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NSW Y12 Maths - Advanced Bivariant Data Analysis Scatterplots and Association

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Scatterplots and Association Theory

Bivariate data measures 2 variables on the same data set to see if they correlate with each other.\\ Scatterplots are graphed to represent the bivariant data.\\ The independent variable is on the horizontal axis and the dependent variable is on the vertical axis.\\ For example consider the number of cars in a car park and pollution. The independent variable is the number of cars and the dependent variable is pollution.\\ \textbf{Shape of Scatterplots}\\ \adjustbox{valign=t}{ \begin{tikzpicture}[ declare function={a(\x)=\x+0.3*rand;}, ] \def \domain{0.4:4} \def \xmax{5} \def \xmin{0} \def \ymax{5} \def \ymin{0} \def \xlabel{x} \def \ylabel{y} \begin{axis}[ axis y line=left, axis x line=bottom, axis line style={-Stealth,very thick}, xlabel = Strong Positive Correlation, width=2in, height=2in, ymin=\ymin, ymax=\ymax, xmin=\xmin, xmax=\xmax, xlabel style={below}, ylabel style={above}, axis on top=false, xtick distance = 6, ytick distance = 6, xtick={}, ytick={}, xticklabels={}, yticklabels={} ] %FUNCTION \addplot[only marks,samples=6,domain=\domain]{a(x)}; \end{axis} \end{tikzpicture} } \qquad \adjustbox{valign=t}{ \begin{tikzpicture}[ declare function={a(\x)=-\x+4+0.3*rand;}, ] \def \domain{0.4:4} \def \xmax{5} \def \xmin{0} \def \ymax{5} \def \ymin{0} \def \xlabel{x} \def \ylabel{y} \begin{axis}[ axis y line=left, axis x line=bottom, axis line style={-Stealth,very thick}, xlabel = Strong Negative Correlation, width=2in, height=2in, ymin=\ymin, ymax=\ymax, xmin=\xmin, xmax=\xmax, xlabel style={below}, ylabel style={above}, axis on top=false, xtick distance = 6, ytick distance = 6, xtick={}, ytick={}, xticklabels={}, yticklabels={} ] %FUNCTION \addplot[only marks,samples=6,domain=\domain]{a(x)}; \end{axis} \end{tikzpicture} } \qquad \adjustbox{valign=t}{ \begin{tikzpicture}[ declare function={a(\x)=\x+0.2+0.3*rand;}, ] \def \domain{0.4:4} \def \xmax{5} \def \xmin{0} \def \ymax{5} \def \ymin{0} \def \xlabel{x} \def \ylabel{y} \begin{axis}[ axis y line=left, axis x line=bottom, axis line style={-Stealth,very thick}, xlabel = Moderate Positive Correlation, width=2in, height=2in, ymin=\ymin, ymax=\ymax, xmin=\xmin, xmax=\xmax, xlabel style={below}, ylabel style={above}, axis on top=false, xtick distance = 6, ytick distance = 6, xtick={}, ytick={}, xticklabels={}, yticklabels={} ] %FUNCTION \addplot[only marks,samples=6,domain=\domain]{a(x)}; \addplot[only marks,samples=5,domain=\domain]{x+1+0.3*rand}; \end{axis} \end{tikzpicture} } \\ \adjustbox{valign=t}{ \begin{tikzpicture}[ declare function={a(\x)=-\x+4+0.3*rand;}, ] \def \domain{0.4:4} \def \xmax{5} \def \xmin{0} \def \ymax{5} \def \ymin{0} \def \xlabel{x} \def \ylabel{y} \begin{axis}[ axis y line=left, axis x line=bottom, axis line style={-Stealth,very thick}, xlabel = Moderate Negative Correlation, width=2in, height=2in, ymin=\ymin, ymax=\ymax, xmin=\xmin, xmax=\xmax, xlabel style={below}, ylabel style={above}, axis on top=false, xtick distance = 6, ytick distance = 6, xtick={}, ytick={}, xticklabels={}, yticklabels={} ] %FUNCTION \addplot[only marks,samples=6,domain=\domain]{a(x)}; \addplot[only marks,samples=5,domain=\domain]{-x+5+0.3*rand}; \end{axis} \end{tikzpicture} } \qquad \adjustbox{valign=t}{ \begin{tikzpicture}[ declare function={a(\x)=\x^2+1+0.5*rand;}, ] \def \domain{0.4:4} \def \xmax{5} \def \xmin{0} \def \ymax{5} \def \ymin{0} \def \xlabel{x} \def \ylabel{y} \begin{axis}[ axis y line=left, axis x line=bottom, axis line style={-Stealth,very thick}, xlabel = No Correlation, width=2in, height=2in, ymin=\ymin, ymax=\ymax, xmin=\xmin, xmax=\xmax, xlabel style={below}, ylabel style={above}, axis on top=false, xtick distance = 6, ytick distance = 6, xtick={}, ytick={}, xticklabels={}, yticklabels={} ] %FUNCTION \addplot[only marks,samples=6,domain=\domain]{a(x)}; \addplot[only marks,samples=5,domain=\domain]{-x+4+0.7*rand}; \end{axis} \end{tikzpicture} }

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  • Scatterplots and Association - Video - Scatterplots Displaying bivariate numerical data

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