A&A SL: SL textbook: Bivariable Statistics

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Chapter 19: SL textbook: Lessons A-C

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14 Terms

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Poles

  • the highest and lowest data values

  • Interpolating

    • when predicting that the x and y values would lie between the poles

    • the accuracy of the prediction is determined by the fit within the linear model

  • Extrapolating

    • when predicting that the x and y values would lie outside of the poles

    • the accuracy of the prediction is determined by the linear fit and under the assumption that the trend will pass the poles

<ul><li><p>the highest and lowest data values</p></li><li><p><strong>Interpolating</strong></p><ul><li><p>when predicting that the x and y values would lie between the poles</p></li><li><p>the accuracy of the prediction is determined by the fit within the linear model</p></li></ul></li><li><p><strong>Extrapolating</strong></p><ul><li><p>when predicting that the x and y values would lie outside of the poles</p></li><li><p>the accuracy of the prediction is determined by the linear fit and under the assumption that the trend will pass the poles</p></li></ul></li></ul>
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Line of Best Fit

  • only worth drawing when there is a strong correlation between variables

  • How to draw:

  1. calculate the mean values of both x and y

  2. mark the mean points

  3. draw a line between the mean points which best fits the data so the points are equally distributed around the line

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Line of Best Fit by Eye

  • when drawing a line by observation

  • will vary from person to person

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Correlations of r

  • sign indication of r

    • when + r = positive correlation

    • when - r = negative correlation

    • when 0 = r = no correlation

  • size indication of r

    • when r is close to + 1 or - 1 then there will be a strong correlation

    • when r is close to 0 then there will be a weak correlation

<ul><li><p>sign indication of <em>r</em></p><ul><li><p>when +<em> r</em> = positive correlation</p></li><li><p>when - <em>r</em> = negative correlation</p></li><li><p>when 0 = <em>r</em> = no correlation</p></li></ul></li><li><p>size indication of <em>r</em></p><ul><li><p>when <em>r</em> is close to + 1 or - 1 then there will be a strong correlation</p></li><li><p>when <em>r</em> is close to 0 then there will be a weak correlation</p></li></ul></li></ul>
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Pearson”s Product-moment Correlation Coefficient

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Causal Relationship

  • AKA: explanatory variable/response variable

  • if a change in one variable explains the change in the other variable

    • independent variable explains the dependent variable

  • a causal relationship can not be determined based on high occurrence alone

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Outlier

  • isolated points from the trend formed by the main data body

  • discard if it is a result of a recording error

  • keep if it is genuine data

<ul><li><p>isolated points from the trend formed by the main data body</p></li><li><p>discard if it is a result of a recording error</p></li><li><p>keep if it is genuine data</p></li></ul>
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Strength

  • used to determine how closely a trend is followed

  • correlation will be described as either:

    • strong

    • moderate

    • weak

  • subjective way to determine data trends

<ul><li><p>used to determine how closely a trend is followed</p></li><li><p>correlation will be described as either:</p><ul><li><p>strong</p></li><li><p>moderate</p></li><li><p>weak</p></li></ul></li><li><p>subjective way to determine data trends</p></li></ul>
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Linear

  • when a trend exists

  • the points will form an approximately straight line

<ul><li><p>when a trend exists</p></li><li><p>the points will form an approximately straight line</p></li></ul>
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randomly scattered

  • no correlation

<ul><li><p>no correlation</p></li></ul>
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Downward Trend

  • a negative correlation

  • an increase in the independent variable

  • a decrease in the dependent variable

<ul><li><p>a negative correlation </p></li><li><p>an increase in the independent variable</p></li><li><p>a decrease in the dependent variable</p></li></ul>
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Upward Trend

  • a positive correlation

  • an increase in the independent variable

  • an increase in the dependent variable

<ul><li><p>a positive correlation</p></li><li><p>an increase in the independent variable</p></li><li><p>an increase in the dependent variable </p></li></ul>
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Correlation

  • the relationship or association between two numerical values

  • one variable does not inherently cause the other

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Scatter Diagram

  • shows the relationship between two numerical values

  • the independent variable is on the horizontal axis

  • the dependent variable is on the vertical axis

<ul><li><p>shows the relationship between two numerical values</p></li><li><p>the independent variable is on the horizontal axis</p></li><li><p>the dependent  variable is on the vertical axis</p></li></ul>