968694516, 0.9894084308154665, 0.7896029663789065, 0.32234525122525054, 0.4200129645007738, 0.23279154027177465, 0.4607180246765904, 0.6064201298084927, 0.9312989784248837, 0.8834352114638572, 0.7373820629065633, 0.5082279270161856, 0.3824892854357519, 0.7800342188570007, 0.4514300756496208, 0.1934496051868543, 0.15709841694540735, 0.9429407589169807, 0.7599014125879946, 0.4024380355183621, 0.05258890539530744, 0.7969874235892996, 0.6039492221419567, 0.9048016436502337, 0.31161562756063693, 0.7781090763907477, 0.6714999982811201, 0.34740772036289974, 0.6565027239495261, 0.9252583451627913, 0.16798745698732362, 0.9709870237167006, 0.19586313483674492, 0.20171763182908148, 0.9882649933736496, 0.8273470820430838, 0.9440179150668241, 0.13845471968988513, 0.5950172581162366, 0.6569660617028897, 0.01405887654385427, 0.9166519620221508, 0.6046461111981203, 0.12543948979859798, 0.5140207351037469, 0.6769587295036426, 0.6006973999614473, 0.726891145951502, 0.5926893709673593, 0.35937435515001614, 0.8674252782465598, 0.06303577539399921, 0.2570713589947412, 0.4999634769331063, 0.6120563721654704, 0.9180943673998349, 0.5074849047567903, 0.6588386202089936, 0.3037213724494516, 0.2722146242778566, 0.5686056085338127, 0.2980141224897493, 0.9798632298357035, 0.7794373499136129, 0.8056113931419818, 0.4778433832784282, 0.14720960919806028, 0.3105760554846783, 0.2138180862764316, 0.8767962399078681, 0.3641156295199407, 0.5266403727462795, 0.527883715555843, 0.12131569042686044, 0.4642354270159115, 0.464635490167917, 0.9527817486033195, 0.6304129410236118, 0.9480744252072287, 0.8047080729498919, 0.143304890826578, 0.05351749736069863, 0.5890023891738138, 0.2556854697758978, 0.5118580995511132, 0.09989361060238758, 0.6537747776808859, 0.49506894549105235, 0.5557361678934163, 0.9336670690248512, 0.004513945778141123, 0.8394921623312959, 0.2949531643448086, 0.07017604750980537, 0.29944349820414917, 0.8625457297439956, 0.4400024773455257, 0.6569673898135652, 0.013448624259287324, 0.9086939022278764, 0.02567360863885439, 0.6963042696259921, 0.42675196765106244, 0.8247739074903429, 0.8522379435583558, 0.965533983780746, 0.8506483673967392, 0.704269027398394, 0.26893797799992525, 0.4870842730954474, 0.3933348462600791, 0.05418557074736222, 0.566776308411195, 0.8012141053625785, 0.026399771209549634, 0.2799399863526015, 0.3680972982449731, 0.16193981891040451, 0.693503760225424, 0.14017570015237465, 0.4893907819583201, 0.34978972212995085, 0.9071877426946389, 0.19088110433253133, 0.3711203135866557, 0.8042105152916426, 0.8075859959018189, 0.22656813435337086, 0.10418801613995202, 0.3735561689466787, 0.1981015436478726, 0.15559722449447055, 0.9168975663193625, 0.8316343500015365, 0.9678175427351839, 0.6169985588003948, 0.8389610045723127, 0.4867690647007498, 0.45857264466137393, 0.3973400306548856, 0.25021921881812637, 0.5122567271471221, 0.6362207738575398, 0.36833131494289806, 0.7913055971269205, 0.2759512898477671, 0.9706241268736999, 0.7189298207153219, 0.6514812715242024, 0.2315085682920754, 0.5973956850224588, 0.8797276016380886, 0.15530504140645893, 0.48455243153193645, 0.7163115055068995, 0.5323495299274656, 