devry math399n week 2 homework latest 2016 july

devry math399n 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

sample correlation coefficient.

? represents the

population correlation coefficient.

3.

Suppose the scatter plot shows the results of a survey of

33

randomly selected males ages

24

to

35.

Using age as the explanatoryvariable, 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

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

farmer

wants to determine if the

temperature received by

similar crop

can be used to predict the

harvest of the crop

The explanatory variable is the

.

The response variable is the

.

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

A.

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

B.

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

C.

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

D.

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

6. Match this description with a description below.

Slope

Choose the correct answer below.

A.

b

B.

yi

C.

m

.

D.

y iyi

7. Match the description below with its symbol(s).

The mean of the y-values

Select the correct choice below.

A.

m

B.

y

.

C.

y iyi

D.

yi

E.

(x,y)

F.

b

8.

Match the regression equation

y=0.00114x+2.53

with the appropriate graph.

Choose the correct answer below.

A.

030600102030405060xy

x y graph

B.

050100050100150200250xy

x y graph

C.

040008000024681012xy

x y graph

D.

020400102030405060xy

x y graph

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 66 (a)

xequals=44

hours (b)

xequals=3.53.5

hours

Test score, y

3838 4343 5050 4747 6363 6969 (c)

xequals=1414

hours (d)

xequals=2.52.5

hours

Find the regression equation.

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

xequals=4.

Choose the correct answer below.

A.

53.5

B.

56.2

C.

48.0

D.

not meaningful

(b) Predict the value of y for

xequals=3.5

.

A.

110.7

B.

53.5

C.

48.0

D.

not meaningful

(c) Predict the value of y for

xequals=14

A.

56.2

B.

110.7

C.

53.5

D.

not meaningful

.

(d) Predict the value of y for

xequals=2.5

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 160160 180180 130130 120120 7070 190190 (a)

xequals=150150

calories (b)

xequals=8080

calories

Sodium, y

420420 470470 340340 360360 290290 530530 (c)

xequals=140140

calories (d)

xequals=6060

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

xequals=150

.

A.

246.4

B.

417.578

C.

398.568

D.

not meaningful

(b) Predict the value of y for

xequals=8080.

.

A.

284.508

B.

398.568

C.

246.48

D.

not meaningful

(c) Predict the value of y for

xequals=140

Choose the correct answer below.

A.

398.568

This is the correct answer.

B.

417.578

C.

284.508

D.

not meaningful

(d) Predict the value of y for

xequals=60.

.

A.

246.488

B.

417.578

C.

284.508

D.

not meaningful

11.

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

x 3939 3535 4141 4545 4242 5050 6161 5656 5252

y 2424 2222 2727 3232 3030 3131 3131 2626 2929

LOADING...

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

(a) Find the equation of the regression line.

Y=

( (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

Your answer is correct.

(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 negative 100?100

font size decreased by 3 100100

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 100100

font size decreased by 3 negative 100?100

font size decreased by 3 2020

font size decreased by 3 7070

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

Your answer is correct.

D.

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

(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.

Question is complete.

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 unexplained variation?

R=-

Calculate the coefficient of determination.

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.

About the unexplained variation?

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

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 unexplained variation?

requals=0.599

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=0.24+0.51x1+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

3.1

and a college board score of

500

The predicted college GPA for a high school GPA of

3.1

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

ModifyingAbove y with caret equals negative y=?115+3.57x1+2.02x2,

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

61

inches tall and has

16%

body fat.

The predicted total body weight for a female athlete who is

61

inches tall and has

16%

body fat is