Correlation Coefficient with Technology
description
Transcript of Correlation Coefficient with Technology
Material Taken From:
Mathematicsfor the international student
Mathematical Studies SL
Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce
Haese and Haese Publications, 2004
Correlation Coefficient with Technology
TI 84
• Turn on the Diagnostics• Enter the data in L1 and
L2• LinReg L1, L2
Autograph• Open a 2D Graph Page• Data > Enter XY Data Set• Enter your data• Select Show Statistics• Click OK• Click Transfer to Results
Box• View > Results Box
Section 18B – Measuring Correlation
At a father-son camp, the heights of the fathers and their sons were measured.
a) Draw a scatter plot of the data.b) Calculate rc) Describe the correlation between the variables.
Example 1
The Botanical Gardens have been trying out a new chemical to control the number of beetles
infesting their plants. The results are shown.
a) Calculate rb) Describe the correlation
between the variables.
Sample Quantity of chemical (g)
Number of surviving beetles
A 2 11B 5 6C 6 4D 3 6E 9 3
Example 2
At a tournament, athletes throw a discus. The age and distance thrown are recorded for each athlete:
Section 18A – Line of Best Fit (By Eye)
Drawing the Line of Best Fit
1. Calculate mean of x values , and mean of y values2. Mark the mean point on the scatter plot3. Draw a line through the mean point that is through
the middle of the data– equal number of points above and below line
x y ,x y
On a hot day, six cars were left in the sun for various lengths of time. The length of time each car was left in the sun was recorded, as well as the temperature inside the car at the end of the period.
a) Calculate andb) Draw a scatter plot for the datac) Plot the mean point and draw a line of best fitd) Predict the temperature of a car which has been
left in the sun for:i. 35 minutesii. 75 minutes
e) Comment on the reliability of your predictions
x y
Example 3
Scatter Plot
Find a linear equation that best-fits the data.
Section 18C – Linear Regression
Best Fit vs. Regression
The problem with drawing a line of best fit by eye is that the line will vary from one
person to the other.
Least Squares Regression Line• Consider the set of points below.• Square the distances and find their sum.• we want that sum to be small.
Least Squares Regression Formula
Note: sxy will be given on an exam, while sx is found with the TI 84.
)(2 xxss
yyx
xy
Consider the data given:
b) Estimate the value of y when x = 6. Comment on the reliability of your estimate.
a) Given sxy ≈ -14.286, find the equation of the least squares regression line.
Example 4
Some things to note:
• The regression line is used for prediction purposes.
• The regression line is less reliable when extended far beyond the region of the data.
The table shows the sales for Hancock’s Electronics established in late 1998.
a) Draw a scatterplot to illustrate this data.b) Given that sxy ≈ 12.5 find the correlation coefficient, r.
c) Find the equation of the regression line, using the formula.d) Predict the sales figures for the year 2006, giving your answer
to the nearest $10,000.e) Comment on the reasonableness of this prediction.
Example 5
Regression Line with Technology
TI 84• LinReg(ax +b) L1, L2• where L1 contains your
independent data.• and L2 contains your
dependent data
Autograph• Open a 2D Graph Page
• Data > Enter XY Data Set
• Enter your data
• Select Show Statistics
• Click OK
• Click Transfer to Results Box
• View > Results Box
The table shows the annual income and average weekly grocery bill for a selection of families
a) Construct a scatter plot to illustrate the data.b) Use technology to find the line of best fit.c) Estimate the weekly grocery bill for a family with an annual income of £95000.Comment on whether this estimate is likely to be reliable.
Example 6
Homework
• Complete Worksheet 2• Pg 590 #6,7,8