0.184674863783432, 0.7436952595206175, 0.9666549734432145, 0.012482142690245666, 0.3060877487765123, 0.738952885455744, 0.9385343955958699, 0.3419781166427332, 0.3647133923479987, 0.028638775613926228, 0.5314323271505411, 0.1332453538725631, 0.5370623061285421, 0.44030465983600386, 0.946898916072253, 0.4778309432040263, 0.20265192050152261, 0.4317152571790735, 0.12139387450878639, 0.26074843002701087, 0.6521351891960148, 0.7842012107628414, 0.8778104370101564, 0.05267378517915921, 0.7948539887979152, 0.41303026124995107, 0.08018206861839672, 0.163648260200504, 0.042715132214380815, 0.17766847969256538, 0.615476278529024, 0.3543781384739694, 0.3196600127070259, 0.9189734965074922, 0.9692222734147344, 0.9446097905668865, 0.9568093368320497, 0.32046917472407527, 0.16799825382786043, 0.3023846714307851, 0.14261237078142405, 0.20689578733995787, 0.05152103852424927, 0.7532425291868539, 0.15501602826866842, 0.865212724552379, 0.11023453945286005, 0.5546422332876457, 0.408791567791371, 0.7011499967537764, 0.11088646983342437, 0.35800865745774874, 0.9157180031743896, 0.418262880364189, 0.952610625127224, 0.42888942100151817, 0.37831840679260303, 0.22623837944093741, 0.8794998967376885, 0.8847199807588139, 0.37928199435765303, 0.1109352249194545, 0.5425591434164342, 0.7596460199219328, 0.19857666521510142}
  2. Take(allRandoms, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. Element({randomSlope1, randomSlope2, 0}, randomProb) → randomSlope
  4. If(randomProb ≟ 1, 150 - floor((currentRandomSeeds(40) * 40)), 20 + floor((currentRandomSeeds(40) * 10))) → yInt
  5. If(randomProb ≟ 1, 150, randomProb ≟ 2, 100, 30) → numMax
  6. If(randomProb ≟ 1, 5, multiplier) → rounding
  7. If(randomProb ≟ 1, 40, randomProb ≟ 2, 20, 5) → numMin
  8. Sample(Sequence[1, 10], 6, false) → sampleY1, {7, 1, 2, 6, 4, 9}
  9. Sample(Sequence[1, 10], 6, false) → sampleY2, {4, 1, 6, 3, 5, 7}
  10. Sample(Sequence[1, 10], 6, false) → sampleY3, {9, 2, 5, 10, 1, 3}
  11. Sample(Sequence[1, 10], 6, false) → sampleY4, {3, 7, 4, 8, 9, 10}
  12. Sample(Sequence[2, 5], 4, true) → sampleX1, {4, 3, 5, 3}
  13. Sample(Sequence[2, 5], 4, true) → sampleX2, {4, 4, 2, 5}
  14. Sample(Sequence[2, 5], 4, true) → sampleX3, {5, 5, 3, 3}
  15. Element({sampleY1, sampleY2, sampleY3, sampleY4}, 1 + Mod[countQuestion, 4]) → sampleYUnordered
  16. Element({Reverse[Sort[sampleYUnordered]], Sort[sampleYUnordered], sampleYUnordered}, caseNum) → sampleY
  17. Sort(Join[{{1, 6}, Element[{sampleX1, sampleX2, sampleX3}, 1 + Mod[countQuestion, 3]]}]) → sampleX
  18. Element({20, 40, 30}, caseNum) → yRange
  19. Element({105, 35, 0}, caseNum) → yOffset
  20. Zip((A, (yRange * B / 10) + yOffset), A, sampleX, B, sampleY) → allPoints
  21. Polygon(polygonCoords) → dragArea
  22. Midpoint(Vertex[dragArea, 1], Vertex[dragArea, 3]) → DragCenter
  23. If(¬correctLabels, 1, 2) → step
  24. If(randomProb ≠ 2, ((42 + 2) * pixelHeightConvert), ((55 + 2) * pixelHeightConvert)) → titleHeight
  25. If(randomProb ≟ 2, 0.2, 1) → scalingFactor
  26. Polygon(graphDimPoints) → graphArea
  27. Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBox
