- In a regression problem the following pairs of (x, y) are...

- In a regression problem the following pairs of (x, y) are given: (3, 3), (-3, -3), (0, 0), (-2, -2) and (2, 2). That indicates that the: Select one: a. coefficient of determination is 3. b. correlation coefficient is 1. c. None of these choices. d. correlation coefficient is - 1. e. correlation coefficient is 0. In a linear regression problem, if the coefficient of determination is 0.9025, this means that: Select one: a. None of these choices. b. 95% of the y values are positive. c. 95% of the variation in y can be explained by the variation in x. d. Correlation coefficient value is either +0.95 or -0.95. e. 95% of the y values are predicted correctly by the model.

Transcript

00:01 Let's have some questions about coefficient of determination and the correlation coefficient.

00:06 So the first one, in a regression problem, the following pairs of xl are given.

00:10 It's right here, and that indicates which of these.

00:14 Well, before we can answer this, let's go ahead and plot the data.

00:18 So i have a handy graph here, or a handy graph here.

00:23 So 3 -3 is going to go here.

00:27 Negative 3 and negative 3 is going to go here.

00:31 0 -0, negative 2, negative 2, and 2 and 2.

00:37 Great.

00:38 Now, if we know our lines, this is going to be a perfect line with a slope of 1, the equation y equals x.

00:49 It is that line.

00:51 And so what that tells us is that the correlation coefficient is positive 1.

00:57 So this section is b right here.

01:00 We could have said negative 1.

01:01 That would be if it's going in the negative direction.

01:05 But here it's a positive one because the correlation coefficient measures strength and direction.

01:25 And strength in the sense of it being on the line, so all these points are right on the line.

01:32 And since it's, that means the strength, it's strong, it's one.

01:38 And the direction, it's positive ones.

01:41 That means it's going up.

01:42 You could have a, say, i'm going to do this in a separate color, because some of my students will sometimes get this confused.

01:49 They think correlation coefficient is the same as slope, which is not true.

01:54 In this case, it just so happens the slope is one, but we could have had, say, a point here at negative 3, negative 1, 0 .00, and then at 3 .1 here.

02:05 This does not have a slope of 1, but its correlation coefficient is also positive 1.

02:15 In a, so next one, in a linear regression problem, if the coefficient of determination is 0 .9025, this means that, which are these? so, let's see, 95 % of the y values are positive.

02:33 Nope, that's not 95%.

02:34 So just really quickly what this means, the coefficient of determination tells us, it's the percentage variation.

02:46 In the y variable that can be explained by the variation of the x variable...

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