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Bivariate Data

This guide covers essential concepts in bivariate data analysis, focusing on the interpretation of scatterplots and key statistical measures. It defines important terms such as correlation (r), coefficient of determination (r²), slope (b₁), and y-intercept (b₀). Discover how to evaluate the strength, direction, and significance of linear relationships using these formulas. By understanding how these components relate to the explanatory and response variables, you can make informed predictions and analyses based on data trends.

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Bivariate Data

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  1. Bivariate Data Chapters 7-10

  2. Formulas PredictedResponse Variable = Bo + B1(Explanatory Variable)

  3. When analyzing a scatterplot you will want to note strength, direction, form, and outliers.

  4. Key Players: r: Correlation – tells strength and direction of a linear relationship r2: Coefficient of determination – tells the amount of variability in the Response variable explained by the LSRL or by the explanatory variable bo: y-intercept – tells the starting point or the amount when the explanatory variable = 0. Can be an extrapolation. b1: Slope – Rate of change, tells how much the response variable changes when the explanatory variable goes up by 1 (or by the units Indicated on the x-axis)

  5. Interpreting r, r2, b0, and b1 r = .99: Strong, positive linear relationship between time in hours and log of pop r2 = .982: 98.2% of the variation in log of population is explained by hours or by the LSRL b1 = .115: As hours increases by 1, log of pop will increase by about .115 b0 = .322: When hours = 0, log predicted pop will equal .322, substituting 0 into equation we get 103.22 = about 2.1 or predicted pop = about 2.1 thousand

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