  28. Corner(5) → layoutAppSize
  29. Segment((0, 0), (graphDims(3), 0)) → axisX
  30. Segment((0, 0), (0, graphDims(4))) → axisY
  31. Zip(PixelsToPoint[(dimensions(1), dimensions(2)), (dimensions(3), dimensions(4)), (800, 500), TablePX + A], A, {(55, 35 / 2 + 5), (155, 35 / 2 + 5)}) → homePoints
  32. Text(currentMoveLabel(1), PMoveX, true, true, 0, 0) → textLabelX
  33. If(countQuestion ≟ 0, 1, 1 + floor((currentRandomSeeds(1) * 2))) → randomOrder
  34. Sequence(Corner[textLabelX, n], n, 1, 4) → xLabelCorners
  35. If(numTime ≤ 12, numTime + "\;am", numTime - 12 + "\;pm") → textTime
  36. Sequence(Text[If[randomProb ≟ 1, 10, 0] + (n * If[randomProb ≟ 1, 10, 1]), (n, (-0.5 * multiplier)), true, true, 0, -1], n, 1, 6) → textXAxis12
  37. Sequence(Text[ConvertTime[(2 * n) + 6], (n, 0), true, true, 0, -1], n, 1, 6) → textXAxis3
  38. If(caseNum < 3, textXAxis12, textXAxis3) → textXAxis
  39. Append(((((("\cellcolor{" * If[step ≟ 2 ∨ PMoveX ≠ homePoints(1), "#FFFFFF", colorShade]) * "}") * If[PMoveX ≟ homePoints(1), "\phantom{", "{"]) * tableLabel(1)) * "}"), Zip[(((("\cellcolor{" * If[animateStage ≟ B, colorPinkLight, "#FFFFFF"]) * "}{") * textXAxis(x(A))) * "}"), A, allPoints, B, {1, 2, 3, 4, 5, 6}]) → col1
  40. Append(((((("\cellcolor{" * If[step ≟ 2 ∨ PMoveY ≠ homePoints(2), "#FFFFFF", colorShade]) * "}") * If[PMoveY ≟ homePoints(2), "\phantom{", "{"]) * tableLabel(2)) * "}"), Zip[(((("\cellcolor{" * If[animateStage ≟ B, colorPinkLight, "#FFFFFF"]) * "}{") * y(A)) * "}"), A, allPoints, B, {1, 2, 3, 4, 5, 6}]) → col2
  41. TableText(col1, col2, "vc_|", 100, 35) → displayTable
  42. Min(1, ((1 + animateControl - animateStage) * 1.5)) → animateValue
  43. Take(allPoints, 1, animateStage - If[animateValue ≟ 1, 0, 1]) → displayPoints
  44. centerBox(boxWidthX, boxHeightX, PMoveX) → moveLabelX
  45. centerBox(boxWidthY, boxHeightY, PMoveY) → moveLabelY
  46. ReplaceAll(tableLabel(2), "$", "\$") → yMoveLabel
  47. Text(currentMoveLabel(2), PMoveY, true, true, 0, 0) → textLabelY
  48. VerticalText(currentMoveLabel(2)) → lblY
  49. Text(currentMoveLabel(If[PMoveX ≟ DragCenter, 1, 2]), DragCenter, true, true, 0, 0) → axisLabelX
  50. Zip(PulsePoint + (((A * xPX10) * 5), ((B * yPX10) * 1.75)), A, {-1, 1, 1, -1}, B, {-1, -1, 1, 1}) → onboardingCorners
  51. Polygon(onboardingCorners) → backgroundPulsing
  52. Polygon(onboardingCorners) → pulsingQuad
  53. Polygon({(dimensions(1), dimensions(2)), (dimensions(1), dimensions(4)), (dimensions(3), dimensions(4)), (dimensions(3), dimensions(2))}) → coverBox

AI Drawing Prompt Reference

Create a scatter plot to display a set of randomly generated data points. First, generate 400 random numbers between 0 and 0.99, then use these numbers to create corresponding y-axis intercepts and data points. Next, randomly select some x-axis and y-axis sample values, and use these values to generate specific points. Arrange these points according to a certain pattern. Finally, draw the x-axis and y-axis, add axis labels and tick marks, and show the distribution of the data points.
The prompt above was compiled from the original drawing commands and is for reference only.