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**STAT213 Assignment 6 | Complete Solution**

- From Mathematics, Statistics

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The number of attempts available for each question is noted beside the question. If you are having trouble figuring out your error,

you should consult the textbook, or ask a fellow student, one of the TA’s or your professor for help.

There are also other resources at your disposal, such as the Engineering Drop in Centre and the Mathematics Continuous Tutorials.

Don’t spend a lot of time guessing – it’s not very efficient or effective.

Make sure to give lots of significant digits for (floating point) numerical answers. For most problems when entering numerical

answers, you can if you wish enter elementary expressions such as 2^3 instead of 8, sin(3 pi=2)instead of -1, e^(ln(2)) instead

of 2, (2+tan(3)) (4sin(5))^67=8 instead of 27620.3413, etc.

1. (1 pt) Match the following sample correlation coefficients

with the explanation of what that correlation coefficient means.

Type the correct letter in each box.

1. r = 1

2. r = 0

3. r = :1

4. r = :92

A. a perfect negative relationship between x and y

B. a weak positive relationship between x and y

C. no relationship between x andy

D. a strong positive relationship between x and y

Answer(s) submitted:

(incorrect)

2. (1 pt) Match the correlation coefficients with their scatterplots.

Select the letter of the scatterplot below which corresponds

to the correlation coefficient. (Click on image for a

larger view.)

? 1. r = 0:76

? 2. r = 0:97

? 3. r = 0:49

? 4. r = 0:22

A B C D

Answer(s) submitted:

(incorrect)

3. (1 pt) Use a scatterplot and the linear correlation coefficient

r to determine whether there is a correlation between the

two variables. (Note: Use software, and don’t forget to look at

the scatterplot!)

x 0 1:4 2:7 3:3 4:1 5:7 6:7 7:6 8:9 9:4 10:7 11:9 12y 0 1:9 1:6 3:2 4:7 7:3 8:5 9:5 10:7 8:4 11:4 10:5 10(a) r =

(b) There is

A. a perfect negative correlation between x and y

B. a positive correlation between x and y

C. a perfect positive correlation between x and y

D. a nonlinear correlation between x and y

E. a negative correlation between x and y

F. no correlation between x and y

Answer(s) submitted:

(incorrect)

4. (1 pt)

Keeping water supplies clean requires regular measurement of

levels of pollutants. The measurements are indirect- a typical

analysis involves forming a dye by a chemical reaction with the

dissolved pollutant, then passing light through the solution and

measuring its ” absorbence.” To calibrate such measurements,

the laboratory measures known standard solutions and uses regression

to relate absorbence and pollutant concentration. This

is usually done every day. Here is one series of data on the absorbence

for different levels of nitrates. Nitrates are measured

in milligrams per liter of water.

Nitrates 100 100 150 150 250 600 800 1200 1500 Absorbance 5.1 7.2 12.6 20.7 46.2 94.6 140.2 195.7 209.2 Chemical theory says that these data should lie on a straight

line. If the correlation is not at least 0.997, something went

wrong and the calibration procedure is repeated.

(a) Find the correlation r.

r =

(b) Must the calibration be done again? (Answer YES or

NO).

ANSWER:

1

Answer(s) submitted:

(incorrect)

5. (1 pt) For each problem, select the best response.

(a) You have data for many years on the average price of a

barrel of oil and the average retail price of a gallon of unleaded

regular gasoline. When you make a scatterplot, the explanatory

variable on the x -axis

A. is the price of oil.

B. can be either oil price or gasoline price.

C. is the price of gasoline.

D. None of the above.

(b) What are all the values that a correlation r can possibly

take?

A. -1 r 1

B. 0 r 1

C. r 0

D. None of the above.

(c) In a scatterplot of the average price of a barrel of oil and

the average retail price of a gallon of gasoline, you expect to see

A. a positive association.

B. very little association.

C. a negative association.

D. None of the above.

Answer(s) submitted:

(incorrect)

6. (1 pt) For each problem, select the best response.

