Axes Quadrants Ordered Pairs Correlations Scatter plots Axes Quadrants Ordered Pairs Correlations

Scatter plots A scatter plot is a graph of data that is a series of points. It is a powerful visual method for representing relationships for pairs of quantities. A scatter plot shows individual relationships for single pairs, as well as the trend in relationships for the full set of data.

Ordered Pairs (2,3) is an ordered pair. y coordinate x coordinate

The Cartesian Plane

The Axes y axis (vertical) Origin (0,0) x axis (horizontal)

The Quadrants 1 2 (-,+) (+,+) 3 4 (+,-) (-,-)

In which quadrant can we find the following ordered pairs In which quadrant can we find the following ordered pairs? (Quadrant 1, 2 ,3 or 4?) A) (2,3) B) (-2,3) C) (-2,-3) D) (2,-3) E) (4,-5) F) (-3,-7) G) (-2,6) H) (1,4) 2 1 3 4

Place the following points on the Cartesian plane (using graph paper please) Identify the axes, quadrants and origin. Be sure to write the letter beside the point for the following ordered pairs: A. (6,6) B. (-2,4) C. (3,-5) D. (0,0) E. (5,7) F. (-4,-1) G. (0,7) H. (4,0) I. (-2,-3) J. (-5,4) K. (7,1) L. (4,-6)

INDEPENDENT VARIABLE DEPENDANT VARIABLE The variable that we CAN CONTROL. DEPENDANT VARIABLE The variable that we CANNOT control. Taste of Pepsi dependant variable Temperature of Pepsi independent variable (controlled)

The Line of Best Fit. When the points on a scatter plot become close to forming a straight line, we can draw “the line of best fit.” This line is the line that is closest to connecting as many points as possible on a scatter plot. We can use this line to make predictions. The closer the points are to the line, the more accurate our predictions.

Richard runs 8km. After each 2 km, he checks the time. Time in minutes Distance ran in km

INTERPOLATE EXTRAPOLATE Predict a value between two known values. Ex. It takes Richard ___ minutes to run 5 km. EXTRAPOLATE Make predictions beyond known points on a graph. Ex. Richard can run ___ km in 120 minutes.

Quadrant #1 and Correlations: The relationship between two variables is called a CORRELATION. The correlation can be positive or negative. Sometimes there is NO correlation. The correlation can be STRONG or WEAK.

A Positive Correlation: As x increases, y increases. STRONG POSITIVE CORRELATION when the points are close to forming a line that goes up and to the right. We can make VERY ACURATE PREDICTIONS! WEAK POSITIVE CORRELATION when the points are NOT as close but we can still form a line up and to the right. We can make predictions, but not as accurate as those when the points are closer together.

A Negative Correlation: As your x increases, your y decreases. STRONG NEGATIVE CORRELATION when the points are close to forming a line that goes DOWN and to the right. WE can make VERY ACCURATE PREDICTIONS! WEAK NEGATIVE CORRELATION when the points are NOT as close but we can still form a line DOWN and to the right. We can make predictions, but not as accurate as those when the points are closer together.

No Correlation: Given the points, we are unable to draw a line either up and to the right or down and to the right or straight up or straight down thus we are unable to make any valid predictions.