00:01
In this problem, we need to determine which one of the given statements is correct when all the actual values of y are on an upward sloping regression line.
00:09
Now, if we have a look at the given options, we can see that they have information regarding the correlation coefficient, the coefficient of determination, and the slope.
00:19
So let us consider an example of a scatter plot.
00:23
Suppose these are the coordinate axes and scatter plot will be something like this.
00:28
The points will be like this so that if we draw the regression line, it's just directly going to pass through all of these points.
00:37
So the points are going to lie on the regression line, and this is because it is said that the actual values of wire on an upward sloping regression line.
00:49
So first of all, note that it's on an upward sloping regression line.
00:54
So that means that as the x variable increases, the variable y also increases.
01:01
So there is a positive relationship between the two variables, and because of that, the correlation coefficient r must be positive.
01:08
Also, since the actual values of y lie on the regression line, this means that there is a perfect linear correlation between the two variables, and so r is either going to be plus or minus 1.
01:18
But it's going to be greater than 0, so that means that the value of r will actually be equal to 1.
01:25
So the correlation coefficient, r will be 1.
01:27
And the coefficient of determination is simply r squared, which is 1 squared, so that's 1...