(a) draw a scatter diagram of the data, (b) by hand, compute the correlation coefficient, and (c

step 1 All right, guys, here we go. So the first thing we need to do for this problem, problem number 2

(a) draw a scatter diagram of the data, (b) by hand, compute...

Key Concepts

Correlation Coefficient

The correlation coefficient is a numerical measure that quantifies the strength and direction of a linear relationship between two variables. Its value ranges from -1 to +1, where values close to +1 indicate a strong positive linear association, values close to -1 indicate a strong negative linear association, and values near zero suggest a weak or no linear relationship.

Relationship Analysis

Relationship analysis involves interpreting the visual and numerical measures derived from a scatter diagram and the correlation coefficient, respectively, to understand the nature of the association between the variables. This includes evaluating whether the variables tend to increase or decrease together (indicating a positive or negative relationship) and considering any deviations or non-linear patterns that might affect the strength and reliability of the observed relationship.

Scatter Diagram

A scatter diagram is a graphical tool used to display and visually assess the relationship between two quantitative variables. By plotting data points on a two-dimensional graph, it provides a clear picture of the distribution and potential patterns or trends in the data, such as clustering, gaps, or any form of association between the variables.

Transcript

00:01 All right, guys, here we go.

00:03 So the first thing we need to do for this problem, problem number 21, is to first draw a scatterplot diagram of the data.

00:10 So i went ahead and took the liberty of taking an example from the text.

00:14 I believe it was example number.

00:16 Let me actually double check that.

00:18 It was example number two.

00:19 So i'm actually using a very similar strategy as example number two on our textbook to do this problem.

00:26 So all this stuff over here, that's just from example number two.

00:29 So we'll get to that in a second.

00:31 For the time being, first we need to input our values.

00:33 So our x values in problem number 21 are 3, 5, 8, 9, and then 212.

00:41 And our y values, oops, that's weird.

00:44 Okay, and our y values are 18, 20, 16, 10, 12, and 8.

00:56 Okay, so those are our values there.

00:59 So let's go ahead and start creating our scatter plot.

01:02 The way you do that in google sheets, very simple.

01:05 So you're going to highlight all the stuff.

01:06 I'm going to include the x and y is i'm going to do inserts chart.

01:12 And there it is.

01:13 Great.

01:13 Okay, cool.

01:14 And there is my scattered chart.

01:16 I'm not actually a super big fan of this, by the way.

01:19 I can see a couple dots got cut off there.

01:21 So how i fix that actually is very simple.

01:24 I'm going to go to customize over here on the right.

01:27 And i'm going to go to the horizontal axis.

01:29 It looks like i'm going to make it a little bit longer here.

01:33 I noticed the x starts at three, so i'm actually gonna start it at one, and then the maximum value, the biggest x value is 12, so i ended at 14, and so that's what we'll do there.

01:44 Okay, it gives it a little bit more room.

01:46 Let's do the same to the y -axis, give everybody a little bit more room here.

01:50 The minimum y value looks like was eight, and so let's actually make that like, i don't know, six, and then the max y value was 20, so let's make it 22.

02:00 And that makes everything a little bit too.

02:02 Perfect.

02:02 Okay, cool.

02:03 So now our scatterplots a little bit easier to see.

02:05 And so let's go and leave that there.

02:08 Okay, so guys, i'm going to go ahead and give you guys a second here to either copy that down on a piece of paper or to take a screenshot or something, if you would like.

02:16 But i'm going to go ahead and delete this in a second.

02:21 But because, yeah, if i'm going to input more values in my spreadsheet.

02:26 And then, first thing about google shees, if i input more values might mess up my data.

02:30 So i don't want to do that.

02:32 So yeah, there we go.

02:34 So, but before i actually delete this, i'll just make a few comments on this.

02:37 There seems to be a kind of negative correlation between this.

02:42 Remember, a really strong positive correlation would be everything's going like up.

02:47 Really strong negative correlation means everything's going down.

02:50 It seems like things are kind of trending downward.

02:53 But that being said, it kind of goes up and down a little bit at the same time.

02:56 So i'm not sure how strong a correlation this is.

02:59 I'm going to guess that my linear correlation coefficient is going to be negative, but i don't know how close it will be to negative one.

03:05 So that's my guess for now.

03:07 Okay, hopefully that gave you enough time to take a screenshot or copy that down.

03:12 If you need to do so, pause the video.

03:14 But other than that, i'm going to go ahead and move on here.

03:17 All righty.

03:18 So the first thing we need to do to calculate the linear correlation coefficient.

03:22 I know they asked us to do it by hand, but we kind of do need a calculator here to get a good estimation.

03:28 So i'm going to assume they just mean go step by step.

03:31 And so the first thing we're going to do is we're going to find the mean of each of the variables.

03:35 I'm going to call the mean of x capital x and the mean of y capital y.

03:39 So let's start there.

03:40 And how you find that on google sheet, very simple.

03:42 Start by pressing the equal signer of keyboard, writing the word average.

03:46 It's already guessing what i want, by the way.

03:48 And then open parentheses, highlight everything you want.

03:52 Close the parentheses, hit enter.

03:54 And there is our mean.

03:56 Okay, for the next one, also you might be thinking, wait a second, that was a shortcut, and that's totally fine.

04:01 Sometimes it will guess your shortcut, and there you go.

04:04 If it gets your shortcut, more power to you.

04:06 Oh, it's interesting.

04:07 X is a lot of decimal places.

04:09 Why does not? let's actually make sure that it's actually not.

04:12 Okay, cool.

04:13 I just made sure it wasn't an estimation.

04:16 All right.

04:16 Now for standard deviation...

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