Q4. You have fit a multiple linear regression model and the...

Q4. You have fit a multiple linear regression model and the (X'X)^-1 matrix is: (X'X)^-1 = [ 0.893758 -0.0282448 -0.0175641 ] [-0.028245 0.0013329 0.0001547 ] [-0.017564 0.0001547 0.0009108 ] (a) How many regressor variables are in this model? (b) If the error sum of squares is 307 and there are 15 observations, what is the estimate of ??^2? (c) What is the standard error of the regression coefficient ??_1?

Transcript

00:01 The following is a solution to number five, and this one we're asked to compute the least squares regression line from section 10 .2 number five.

00:08 And so that data, if you remember, i'm going to use a ti84, but if you go to stat and then edit, you can punch in your data value.

00:15 So in l1, i put my x values, 1 -1 -3 -5, and then in l2, i put my y values, 215 ,34.

00:23 So if i want to find my least squares regression line, again, using technology, you can just go to stat and then arrow over to calc.

00:29 And then we're going to go to this fourth option here, lin -reg ax plus b.

00:33 So click 4.

00:35 The x list will be l1.

00:37 The y list will be l2.

00:39 And then we're going to calculate.

00:42 And the slope is 0 .625 and then the y intercept is 1 .25.

00:46 So let's go and write that down.

00:48 So the way we write the least squares regression line, we write it as y hat equals 0 .625x.

01:00 Plus 1 .25.

01:05 Okay.

01:07 So the second part is to compute the sum of the squared estimates using the summation, or some of the standard errors, using the summation of y minus y hat quantity squared.

01:20 So that's the actual y value minus the predicted y value.

01:24 We can use this equation for that quantity squared.

01:27 So i'm going to do the calculator again because it cuts down a lot of the work.

01:31 So if you go back to stat and then edit.

01:33 On this third column, we're going to make that into our predicted y values.

01:37 And the way you do that, you just click up where the l3 is highlighted.

01:41 And we're just going to type in our equations.

01:43 So remember that this is equal to y hat.

01:45 So we can just type in 0 .625, which was the slope.

01:50 And then it was times x.

01:52 Now i'm not going to use x because i actually want data value.

01:54 So i'm going to do l1.

01:55 So second l1, and then plus that 1 .25.

02:02 Okay, so you can do this manually, but you would have to do it five different times.

02:06 This is basically just plugging in one for x, and then one for x and then three for x and so on.

02:12 So whenever you click enter, you should get five data values here...

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