Scatterplots

ScatterplotsCorrelation, Least-Squares Regression, ResidualsGet That ProgramANSCOMBECRICKETSGESSELCorrelationCorrelation isA measurement that combines the strength and direction of relationshipCorrelationCoefficient (r)The r value is a number that describes the strength & direction of the relationshipYou can find this value using your calculator.Diagnostics ON2nd 0 (catalog)x-1Diagnostics On EnterFinding rStatCalc 8: LinReg (a + bx)

R ValuesStrongModerateWeakWeakModerate Strong-1.0 -.7-.7 -.3

-.3 00 .3.3 .7.7 1.0

rStrong, Negative-1 = Perfect Negative CorrelationModerate, NegativeSome, Negative CorrelationWeak, NegativeNot much Negative Correlation0 = No CorrelationWeak, PositiveModerate, PositiveStrong, PositiveNot much Positive CorrelationSome, Positive Correlation1 = Perfect Positive CorrelationRemember, Correlation means Relationship Between the Variables

Are these Bones Connected?

Scientists are studying the relationship of the lengths of two different bones. Use the Correlation Coefficient to describe the relationship.FemurHumerus38415663597064727484

R = .9941This means there is a strong positive relationship between the length of the femur and humerus bones.Fun Facts about Rr needsThe data have a linear patternThe data to be quantitativer doesnt care aboutWhich variable is x and which is yUnits of measurementr IS effected by outliers

Want to see the future?Then use the Least Squares LineThe Least Squares LineStraight Line (mathematical model) that best describes the scatter plot data of y based on x.Gives the smallest sum of the squared vertical distances from the points to the line.Least Squares Line is Your Crystal Ball

By plugging in values into this line, you can predict values based on your collected dataLeast Squares Line

Slopey - interceptPredicted valueX = explanatory variableY = response variableStat: Calc: 8Finds this equation on your calculator, butWe need to know how to do it by hand

Standard Deviation of ysStandard Deviation of xsMean of ysMean of xsUse 2 Variable Stats to get the means and std. devs. Graphing the LSL on your Scatter PlotUsing the Bone Data, Lets look at the equation and then the graph of the scatter plotFemurHumerus38415663597064727484

Lin Reg Stats

Then, go to y=VARS: 5(Statistics)

Over to EQ, and Hit RegEQ:This puts your equation into your graph. Now just hit ZOOM 9.

How Noisy is Your Cricket?

Scientists are investigating to see if the outside temperature has an effect on the rate of chirping by a cricket. Run the CRICKETS program to see the data collected2) Calculate by hand the Equation of the Least Squares Line3) Use Your Calculator to Make a Scatter Plot of the Data and Plot the LSL on your graph.1) Use Your Calculator to Calculate the Equation of the LSL.X-bar = 80.04; Y-bar = 16.65sx = 6.707; sy = 1.702; r = .835

=.2119=-.3105

Interpreting the Equation in ContextThe SlopeThe rate of changeThe amount of change in y-hat when x increases by 1The InterceptValue of y-hat when x = 0Often the base valueBack to The Crickets

Describe the Slope and Y-Intercept in the context of the cricket problem.Slope: on average, each degree predicts .2119 more chirpsIntercept: Not statistically significant because it would describe the number of chirps to be negative at 0 degrees.How Noisy is Your Cricket?Making Predictions

Using your equation, predict the rate of chirps per second for a cricket in:90 degree weather

74 degree weather

60 degree weather18.76 chirps15.37 chirps12.41 chirps

What About the Temperature if you hear 16.5 cricket chirps per second?

79 degreesThe Coefficient Of Determination (r2)Tells the percent of the variation in the values of y that is explained by the equationGives a measure of error in the equationHigher r2 More accurate predictions

The r2 value associated with our cricket example is.697.This says that 69.7% of the variation in cricket chirps is explained by the LS equation (temperature).Facts About Least Squares LineMust be clear on Explanatory & Response VariablesSwitching the variables changes your equationLine always passes through the point (x-bar,y-bar)This always gives us a point to start w/ or use during graphingCorrelation is closely related to slopeSmaller r = smaller effect of x on predictionsr and r2 help define the strength of a straight line relationship between the variablesHigher values = stronger relationshipWorkOlympic Gold Wksht#30,32,34-37,41,43-45