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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!

Positive and negative linear associations from 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

Practice

Eyeballing the line of best fitGet 3 of 4 questions to level up!

Estimating equations of lines of best fit, and using them to make predictionsGet 3 of 4 questions to level up!

Estimating slope of line of best fitGet 3 of 4 questions to level up!

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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

Practice

Calculating and interpreting residualsGet 3 of 4 questions to level up!

Calculating the equation of the least-squares lineGet 3 of 4 questions to level up!

Interpreting slope and y-intercept for linear modelsGet 3 of 4 questions to level up!

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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