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Exploring bivariate numerical data

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Constructing a scatter plotExample of direction in scatterplotsScatter plot: smokersBivariate relationship linearity, strength and directionPositive and negative associations in scatterplotsOutliers in scatter plotsClusters in scatter plotsDescribing scatterplots (form, direction, strength, outliers)Scatterplots and correlation review
Practice
Constructing scatter plotsGet 3 of 4 questions to level up!
Making appropriate scatter plotsGet 3 of 4 questions to level up!
Describing trends in scatter plotsGet 3 of 4 questions to level up!
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Example: Correlation coefficient intuitionCalculating correlation coefficient rCorrelation coefficient review
Practice
Correlation coefficient intuitionGet 3 of 4 questions to level up!
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Fitting a line to dataEstimating the line of best fit exerciseEstimating with linear regression (linear models)Line of best fit: smoking in 1945Equations of trend lines: Phone dataLinear regression review
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Introduction to residuals and least squares regressionIntroduction to residualsCalculating residual exampleCalculating the equation of a regression lineInterpreting slope of regression lineInterpreting y-intercept in regression modelInterpreting a trend line
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Residual plotsR-squared intuitionR-squared or coefficient of determinationStandard deviation of residuals or Root-mean-square error (RMSD)Interpreting computer regression dataInterpreting computer output for regressionImpact of removing outliers on regression lines
Practice
Residual plotsGet 3 of 4 questions to level up!
Influential pointsGet 3 of 4 questions to level up!
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Squared error of regression lineProof (part 1) minimizing squared error to regression lineProof (part 2) minimizing squared error to regression lineProof (part 3) minimizing squared error to regression lineProof (part 4) minimizing squared error to regression lineRegression line exampleSecond regression exampleR-squared or coefficient of determinationCalculating R-squaredCovariance and the regression line

About this unit

We use scatter plots to explore the relationship between two quantitative variables, and we use regression to model the relationship and make predictions. This unit explores linear regression and how to assess the strength of linear models.