00:01
For this problem, we are told that 16 couples participated in an experiment where the female partner watched while painful stimulation was applied to the finger of her male partner.
00:09
Two variables were measured for each female.
00:12
Y equaling the pain -related brain activity, measured on a scale ranging from negative 2 to 2, and x being the score on the empathic concern scale.
00:20
The data are listed in a table, which i will show in a moment, and we're told that the research question of interest was, do people scoring higher in empathy show higher pain -related brain activity? and we are asked to use simple linear regression analysis to answer this question.
00:36
As i said, i'll show the data on screen in a moment, but we'll first state our hypotheses.
00:41
The null hypothesis is that the slope of our linear regression line is zero.
00:46
There's no relation.
00:48
And the alternative hypothesis will be that beta 1 is greater than zero.
00:53
There's a positive relationship.
00:56
So what i've actually done here, as we can see, i have a bit of an excel template set up for doing most of the calculations ahead of time here.
01:04
But we have our actual data, the x's and y's, put over here.
01:10
And then all of the different quantities needed for performing our linear regression.
01:15
So the first thing that we would want for finding our least squares estimate would be finding the slope, which will be equal to ssxy over ssxx.
01:26
That would be the sum of the x or x i minus x bar times y i minus y bar column divided by the sum of the x minus x bar squared column.
01:37
I have that data over here.
01:39
We have ssxx is 178.
01:42
Oops, we want ssxy up top.
01:46
So it would be 6 .44 divided by 178, which then, according to the calculations, gives a result of 0 .0 .0 .4.
01:56
And that seems about right.
02:00
Then we want our beta knot value, which will be equal to y bar, or the mean of y minus beta hat 1 times x bar.
02:11
We have the mean of y is 0 .26.
02:14
We have beta hat 1 is 0 .04, and we have that the mean of x is 18, which then gives us that beta not should be equal to negative 0 .39...