Scatter Plots and Correlations Dittamo Lewis Notes 2013

Scatter Plots A Scatter Plot is a picture of numerical data in which each point (x,y) is located on a rectangular coordinate plane. The horizontal axis is identified with values of x and the vertical axis with values of y. Dittamo Lewis Notes 2013

A Scatter Plot is the graph of ordered pairs (x,y) Scatter Plots A Scatter Plot is the graph of ordered pairs (x,y) Correlation A Correlation is a relationship between points. Dittamo Lewis Notes 2013

(x, y) (1,4) (3,2) (2,5) (4,6) (7,9) (6,8) (5,7) Scatter Plots Look at this Scatter Plot Dittamo Lewis Notes 2013

(x, y) (1,4) (3,6) (2,1) (4,3) (7,2) (6,4) (5,1) Scatter Plots Look at this Scatter Plot (x, y) (1,4) (3,6) (2,1) (4,3) (7,2) (6,4) (5,1) Dittamo Lewis Notes 2013

Scatter Plots Any comments on these two graphs? Is there anything special about them? Looking at a scatter plot can sometimes allow us to determine if a relationship exists between two variables. If all of the points are close to forming a line there could be a relationship. Dittamo Lewis Notes 2013

Scatter Plots Brain Weight (g) Max. Life (yr.) Animal y Mouse 0.4 3.2 50 40 30 20 10 Fox 50.4 9.8 Tiger 157 22.4 Max. Life (yrs.) Sheep 175 20 Pig 180 27 Seal 325 41 x Donkey 419 40 0 100 200 300 400 500 600 Brain Weight (g) Monkey 440 50 Dittamo Lewis Notes 2013

Scatter Plots Scatterplot - a coordinate graph of data points. y 50 40 30 20 10 Trend is increasing Trend looks linear Max. Life (yrs.) Line of Best Fit -Points act like magnets attracting the line. x 0 100 200 300 400 500 600 Brain Weight (g) Dittamo Lewis Notes 2013

Scatter Plots Scatterplot - a coordinate graph of data points. y 50 40 30 20 10 Trend is increasing Trend looks linear Max. Life (yrs.) Line of Best Fit -Points act like magnets attracting the line. x 0 100 200 300 400 500 600 Brain Weight (g) Dittamo Lewis Notes 2013

Scatter Plots Scatterplot - a coordinate graph of data points. y 50 40 30 20 10 Trend is increasing Trend looks linear Max. Life (yrs.) Line of Best Fit -Points act like magnets attracting the line. x 0 100 200 300 400 500 600 Brain Weight (g) Dittamo Lewis Notes 2013

Scatter Plots Scatterplot - a coordinate graph of data points. y 50 40 30 20 10 Trend is increasing Trend looks linear Max. Life (yrs.) Line of Best Fit -Points act like magnets attracting the line. x 0 100 200 300 400 500 600 Brain Weight (g) Dittamo Lewis Notes 2013

Which scatterplots below show a linear trend? 1) 2) 3) Negative Correlation Positive Correlation Dittamo Lewis Notes 2013

Which scatterplots below show a linear trend? 1) 2) 3) Constant Correlation Dittamo Lewis Notes 2013

Scatter Plots The independent variable is on the x-axis and the dependent variable is on the y-axis. Dependent Variable (Y) Independent Variable (X) Dittamo Lewis Notes 2013

Scatter Plots If the x increases and the y increases there is a positive correlation. Examples: Father’s height vs. Son’s height Daily grade vs. Final grade 3 2 1 1 2 3 4 5 6 7 8 Dittamo Lewis Notes 2013

Scatter Plots Notice as the Father’s Height increases so does the Son’s Height. Dittamo Lewis Notes 2013

Father’s Height in Inches Scatter Plots Notice all of the points center close to a line which shows us a relation-ship also known as a correlation Son’s Height in Inches Father’s Height in Inches Dittamo Lewis Notes 2013

Scatter Plots Dittamo Lewis Notes 2013

Zero Correlation: There appears to be no linear relationship Scatter Plots Zero Correlation: There appears to be no linear relationship Example: Height vs. IQ score 4 3 2 1 Your height doesn’t determine how smart you are. No obvious correlation. 1 2 3 4 5 6 Dittamo Lewis Notes 2013

No Correlation because the points are scattered everywhere. Scatter Plots No Correlation because the points are scattered everywhere. Dittamo Lewis Notes 2013

Scatter Plots Negative Correlation: If the x increases and the y decreases there is a negative correlation. Examples: Car weight vs. Miles per gallon Days absent vs. Final grade 4 3 2 1 1 2 3 4 5 6 7 Dittamo Lewis Notes 2013

Scatter Plots TAKE OUT YOUR STUDY GUIDE Dittamo Lewis Notes 2013

#9 Scatter Plots Height vs. IQ A Scatter Plot is the graph of ordered pairs (x,y). A Correlation is a relationship between points. A ZERO CORRELATION is when there appears to be no linear relationship. Example: Height vs. IQ *Your height doesn’t determine how smart you are. No obvious correlation. Dittamo Lewis Notes 2013

#10 Positive Correlation: If the x increases and the y increases. Correlation Negative Correlation: If the x increases and the y decreases. Negative Correlation Positive Correlation Examples: Dad’s height vs. Son’s height Daily grade vs. Final grade Examples: Car weight vs. MPG Days absent vs. Final grade Dittamo Lewis Notes 2013

Correlations and Graphing

Correlation If the x increases and the y increases there is a positive correlation. Examples: Father’s height vs. Son’s height Daily grade vs. Final grade 3 2 1 1 2 3 4 5 6 7 8 Dittamo Lewis Notes 2013

Correlation If the x increases and the y decreases there is a negative correlation. 4 3 2 1 Examples: Car weight vs. Miles per gallon Days absent vs. Final grade 1 2 3 4 5 6 7 Dittamo Lewis Notes 2013

A Zero Correlation is when there appears to be no linear relationship Example: Height vs. IQ score 4 3 2 1 Your height doesn’t determine how smart you are. No obvious correlation. 1 2 3 4 5 6 Dittamo Lewis Notes 2013

I II IV III Graphing Review A point (x,y) 4 QUADRANT GRAPH 1st QUADRANT GRAPH y-axis y 3 2 1 -1 -2 -3 I II (-1,2) x (-2,0) Origin (0,0) x-axis ORDERED PAIR -3 -2 -1 0 1 2 3 (3,-1) NOT in a quadrant A point (x,y) IV III Dittamo Lewis Notes 2013

Independent/Dependent Events #? The independent variable is on the x-axis and the dependent variable is on the y-axis. Dependent Variable (y) Independent Variable (x) The dependent event depends on the independent event.