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Exploring Relationships Between Numerical Variables

Explore correlations between numerical variables with scatterplots. Learn to interpret relationships, analyze data, and make informed decisions. Understand key concepts like slope, association, and strength of relationships.

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Exploring Relationships Between Numerical Variables

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  1. Exploring Relationships Between Numerical Variables Scatterplots

  2. Seating Chart

  3. Try this … graph • The first step in analyzing data it to make a ______. • What is the slope of the following line? -1

  4. Vocabulary scatterplot • A __________ helps us decide if there is a relationship between two numerical variables. • The __________ variable is plotted on the x-axis. • The ________ variable (the one we are most interested in) is plotted on the y-axis. explanatory response explanatory response

  5. Golf • The goal of golf is to putt at or under ___. • Every round starts off at the_______. • The golfer must decide: • Hit ____(use a driver & hit off a tee) • Hit ______(fairway has short grass) • Very difficult to be accurate when hitting __. par tee box long straight far Does the average driving distance affect accuracy?

  6. Making a Scatterplot (by hand) • Decide which variable is the explanatory variable and label the x-axis. Label the y-axis with the response variable. • Scale each axis individually. • Draw a dot to represent each athlete. 0.88 0.84 0.80 0.76 Driving Accuracy 0.72 0.68 0.64 255 260 265 270 275 245 250 Average Driving Distance

  7. Making a Scatterplot (TI-84) • Enter L1 (explanatory variable / x-axis) Enter L2 (response variable / y-axis) • Turn the Scatterplot on

  8. Making a Scatterplot (TI-84) • Look at the scatterplot • Check out the scale

  9. Association: direction There exists a relationship between the two variables. Negative Positive

  10. Association: no direction If there is no relationship between the two variables, we say there is __ association. no Bad Drivers Bad Putters Good Drivers Bad Putters Mean Driving Accuracy Mean Putting Average Bad Drivers Good Putters Good Drivers Good Putters

  11. Association: form • Linear • Non-Linear

  12. Association: strength • Very Strong • Strong • Moderate • Weak

  13. Sum it Up scatterplot • The _________ is a graph that displays the relationship between two numerical variables. • In a scatterplot, the __________ variable is plotted on the horizontal axis and the ________ variableis plotted on the vertical axis. • We can describe the __________ of two variables: • direction (________ or _______ ) • form ( _____ or_________ ) • strength (_____ to ____ ) explanatory response association positive negative linear non-linear weak strong

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