Use the following table to answer the questions. (Give your answers correct to two decimal places.)
x 1 1 3 3 5 5 7 7 9 9
y 3 2 6 1 3 3 3 2 5 3
(a) Find the equation of the line of best fit.
yhat = + x
(ii) Graph this equation on a scatter diagram. (Do this on paper. Your instructor may ask you to turn in this work.)
(b) Find the ordinates yhat for the points on the line of best fit whose abscissas are x = 1, 3, 5, 7, and 9.
1
3
5
7
9
(c) Find the value of e for each of the points above (e = y - yhat).
y e y e
3 3
2 3
6 2
1 5
3 3
(d) Find the variance se2 of those points about the line of best fit.
Sue12/Nora4/whoever ~
No one will do your work for you.
However, if you include what you have done so far to solve your assigned problems, someone might be able to help you.
Never ask you to do the work for me, If I can get the formulas and write them down then I usually do the work on my own. But no thanks to you.......This is a site to assist not criticize people that ask for help......Never mind with helping me.....
This site is called Homework Help for a reason. The math tutors will HELP you if you let them know what you know or have done so far.
If all you do is post ten or more complicated problems or assignments without including YOUR thoughts or questions, they assume you want someone to do your work for you ... and they will skip your posts.
Add your own thoughts to each problem you've posted, and MAYBE someone will be able to help.
I have done that to another one and posted how I worked it out, so if you don't mind will you look at it and see if I am on the right track. I have done several but I found formulas to use from the book but sometimes I do not understand what the book has..
Sorry my mouse keeps moving and I type on the wrong one...
To find the equation of the line of best fit, we can use the least squares method.
Step 1: Calculate the means of x and y.
mean(x) = (1 + 1 + 3 + 3 + 5 + 5 + 7 + 7 + 9 + 9) / 10 = 5
mean(y) = (3 + 2 + 6 + 1 + 3 + 3 + 3 + 2 + 5 + 3) / 10 = 3.1
Step 2: Calculate the deviations of x and y from their means.
x - mean(x): -4, -4, -2, -2, 0, 0, 2, 2, 4, 4
y - mean(y): -0.1, -1.1, 2.9, -2.1, -0.1, -0.1, -0.1, -1.1, 1.9, -0.1
Step 3: Calculate the products of these deviations.
(-4 * -0.1), (-4 * -1.1), (-2 * 2.9), (-2 * -2.1), (0 * -0.1), (0 * -0.1), (2 * -0.1), (2 * -1.1), (4 * 1.9), (4 * -0.1) = 0.4, 4.4, -5.8, 4.2, 0, 0, -0.2, -2.2, 7.6, -0.4
Step 4: Calculate the sum of the squares of x deviations.
(-4)^2 + (-4)^2 + (-2)^2 + (-2)^2 + 0^2 + 0^2 + 2^2 + 2^2 + 4^2 + 4^2 = 80
Step 5: Calculate the sum of the squares of y deviations.
(-0.1)^2 + (-1.1)^2 + (2.9)^2 + (-2.1)^2 + (-0.1)^2 + (-0.1)^2 + (-0.1)^2 + (-1.1)^2 + (1.9)^2 + (-0.1)^2 = 18.4
Step 6: Calculate the sum of the products of x and y deviations.
0.4 + 4.4 + (-5.8) + 4.2 + 0 + 0 + (-0.2) + (-2.2) + 7.6 + (-0.4) = 7
Step 7: Calculate the slope (β1) of the line of best fit.
β1 = sum of products of deviations of x and y / sum of squares of x deviations
β1 = 7 / 80 = 0.0875
Step 8: Calculate the intercept (β0) of the line of best fit.
β0 = mean(y) - β1 * mean(x)
β0 = 3.1 - 0.0875 * 5 = 2.6625
Hence, the equation of the line of best fit is:
yhat = 2.6625 + 0.0875 * x
To find the ordinates yhat for the points on the line of best fit whose abscissas are x = 1, 3, 5, 7, and 9, substitute these values into the equation:
yhat(1) = 2.6625 + 0.0875 * 1 = 2.75
yhat(3) = 2.6625 + 0.0875 * 3 = 2.925
yhat(5) = 2.6625 + 0.0875 * 5 = 3.1
yhat(7) = 2.6625 + 0.0875 * 7 = 3.275
yhat(9) = 2.6625 + 0.0875 * 9 = 3.45
The ordinates yhat for the points on the line of best fit whose abscissas are x = 1, 3, 5, 7, and 9 are:
yhat(1) = 2.75
yhat(3) = 2.925
yhat(5) = 3.1
yhat(7) = 3.275
yhat(9) = 3.45
To find the value of e (e = y - yhat) for each of the points above, subtract the corresponding yhat value from the given y value:
e(1) = 3 - 2.75 = 0.25
e(3) = 2 - 2.925 = -0.925
e(5) = 6 - 3.1 = 2.9
e(7) = 1 - 3.275 = -2.275
e(9) = 3 - 3.45 = -0.45
The values of e for the given points are:
e(1) = 0.25
e(3) = -0.925
e(5) = 2.9
e(7) = -2.275
e(9) = -0.45
To find the variance se^2 of those points about the line of best fit, square each value of e, then calculate their sum and divide by (n - 2), where n is the number of points:
se^2 = (e(1)^2 + e(3)^2 + e(5)^2 + e(7)^2 + e(9)^2) / (10 - 2)
se^2 = (0.25^2 + (-0.925)^2 + 2.9^2 + (-2.275)^2 + (-0.45)^2) / 8
se^2 = (0.0625 + 0.855625 + 8.41 + 5.177625 + 0.2025) / 8
se^2 = 14.70725 / 8
se^2 ≈ 1.838
Therefore, the variance se^2 of those points about the line of best fit is approximately 1.838.