00:01
Here we have some data that's looking at the heaters and the areas they heat.
00:10
And we're looking at the correlation between wattage of the heaters and their heating area.
00:15
Is there a director in direct relationship? so let's go ahead and do that.
00:24
And i cheated.
00:25
I did all this before i did because i used my spreadsheet to do it.
00:27
So this is everything there.
00:28
I'll isolate what we should look at here.
00:31
But i took the data and put it in the spreadsheet.
00:33
This is the initial data here.
00:35
So let's give them to us the heater number, the wattage in the area.
00:41
And i call the wattage x in the area, y.
00:45
And the way i calculated the correlation coefficient r is with this formula here, which is using these sums.
00:54
And so what you do is you take the x values and the y values and you sum them up.
00:57
So 28 ,250s is some of the x is.
01:01
3404 is the y's.
01:02
And you take, you need the x squares.
01:05
The sum of the x squares some of the y squares you just need this some of the product of x and y's in well so i have this spreadsheet where i took each of the wattage the x value squared them that's what this column is x squared the y's the y's the area square those add them up that's down here the sum of the x ys are it's right down here so spreadsheets will make your life so much easier um so there we go so you substitute in all these values boom boom boom into your equation here.
01:36
Just make sure you do order of operations.
01:40
And then, oh, n is 20.
01:43
So i have to make sure we get that.
01:44
And it's 20.
01:45
And we get the correlation coefficient of 0 .164.
01:52
0 .164, which shows a direct relationship because it's going up.
02:03
As one goes up, the other goes up.
02:05
It's positive.
02:05
It was negative.
02:06
It would be indirect.
02:07
So now we're going to conduct the hypothesis test at the alpha of 0 .025.
02:13
Whether or not the correlation coefficient is significantly greater than zero.
02:18
And we have this.
02:19
We're told that t critical value already is 2 .101.
02:23
So we're going to go ahead and do that with the t test.
02:27
And the formula i used for that is right here.
02:32
T equals r root n minus two all over square root of one minus r squared.
02:37
And r is the same as row.
02:39
In this case, it's in the question it says row, but for us here it would be the same.
02:44
So you take our value, you substitute in the values that we have.
02:49
We get this .707 and compare that with the t alpha score of 2 .101.
02:57
We fail to reject.
03:00
So it's not reasonable to say that the population correlation is significant.
03:10
So we don't have evidence to suggest that there is a direct relationship.
03:17
But that's it, we're going to continue.
03:20
We failed to reject.
03:21
Let's see.
03:21
So we fail to reject.
03:30
And h0 is that this correlation coefficient is less than equal to zero.
03:36
So now that said, we're still going to develop our regression equation.
03:44
And the regression equation formulas i used, i used it right here...
