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March 20th, 2017, 06:03 PM   #1
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Method of Least Squares

Hi,

I've attached the question and my worked solution.

I am confident I have the correct least squares straight line of best fit to the data to 2 d.p., but I'm unsure what is being asked in the next part.

Am I to sub the xi values into the least squares straight line of best fit to acquire yi estimates?

And if so, I know there will be variation. How would you explain the accuracy of such variation?
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March 29th, 2017, 09:10 PM   #2
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Was this for some class?
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March 29th, 2017, 10:16 PM   #3
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The parameters that you calculated for your regression line look correct.

Quote:
Originally Posted by ChrisHughes View Post
Am I to sub the xi values into the least squares straight line of best fit to acquire yi estimates?
Yes, that's how I understand the question. Not sure what they want you to comment on exactly. Sometimes, the data will fit the regression line very closely, and sometimes it won't. I'm not sure there's much more that you can say. If there were some outliers, you could comment on that, but I don't see any.
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March 29th, 2017, 10:20 PM   #4
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you've estimated a linear model given this data.

$y(x) = 8.71x + 31.91$

for each $x_i$ find $y(x_i) = 8.71x_i + 31.91$

Plot these points in one color and your actual data points in another.

You'll find the data isn't particularly linear in this case.
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April 2nd, 2017, 04:08 PM   #5
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Quote:
Originally Posted by romsek View Post
you've estimated a linear model given this data.

$y(x) = 8.71x + 31.91$

for each $x_i$ find $y(x_i) = 8.71x_i + 31.91$

Plot these points in one color and your actual data points in another.

You'll find the data isn't particularly linear in this case.
In order to provide as much help to ChrisHughes as possible, we need to know if he has studied regression that isn't linear.
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