open query 19

#$&*

course Mth 152

03/25/2014, 9:51 p.m.

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

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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.

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

sum of all x=663

sum of all y=1439

sum of all x*y=95748

sum of all x^2=44059

a=10[95748]-[663][1439]/10[44059]-[439569]

b=1439-3.35[663]/10

y=3.35{70}-78.4

y=156.1

confidence rating #$&*:

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3

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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. **

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Self-critique (if necessary):

ok

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Self-critique Rating:

ok

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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

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

a=10[90437]-[811][1104]/10[66225]-[657721]

904370-895344/662250-657721

9026/4529=1.993

b=1104-1.993[811]/10

1104-1616.323/10

-512.323/10=-51.232

y=1.993x + -51.232

confidence rating #$&*:

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3

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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

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Self-critique (if necessary):

ok

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Self-critique Rating:

ok

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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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

sum x=15

sum y=418

sum xy=1186

sum x^2=55

sum y^2=30266

n=6

r=6[1186]-[15][418]/sqrt 6[55]-[225] * sqrt 6[30266]-[174724]

7116-6270/sqrt 105 * sqrt 174724

846/849.4=.996

confidence rating #$&*:

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3

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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 **

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Self-critique (if necessary):

ok

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Self-critique Rating:

ok

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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?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

n=8

all sum x=56

all sum y=77.7

all sum x^2=560

all sum xy=786.4

a=8[786.4]-[56][77.7]/8[560]-[3136]=1.44

b=77.7-1.44[56]/8=-.39

r=8[786.4]-[56][77.7]/sqrt8[560]-[3136]*sqrt8[110.43]-[6037.29]=.99

y=1.44[9]+.39

y=13.35

I came up with x=9

on page 487 of ed 11 text there is an example involving years and percent of people over 65

each interval of 20 years has an x value as follows, 1900=0, 1910=1, 1920=2 etc.

following this example I concluded x=9

confidence rating #$&*:

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2

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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. **

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Self-critique (if necessary):

2

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Self-critique Rating:

???my x value did not match yours, so neither did my y answer, I explained more fully above."

Self-critique (if necessary):

------------------------------------------------

Self-critique rating:

???my x value did not match yours, so neither did my y answer, I explained more fully above."

@&

Your solution was good, except that b = -.39. You got that, but then appear to have used +.39 in your equation.

*@

Self-critique (if necessary):

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Self-critique rating:

#*&!

???my x value did not match yours, so neither did my y answer, I explained more fully above."

@&

Your solution was good, except that b = -.39. You got that, but then appear to have used +.39 in your equation.

*@

Self-critique (if necessary):

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Self-critique rating:

#*&!#*&!

&#Good responses. See my notes and let me know if you have questions. &#