devry math221n week 2 homework latest 2016 july

devry math221n week 2 homework latest 2016 july

1.

Two variables have a positive linear correlation. Does the dependent variable increase or decrease as the independent variable increases?

Choose the correct answer below.

The dependent variable decreases.

The dependent variable increases

2.

Discuss the difference between r and

?.

Choose the correct answers below.

r represents the

?

Suppose the scatter plot shows the results of a survey of 3434 randomly selected males ages 2424 to 3535. Using age as the explanatory? variable, choose the appropriate description for the graph. Explain your reasoning.

?(a) Age and body temperature

?(b) Age and balance on student loans

?(c) Age and income

?(d) Age and height

24

26

28

30

32

34

36

0

10

20

30

40

50

Age

In thousands of units

x y graph

The response variable is

because you would expect this variable and age to have

and

variation for adult males

4.

Identify the explanatory variable and the response variable.

A

golfer

wants to determine if the

number of lessons receivednumber of lessons received

every year

can be used to predict the

amount of improvement in his game.

The explanatory variable is the

.

The response variable is the

Two variables have a positive linear correlation. Is the slope of the regression line for the variables positive or negative?

A.

The slope is positive. As the independent variable increases the dependent variable tends to decrease.

B.

The slope is positive. As the independent variable increases the dependent variable also tends to increase.

C.

The slope is negative. As the independent variable increases the dependent variable tends to decrease.

D.

The slope is negative. As the independent variable increases the dependent variable also tends to increase.

6.

Match this description with a description below.

The y dash value of a data point corresponding to xi

Choose the correct answer below.

A.

m

B.

b

C.

Y^i

D.

yi

7.

Match the description below with its symbol(s).

The mean of the y-values

Select the correct choice below.

A.

b

B.(x,y)

C.

yi

D.

yi

E.

y

F.

8.

Match the regression equation

^y=?0.667x+52.6

with the appropriate graph.

Choose the correct answer below.

A.

050100050100150200250xy

x y graph

B.

040008000024681012xy

x y graph

C.

030600102030405060xy

x y graph

D.

020400102030405060xy

9.

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.

font size decreased by 1 font size increased by 1 Hours spent studying comma xHours spent studying, x 00 22 33 33 55 55 (a)

x=2

hours (b)

x=2.5

hours

Test score, y

40 41 51 45 65 67 (c)

x=14

hours (d)

xequals=3.53.5

hours

Find the regression equation.

y ^= 5.722x +( 34.333)

(Round to three decimal places as needed.)

Choose the correct graph below.

A.

08080Hours studyingTest score

x y graph

B.

08080Hours studyingTest score

x y graph

C.

08080Hours studyingTest score

x y graph

D.

08080Hours studyingTest score

x y graph

(a) Predict the value of y for

x=2.

Choose the correct answer below.

A.

54.4

B.

45.8

C.

48.6

D.

not meaningful

(b) Predict the value of y for

x=2.5.

Choose the correct answer below.

A.

54..4

B.

48.6

C.

114.4

D.

not meaningful

(c) Predict the value of y for

x=14

Choose the correct answer below.

A.

45.8

B.

114..4

C.

48.6

D.

not meaningful

(d) Predict the value of y for

x=3.5.

Choose the correct answer below.

A.

45.8

B.

54.4

C.

114.4

D.

not meaningful

Question is complete.

10.

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below.

font size decreased by 1 font size increased by 1 Calories comma xCalories, x 150 180 130 130 70 190 (a)

x=160

calories (b)

x=100

calories

Sodium, y

420 470 330 380 260 540 (c)

x=140

calories (d)

x=220

calories

Find the regression equation.

Y^=

(Round to three decimal places as needed.)

Choose the correct graph below.

A.

02000560CaloriesSodium (mg)

x y graph

B.

02000560CaloriesSodium (mg)

x y graph

C.

02000560CaloriesSodium (mg)

x y graph

D.

02000560CaloriesSodium (mg)

x y graph

(a) Predict the value of y for

x=160.

Choose the correct answer below.

A.

574.711

B.

396.311

C.

440..911

.

D.

not meaningful

(b) Predict the value of y for

x=100.

Choose the correct answer below.

A.

307.111

B.

396.311

C.

