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Unit: Exploring bivariate numerical data

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Possible mastery points

Introduction to scatterplots

Learn
Constructing a scatter plot
(Opens a modal)
Example of direction in scatterplots
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Scatter plot: smokers
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Bivariate relationship linearity, strength and direction
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Positive and negative associations in scatterplots
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Outliers in scatter plots
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Clusters in scatter plots
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Describing scatterplots (form, direction, strength, outliers)
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Scatterplots and correlation review
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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!

Correlation coefficients

Learn
Example: Correlation coefficient intuition
(Opens a modal)
Calculating correlation coefficient r
(Opens a modal)
Correlation coefficient review
(Opens a modal)
Practice
Correlation coefficient intuitionGet 3 of 4 questions to level up!

Quiz 1

Level up on the above skills and collect up to 500 Mastery points

Introduction to trend lines

Learn
Fitting a line to data
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Estimating the line of best fit exercise
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Estimating with linear regression (linear models)
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Line of best fit: smoking in 1945
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Equations of trend lines: Phone data
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Linear regression review
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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!

Quiz 2

Level up on the above skills and collect up to 300 Mastery points

Least-squares regression equations

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Introduction to residuals and least squares regression
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Introduction to residuals
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Calculating residual example
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Calculating the equation of a regression line
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Interpreting slope of regression line
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Interpreting y-intercept in regression model
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Interpreting a trend line
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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!

Quiz 3

Level up on the above skills and collect up to 300 Mastery points

Assessing the fit in least-squares regression

Learn
Residual plots
(Opens a modal)
R-squared intuition
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R-squared or coefficient of determination
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Standard deviation of residuals or Root-mean-square error (RMSD)
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Interpreting computer regression data
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Interpreting computer output for regression
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Impact of removing outliers on regression lines
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Practice
Residual plotsGet 3 of 4 questions to level up!
Effects of influential pointsGet 3 of 4 questions to level up!

Quiz 4

Level up on the above skills and collect up to 200 Mastery points

More on regression

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Squared error of regression line
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Proof (part 1) minimizing squared error to regression line
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Proof (part 2) minimizing squared error to regression line
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Proof (part 3) minimizing squared error to regression line
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Proof (part 4) minimizing squared error to regression line
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Regression line example
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Second regression example
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Calculating R-squared
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Covariance and the regression line
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Unit test

Level up on all the skills in this unit and collect up to 1300 Mastery points!

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.