(a) A researcher wishes to determine whether the rate of

water flow (in liters per second) over an experimental soil bed

can be used to predict the amount of soil washed away (in kilograms).

In this study, the explanatory variable is the

A. depth of the soil bed.

B. amount of eroded soil.

C. size of the soil bed.

D. rate of water flow.

E. None of the above.

(b) The Columbus Zoo conducts a study to determine

whether a household’s income can be used to predict the amount

of money the household will give to the zoo’s annual fund drive.

The response variable in this study is

A. the amount of money a household gives to the zoo’s

annual fund drive.

B. the Columbus Zoo.

C. a household’s income.

D. all households in Columbus.

E. None of the above.

(c) A researcher measures the correlation between two variables.

This correlation tells us

A. whether there is a relation between two variables.

B. the strength of a straight line relation between two

variables.

C. whether a cause-and-effect relation exists between

two variables.

D. whether or not a scatterplot shows an interesting pattern.

E. None of the above.

Answer(s) submitted:

(incorrect)

7. (1 pt) For each problem, select the best response.

(a) Smokers don’t live as long (on the average) as nonsmokers,

and heavy smokers don’t live as long as light smokers. You

regress the age at death of a group of male smokers on the number

of packs per day they smoked. The slope of your regression

line

A. must be between -1 and 1.

B. will be less than zero.

C. will be greater than zero.

D. can’t tell without seeing the data.

(b) The points on a scatterplot lie close to the line whose

equation is y = 4x5. The slope of the line is

A. -4

B. 5

C. 9

D. 4

E. None of the above.

(c) Measurements on young children in Mumbai, India,

found this least-squares line for predicting height y from

armspan x:

ˆ y = 6:4+0:93x

All measurements are in centimeters (cm). How much on

the average does height increase for each additional centimeter

of armspan?

A. 6.4 cm

B. 0.93 cm

C. 7.33 cm

D. 0.64 cm

E. None of the above.

Answer(s) submitted:

2

(incorrect)

8. (1 pt) A study of king penguins looked for a relationship

between how deep the penguins dive to seek food and how long

they stay underwater. For all but the shallowest dives, there is

a linear relationship that is different for different penguins. The

study report gives a scatterplot for one penguin titled “ The relation

of dive duration (DD) to depth (D).” Duration DD is measured

in minutes and depth D is in meters. The report then says,

“ The regression equation for this bird is: DD = 2.48 + 0.0035

D.

(a) What is the slope of the regression line?.

ANSWER minutes per meter.

(b) According to the regression line, how long does a typical

dive to a depth of 400 meters last?

ANSWER minutes.

Answer(s) submitted:

(incorrect)

9. (1 pt) We have data on the lean body mass and resting

metabolic rate for 12 women who are subjects in a study of dieting.

Lean body mass, given in kilograms, is a person’s weight

leaving out all fat. Metabolic rate, in calories burned per 24

hours, is the rate at which the body consumes energy.

Mass 39.3 36.1 37.7 37.4 44.2 41.9 46 38.2 45.3 46.4 45.3 53.3

Rate 1290 980 1150 900 1230 1050 940 1470 1330 1300 1410 1010

Find the least-squares regression line for predicting metabolic

rate from body mass.

ANSWER: ˆ y =

Answer(s) submitted:

(incorrect)

10. (1 pt) Heights (in centimeters) and weights (in kilograms)

of 7 supermodels are given below. Find the regression equation,

letting the first variable be the independent (x) variable, and predict

the weight of a supermodel who is 167 cm tall.

Height 178 176 166 174 172 168 176

Weight 57 55 47 54 53 50 56

The regression equation is ˆ y = + x:

The best predicted weight of a supermodel who is 167 cm

tall is .

Answer(s) submitted:

(incorrect)

11. (1 pt) Empathy means being able to understand what others

feel. To see how the brain expresses empathy, researchers

recruited 16 couples in their midtwenties who were married or

had been dating for at least two years. They zapped the man’s

hand with an electrode while the woman watched, and measured

the activity in several parts of the woman’s brain that would respond

to her own pain. Brain activity was recorded as a fraction

of the activity observed when the woman herself was zapped

with the electrode. The women also completed a psychological

test that measures empathy.