574.711

D.

not meaningful

(c) Predict the value of y for

x=140.

Choose the correct answer below.

A.

396.311

B.

440.911

C.

307.111

D.

not meaningful

(d) Predict the value of y for

x=220.

Choose the correct answer below.

A.

440.911

B.

574.711

C.

307.111

D.

not meaningful

Question is complete.

11.

Use the data in the table below to complete parts (a) through (d).

x 38 34 40 47 44 50 60 5555 5151

y 23 22 25 29 27 28 26 2323 2525

LOADING...

Click the icon to view details on how to construct and interpret residual plots.

(a) Find the equation of the regression line.

Y^=

(Round to three decimal places as needed.)

(b) Construct a scatter plot of the data and draw the regression line. Plot the x-values on the horizontal axis and the y-values on the vertical axis. Choose the correct graph below.

A.

font size decreased by 3 00

font size decreased by 3 2020

font size decreased by 3 7070

font size decreased by 3 2020

font size decreased by 3 3434

x y graph

B.

font size decreased by 3 00

font size decreased by 3 2020

font size decreased by 3 7070

font size decreased by 3 2020

font size decreased by 3 3434

x y graph

C.

font size decreased by 3 00

font size decreased by 3 2020

font size decreased by 3 7070

font size decreased by 3 2020

font size decreased by 3 3434

x y graph

D.

font size decreased by 3 00

font size decreased by 3 2020

font size decreased by 3 7070

font size decreased by 3 2020

font size decreased by 3 3434

x y graph

(c) Construct a residual plot. Plot the x-values on the horizontal axis and the residuals on the vertical axis. Choose the correct graph below.

A.

font size decreased by 3 00

font size decreased by 3 100100

font size decreased by 3 negative 100?100

font size decreased by 3 2020

font size decreased by 3 7070

x y graph

B.

font size decreased by 3 00

font size decreased by 3 66

font size decreased by 3 negative 6?6

font size decreased by 3 2020

font size decreased by 3 3434

x y graph

C.

font size decreased by 3 00

font size decreased by 3 66

font size decreased by 3 negative 6?6

font size decreased by 3 2020

font size decreased by 3 7070

x y graph

D.

font size decreased by 3 00

font size decreased by 3 negative 100?100

font size decreased by 3 100100

font size decreased by 3 2020

font size decreased by 3 3434

x y graph

(d) Determine if there are any patterns in the residual plot and explain what they suggest about the relationship between the variables.

The residual plot

a pattern because the residuals

about 0. This implies the regression line

a good representation of the relationship between the variables.

12.

Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplainedvariation?

r?0.488

Calculate the coefficient of determination.

(Round to three decimal places as needed.)

What does this tell you about the explained variation of the data about the regression line?

of the variation can be explained by the regression line.

(Round to one decimal place as needed.)

About the unexplained variation?

of the variation is unexplained and is due to other factors or to sampling error.

(Round to one decimal place as needed.)

13.

Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplainedvariation?

R=?0.999

Calculate the coefficient of determination.

(Round to three decimal places as needed.)

What does this tell you about the explained variation of the data about the regression line?

of the variation can be explained by the regression line.

(Round to one decimal place as needed.)

About the unexplained variation?

of the variation is unexplained and is due to other factors or to sampling error.

(Round to one decimal place as needed.)

14.

The equation used to predict college GPA (range 0-4.0) is

Y^=0.21+0.53x1+0.002x2,

where

x1

is high school GPA (range 0-4.0) and

x2

is college board score (range 200-800). Use the multiple regression equation to predict college GPA for a high school GPA of

3.4

and a college board score of

500

The predicted college GPA for a high school GPA of

3.4

and a college board score of

500

is

.

(Round to the nearest tenth as needed.)

15.

The equation used to predict the total body weight (in pounds) of a female athlete at a certain school is

Y^=?113+3.05x1+2.07x2,

where

x1

is the female athlete's height (in inches) and

x2

is the female athlete's percent body fat, measured as

x2%.

Use the multiple regression equation to predict the total body weight for a female athlete who is

65

inches tall and has

18%

body fat.

The predicted total body weight for a female athlete who is

65

inches tall and has

18%

body fat is

pounds. (Round to the nearest tenth as needed.)