In Exercises 57 - 60, find the least squares regression line...

In Exercises 57 - 60, find the least squares regression line $ y = ax + b $ for the points $ \left(x_1,y_1\right) $, $ \left(x_2,y_2\right) $, . . . ,$ \left(x_n,y_n\right) $ by solving the system for $ a $ and $ b $. $ nb + \left(\sum_{i=1}^{n}x_i\right) a = \left(\sum_{i=1}^{n}y_i\right) $ $ \left(\sum_{i=1}^{n}x_i\right)b + \left(\sum_{i=1}^{n}x_i^2\right)a = \left(\sum_{i=1}^{n}x_i y_i\right) $ Then use a graphing utility to confirm the result. (If you are unfamiliar with summation notation, look at the discussion in Section 9.1 or in Appendix B at the website for this text atacademic.cengage.com.)

In Exercises 57 - 60, find the least squares regression line $ y = ax + b $ for the points

$ \left(x_1,y_1\right) $, $ \left(x_2,y_2\right) $, . . . ,$ \left(x_n,y_n\right) $

by solving the system for $ a $ and $ b $.

$ nb + \left(\sum_{i=1}^{n}x_i\right) a = \left(\sum_{i=1}^{n}y_i\right) $

$ \left(\sum_{i=1}^{n}x_i\right)b + \left(\sum_{i=1}^{n}x_i^2\right)a = \left(\sum_{i=1}^{n}x_i y_i\right) $

Then use a graphing utility to confirm the result. (If you are unfamiliar with summation notation, look at the discussion in Section 9.1 or in Appendix B at the website for this text atacademic.cengage.com.)

Transcript

00:01 So in problem 58, we have to use formula, it looks like nb, plus the sum of the x values times a equals the sum of the y values.

00:17 And then we have some of the x values again times b plus the sum of this x values squared times a equals the sum of the product of the x and y values.

00:28 Now we're giving a graph, we have six points.

00:31 So when we plug stuff in, we're going to have n equals.

00:34 6.

00:35 If we add up all of our x values, it should be 15.

00:42 Add up all of our y values, it's going to be 23 .6.

00:51 If we add up all of our our x values squared, it's going to be 55.

00:59 And if we add up with the product of all of our x and y values, that's going to give us 48 .8.

01:09 Okay, so in the next slide, i'll set those equations up and get going on it.

01:14 Okay, so we're going to have 6b.

01:19 Plus 15 a equals 23 .6.

01:28 We're also going to have 15b plus 55a equaling 48 .8.

01:40 I'm going to solve this by elimination.