Question

The following table shows total forest and timberland in the United States in millions of acres in the indicated year. Calculate the SSE for the quadratic regression function (with coefficients rounded to three decimal places) from the previous question. Round your answer to one decimal place.

Answer 1

I am not sure how to calculate the SSE (sum of the squares error)? Is it the R^2 0.8823... or 0.9 rounded to on decimal place?

Answer 2

This is the quadratic equation y=0.036x^2-1.976x+761.454

Answer 3

Honestly I've never done this before. A google search gave this formula
\[\sum_{i=1}^{n}(x_i-\bar x)^2\]
The best I can figure is that you're supposed to use the number in the table for \(x_i\) and the corresponding point from your regression function for \(\bar x\).

Answer 4

This is an example I found in my textbook. I guess instead of y=x^2 I would use y=0.036x^2-1.976x+761.454 but its still a little confusing.

Answer 5

ok. the numbers in the timber land row of 1st table are the actual values. You have to use your function to get the other value. What year did your function start at?

Answer 6

1962 but I think you represent that with 0
1970 = 8
1977 = 15
1987 = 25
1992= 30

Answer 7

ok great now find the corresponding y values from your regression function.

Answer 8

It really is easier to set this up in a table like they have it

Answer 9

759
754
737
731
737

Answer 10

ok. those are your actual values. You have to plug in the year after 1962 into your regression formula to get the 3rd column

Answer 11

y=0.036x^2-1.976x+761.454

So for x = 0 you get y = 761.454
For x = 8 you get y = 747.95
and so on

Answer 12

do you follow?

Answer 13

yeah I figured out how to plug it in on my calculator

Answer 14

something's not right with the third column. They shouldn't be that far off from the actuals.

Answer 15

im not sure what happened?

Answer 16

this is what I got

Answer 17

oh ok I must have made a mistake somewhere

Answer 18

oh ok. once you get the right values, sum the L5 column and that's the SSE.

Answer 19

so add everything up on L5. I wonder why my calculator got the first two right and not the rest on the same column it was the same equation.

Answer 20

because with what I got now it would be 1557.127

Answer 21

Yeah, that's huge. I think the smaller the number the better the regression curve is

Answer 22

oh ok thank you for your time and help :)