Subject 1 2 3 4 5 6 7 Empathy Score 42 48 39 55 63 66 66 Brain Activity -0.113 0.383 0.006 0.366 0.013 0.4 0.104 Given that the equation for the regression line is ˆ y=0:00539x+

0:04637, what is the residual for subject 2?

ANSWER:

Answer(s) submitted:

(incorrect)

12. (1 pt) A study was conducted to determine whether the

final grade of a student in an introductory psychology course is

linearly related to his or her performance on the verbal ability

test administered before college entrance. The verbal scores and

final grades for 10 students are shown in the table below.

Student Verbal Score x Final Grade y

1 74 100

2 71 75

3 33 63

4 80 79

5 42 86

6 36 92

7 48 85

8 47 68

9 72 93

10 28 87

Find the following:

(a) The correlation coefficient: r =

(b) The least squares line: ˆ y =

(c) Calculate the residual for the fourth student:

Answer(s) submitted:

3

(incorrect)

13. (1 pt) The amounts of 6 restaurant bills and the corresponding

amounts of the tips are given in the below. Assume

that bill amount is the explanatory variable and tip amount the

response variable.

Bill 64:30 49:72 70:29 106:27 43:58 32:98

Tip 7:70 5:28 10:00 16:00 5:50 4:50

(a) Find the correlation: r =

(b) Does there appear to be a significant correlation?

A. No

B. Yes

(c) The regression equation is ˆ y = .

(d) If the amount of the bill is $95; the best prediction for the

amount of the tip is $ .

Note: Enter your answer as a number xx.xx

(e) According to the regression equation, for every $10 increase

in the bill, the tip should (Enter INCREASE

or DECREASE) by $ .

Answer(s) submitted:

(incorrect)

14. (1 pt) Education and crime ratings for randomly selected

Canadian cities are given in the following table. Education is

a composite rating including pupil/teacher ratio, academic options

in higher education, etc. The higher the education rating,

the better the education system. Crime is expressed in crimes

committed per 100 people.

City Education Rating (%) Crime Rating (%)

Calgary 35 12

Toronto 35 10

Winnipeg 31 16

Vancouver 32 20

Halifax 30 25

Ottawa 36 13

Montreal 33 21

Use two-decimal places in your answers.

(a) State the slope term and the Y -intercept term of

the line which attempts to predict the crime rating of a Canadian

city based on its linear association with its education rating.

(b) Find the correlation

(c) As the education rating of a Canadian city decreases by 1sure

you include the negative sign if warranted) percentage?

(d) What percentage of the variation in the variable Crime Rating

is not explained by its linear relationship to the variable Education

Rating? Use at least one place after the decimal.

(e) Using your answer in (a), predict the mean crime rate of a

Canadian city having an education rating of 34

Answer(s) submitted:

(incorrect)

15. (1 pt) The following data, taken from 8 towns in Alberta,

are the percentage of residents who are university graduates and

the median household incomes (in $ 1000’s) for all households

in each town.

Graduates (%) Median Income ($ 1000)

61.7 47.6

50.9 34.1

57.1 31.5

56.4 41.3

42.8 34.5

42.1 28.1

33.2 23.1

19.2 20.4

Use two-decimal places in your answers.

(a) State the slope term and the Y -intercept term

of the least squares regression line which attempts to predict

the median income of a town in Alberta based on its linear relationship

with the percentage of residents who are university

graduates.

(b) Find the correlation coefficient.

(c) As the percenage of university graduates increases by 10(d)

What percentage of the variation in the variable Median Income

is not explained by its linear relationship to the variable Percentage

of University Graduates? Use at least one place after

the decimal.

(e) Using your answer in (a), predict the average median income

of an Alberta town with 24.0

Answer(s) submitted:

**STAT213 Assignment 6 | Complete Solution**

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- Submitted On 16 Apr, 2015 08:37:44

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