00:01
Okay, so for this question, we were given a set of data from a bookstore, and we have the number of sales people working, and then the sales in thousands that the bookstore brought in.
00:20
And so we have the sample mean and standard deviation given to us, and we want to fit a regression.
00:31
Line to the data and calculate the residuals.
00:37
And we want to estimate what the sales would be if 18 people were working.
00:44
And then we want to calculate how many people are working if the sales are 25 ,000.
00:53
So we're going to do both and compare our answers.
00:58
But i just put the these two columns, the number of people working and the sales in thousands in an excel file and then made a scatter plot since it's trying to kind of tricky to make a scatter plot on these whiteboards to help us visualize these data.
01:19
And then i fit an exponential regression line, which basically just means that this line goes through or around most of the data points with a very strong correlation.
01:35
Since we have a positive slope, we know there's a positive correlation between the number of people working in sales.
01:42
So as x increases, y will also increase.
01:46
So the more people working, the more money the bookstore will make.
01:50
And so because this value is closer to one, so an r squared value can be anywhere from zero to one.
01:58
And the closer to one means a actual perfect relationship.
02:04
But basically anything that's like 0 .6 .7 or up is considered a pretty strong relationship.
02:12
So we have a strong positive relationship here.
02:18
And so the first thing we want to do is calculate the variance.
02:22
And so our variance is actually the standard deviation squared.
02:28
And so since we were already given the standard deviation, we can just go ahead and plug that in.
02:34
Our standard deviation from this problem was 5 .34.
02:39
And so if we square that, we get 28 .52, which is actually 28 ,000, because remember, this is in thousands.
02:51
And so the next thing that we're going to do, we have the variance.
02:56
Let's look at if 18 people work, we want to know what the sales are.
03:04
And so we're just going to use this line, this equation of the line, because this equation describes this line right here.
03:14
And so if we want to use this line to predict the sales, we would just plug in 18 where the x is, because x is our number of people working.
03:25
So we're just going to do that.
03:27
We're going to do y equals 9 ,496 .9 times e raised to the 0 .055 times 18.
03:40
And so we're just going to work that through.
03:44
And if we just plug that into our calculator, we get 25 ,558 .38.
03:50
So this is in dollars.
03:52
This is an estimate of how my...