Investigation - the Correlation Coefficient

MAP4C Investigation – The Correlation Coefficient

You will complete this assignment individually not in groups.  In order to display the correlation coefficient using your graphing calculator, you must first turn on the diagnostic feature. To do this press 2nd then 0 to select the CATALOG FEATURE. Press the Down arrow until the cursor points to DiagnosticOn. Press Enter once to select it, then Enter again to activate the feature.  All the x and y values are in the range of 0 to 10. Therefore set your window from xmin 0, xmax 11 and xscl 1, ymin 0, ymax 11 and yscl 1. Leave xres at 1 for the entire investigation.  Enter the values for Data Set A into L1 and L2  Perform Linear Regression on your data by pressing STAT then Right arrow then 4 to select LinReg(ax+b). You now need to tell the calculator what you want to perform the linear regression on. Press 2nd then 1 then “,” then 2nd then 2 then “,” then VARS the Right arrow then 1 then 1 again.  Your screen should now say LinReg(ax+b) L1 , L2, Y1 then enter. Record the Equation of the Line in slope and y-intercept form as well as the correlation coefficient (r) accurate to 4 decimal places.  Draw the scatter plot and the line of best fit on the same graph. To do this press 2nd then Y= then 1 then enter to access STAT PLOT and turn on Plot1. Press the Down arrow then enter to select the scatter plot. Enter L1 for xlist and L2 for ylist. Press enter to display the graph. Sketch this graph on the handout below.  Answer the question below your sketch about how closely the line of best fit represents your data set.  Repeat for each set of data.

1.a) Data Set A Equation of the Line ( y = ax + b form )

Correlation Coefficient ( r )

b) Sketch the scatter plot and the line of best fit.

2. Describe how well your line of best fit actually fits your data set. Use the terms exactly, very close, somewhat close, weak, not at all.

1.a) Data Set B Equation of the Line ( y = ax + b form )

of 4 Prepared by: Mr. McEwen MAP4C Investigation – The Correlation Coefficient

1.a) Data Set C Equation of the Line ( y = ax + b form )

1.a) Data Set D Equation of the Line ( y = ax + b form )

1.a) Data Set E Equation of the Line ( y = ax + b form )

1.a) Data Set F Equation of the Line ( y = ax + b form )

1.a) Data Set G Equation of the Line ( y = ax + b form )

1.a) Data Set H Equation of the Line ( y = ax + b form )

1.a) Data Set I Equation of the Line ( y = ax + b form )

1.a) Data Set J Equation of the Line ( y = ax + b form )

x 2. Describe how well your line of best fit actually fits your data set. Use the terms exactly, very close, somewhat close, weak, not at all.

3. Looking at your answers to questions # 2 and the correlation coefficient ( r ) for each set of data, what is the connection between how close a set of points is to being linear and its correlation coefficient ( r )?

4. Which data sets display a line with a negative slope?

Which data sets display a line with a positive slope?

What is the connection between the sign of ( r ) and the slope of the line of best fit?

of 4 Prepared by: Mr. McEwen