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Perform Tests of Independence and Correlation

A series of factors were measured in 506 Boston suburbs with the intention of determining how these factors are related to home price.

    
Significant correlations among factors such as nitrogen oxide concentration and median home price serve as a reminder that correlation does not imply causation:
Wolfram Language code: data = ExampleData[{"Statistics", "BostonHomes"}][[All, {3, 5, 6, 13, 14}]]; labs = {"Industrial Percent", "NOX Conc.", "Median Home Value", "Number of Rooms", "Poverty Fraction"}; opts = Sequence[Frame -> True, Axes -> None, AspectRatio -> 1, PlotStyle -> PointSize[Medium], FrameTicks -> None, ImageSize -> {60, 60}, PlotRange -> All, Background -> White];
Wolfram Language code: GraphicsGrid[Table[If[i == j, ListPlot[{0}, PlotStyle -> None, Background -> Lighter[Blue, .9], opts, Epilog -> Inset@Style[labs[[i]], Bold, FontSize -> 12, FontFamily -> "Helvetica"]], ListPlot[#, opts]&[Transpose[{data[[All, j]], data[[All, i]]}]]], {i, 5}, {j, 5}], Spacings -> {4, 4}]
Kendall's matrix for the data:
Wolfram Language code: KendallTau[data]//MatrixForm
IndependenceTest suggests home values drop with increasing nitrogen oxide concentrations:
Wolfram Language code: IndependenceTest[data[[All, 2]], data[[All, 3]], {"TestDataTable", {"KendallTau", "SpearmanRank", "HoeffdingD"}}]
The amount of nitrogen oxide is highly correlated with the level of industrialization:
Wolfram Language code: CorrelationTest[data[[All, 1 ;; 2]], 0, "TestDataTable"]