Overview Correlation - Introduction to Engineering - Lecture Slides, Slides of Engineering Mathematics

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Sections 9-1 and 9-

Overview Correlation

PAIRED DATA

• Is there a relationship?
• If so, what is the equation?
• Use that equation for prediction.

In this chapter, we will look at paired sample data (sometimes called bivariate data ). We will address the following:

SCATTERPLOT

A scatterplot (or scatter diagram ) is a graph in which the paired ( x , y ) sample data are plotted with a horizontal x -axis and a vertical y -axis. Each individual ( x , y ) pair is plotted as a single point.

MAKING SCATTER PLOT ON THE TI-83/

1. Select STAT , 1:Edit….
2. Enter the x -values for the data in L 1 and the y - values in L 2.
3. Select 2nd , Y= (for STATPLOT ).
4. Select Plot.
5. Turn Plot1 on.
6. Select the first graph Type which resembles a scatterplot.
7. Set Xlist to L 1 and Ylist to L 2.
8. Press ZOOM.
9. Select 9:ZoomStat.

POSITIVE LINEAR CORRELATION

NEGATIVE LINEAR CORRELATION

LINEAR CORRELATION COEFFICIENT

The linear correlation coefficient r measures strength of the linear relationship between paired x and y values in a sample.

ASSUMPTIONS

1. The sample of paired data ( x , y ) is a random sample.
2. The pairs of ( x , y ) data have a bivariate normal distribution.

LINEAR CORRELATION COEFFICIENT

( )( ) (∑ 2 ) (∑ )^2 (∑ 2 ) ( ∑ )^2

∑ ∑ ∑ − −

−

n x x n y y

n xy x y r

The linear correlation coefficient r measures strength of the linear relationship between paired x and y values in a sample.

The TI-83/84 calculator can compute r****.

ρ (rho) is the linear correlation coefficient for all paired data in the population. Docsity.com

COMPUTING THE CORRELATION

COEFFICIENT r ON THE TI-83/

1. Enter your x data in L1 and your y data in L.
2. Press STAT and arrow over to TESTS.
3. Select E:LinRegTTest.
4. Make sure that Xlist is set to L1, Ylist is set to L2, and Freq is set to 1.
5. Set β & ρ to ≠.
6. Leave RegEQ blank.
7. Arrow down to Calculate and press ENTER.
8. Press the down arrow, and you will eventually see the value for the correlation coefficient r.

INTERPRETING THE LINEAR CORRELATION

COEFFICIENT

• If the absolute value of r exceeds the value in Table A-5, conclude that there is a significant linear correlation.
• Otherwise, there is not sufficient evidence to support the conclusion of significant linear correlation.

PROPERTIES OF THE LINEAR CORRELATION

COEFFICIENT

1. – 1 ≤ r ≤ 1
2. The value of r does not change if all values of either variable are converted to a different scale.
3. The value of r is not affected by the choice of x and y. Interchange x and y and the value of r will not change.
4. r measures strength of a linear relationship.

COMMON ERRORS INVOLVING

CORRELATION

• Causation: It is wrong to conclude that correlation implies causality.
• Averages: Averages suppress individual variation and may inflate the correlation coefficient.
• Linearity: There may be some relationship between x and y even when there is no significant linear correlation.

FORMAL HYPOTHESIS TEST

• We wish to determine whether there is a significant linear correlation between two variables.
• We present two methods.
• Both methods let H 0 : ρ = 0

(no significant linear correlation) H 1 : ρ ≠ 0 (significant linear correlation)