For the sample data a. Draw the scatter plot. b. Based on...

For the sample data
a. Draw the scatter plot.
b. Based on the scatter plot, predict the sign of the linear correlation coefficient.
Explain your answer.
C. Compute the linear correlation coefficient and compare its sign to your answer
to part (b).

Key Concepts

Scatter Plot

A scatter plot is a graphical representation of two quantitative variables where each point on the plot corresponds to a pair of observations from the data set. It is used to visually assess the pattern, direction, and strength of the potential relationship (e.g., linear or non-linear) between those variables.

Linear Correlation Coefficient

The linear correlation coefficient, often represented by Pearson’s r, is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. Its value ranges from -1 to 1, where a value close to 1 indicates a strong positive linear relationship, a value close to -1 indicates a strong negative linear relationship, and a value near 0 suggests little or no linear relationship.

Visual Prediction of Correlation Sign

Before performing numerical calculations, one can often predict the sign of the linear correlation coefficient by examining the overall trend in a scatter plot. An upward trend, where points tend to rise together, suggests a positive correlation, while a downward trend indicates a negative correlation.

Transcript

00:01 The following is a solution to number five, and we're given a pretty small data set.

00:04 Here are the x values, 11, 3 ,45, and then the y values, 21, 5, 3 ,4.

00:09 And the first part of this asks to make a scatter plot.

00:13 And you can do that just by doing a manual scatter plot on a cartesian plane.

00:17 Just plot these points like you would in algebra 1.

00:19 They're just a bunch of ordered pairs.

00:21 Or you can use technology, and you can use any sort of technology you want.

00:23 I'm going to use the ti -84 because it comes up pretty nicely.

00:26 So if you're using a ti -84, if you go to stat and then edit, l1 is where you find your x values, 11, 3 ,45, l2 is where you find the y values, 21, 5, 3 ,4.

00:39 Then if you go to second, y equals, where in blue it's a stat plot, just make sure this first stat plot is on.

00:46 I like to use the first one, and then the other ones you can just turn off, and just go click into it and click on.

00:54 And then just choose this first one.

00:56 This first one should be highlighted.

00:57 X list is l1, y list is l2, unless you put it in different columns.

01:01 And then as for the mark, you kind of put, just choose whichever one you want.

01:04 I like this first one because it comes up the nicest.

01:08 Then press graph and here are your data values.

01:11 So one, two, three, four, five.

01:12 So those are the five data values.

01:13 Now, if you don't see all of them or if you only see part of them or you don't see any of them, it just means your window's a little bit off.

01:18 So if you go to zoom and then zoom stat, so nine, then you should be able to see that.

01:23 So there's your scatter plot.

01:25 Now, if you were to draw an imaginary line through this, that kind of hits in the middle of all of those.

01:31 Points, the slope of that line would be positive.

01:35 And that kind of answers the second part.

01:37 Predict the sign of r.

01:38 I'm going to say it's positive...

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