If your solution to stated problem does not match the given solution, you should self-critique per instructions at
http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.
Your solution, attempt at solution.
If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.
019. ``q Query 19
Question: `q Query problem 13.6.9 wt vs ht 62,120; 62,140; 63,130; 65,150; 66,142; 67,13068,175; 68,135; 70,149; 72,168. Give the regression equation and the predicted weight when height is 70.
Your solution:
Confidence Assessment:
Given Solution:
`aThe equation is obtained by substituting the weights for y and the heights for x in the formula for the regression line.
You get
y = 3.35 x - 78.4.
To predict weight when height is 70 you plug x = 70 into the equation:
y = 3.35 * 70 - 78.4.
You get
y = 156,
so the predicted weight for a man 70 in tall is 156 lbs. **
Self-critique (if necessary):
Self-critique Rating:
Question: `q Query problem 13.6.12 reading 83,76, 75, 85, 74, 90, 75, 78, 95, 80; IQ 120, 104, 98, 115, 87, 127, 90, 110, 134, 119
Your solution:
Confidence Assessment:
Given Solution:
`a
n = 10
sum x = 811
sum x ^2 = 66225
sum y = 1104
sum y^2 = 124060
sum xy = 90437
a = [10(90437) - (811)(1104)] / [10(66225) - (811^2)] = 1.993
a = 1.99
b = [1104 - (1.993)(811) / 10 = -51.23
y' = 1.993x - 51.23 is the eqation of the regression line.
**
STUDENT QUESTION
How did you get sum x ^2 = 66225??? Is
it not 811 * 811 = 657721?
How did you come up with sum y^2 = 124060??? Is it not 1104 * 1104 = 1218816?
I worked it out, can you tell me where I went wrong??? And I will try to rework
the problem.
INSTRUCTOR RESPONSE
You didn't distinguish between sum x^2
and (sum x)^2.
Sum x^2 means you figure out x^2 for every value of x, then add them. Remember
that exponentiation precedes addition.
(sum x)^2 means you add all the x values then square them.
The same comment applies to sum y^2 vs. (sum y)^2.
You didn't ask, but sum xy can also be confusing:
Sum xy means multiply each x value by the corresponding y value, then add the products. This is order of operations: multiplication before addition
Self-critique (if necessary):
Self-critique Rating:
Question: `q Query problem 13.6.15 years 0-5, sales 48, 59, 66, 75, 80, 89
What is the coefficient of correlation and how did you obtain it?
Your solution:
Confidence Assessment:
Given Solution:
`a **STUDENT SOLUTION:
X Y XY X^2 Y^2
0 48 0 0 2304
1 59 59 1 3481
2 66 132 4 4356
3 75 225 9 5626
4 80 320 16 6400
5 90 450 25 8100
Sums=
15 418 1186 55 30266
The coefficient of the correlation: r = .996
I found the sums of the following:
x = 15, y = 418, x*y = 1186, x^2 = 55
n = 6 because there are 6 pairs in the data
I also had to find Ey^2 = 30266
I used the following formula:
r = 6(1186) - 15(418) / sq.root of 6(55) - (15)^2 * sq. root of 6(30266) - (418)^2 =
846 / sq. root of 105 * 6872 = 846 / sq. root of 721560 = 846 / 849.4 = .996 **
Self-critique (if necessary):
Self-critique Rating:
Question: `q Query problem 13.6.24 % in West, 1850-1990, .8% to 21.2%
What population is predicted in the year 2010 based on the regression line?
What is the equation of your regression line and how did you obtain it?
Your solution:
Confidence Assessment:
Given Solution:
`aSTUDENT SOLUTION:
Calculating sums and regression line:
n = 8
sum x = 56
sum x^2 = 560
sum = 77.7
sum y^2 = 1110.43
sum xy = 786.4
a = 1.44
b = -.39
r = .99
In the year 2010 the x value will be 16.
y' = 1.44(16) - .39 = 22.65.
There is an expected 22.65% increase in population by the year 2010. **
Self-critique (if necessary):
Self-critique Rating: