Loudoun County Public Schools / Overview



Exam

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Suppose you were to collect data for the pair of given variables in order to make a scatterplot. Determine for each variable if it is the explanatory variable, the response variable, or whether it could be both.

1)

Studying consistently, high grade point average

1)

_______

A)

Studying consistently: both

High grade point average: explanatory

B)

Studying consistently: both

High grade point average: both

C)

Studying consistently: explanatory

High grade point average: both

D)

Studying consistently: response

High grade point average: explanatory

E)

Studying consistently: explanatory

High grade point average: response

2)

Teacher: weekly salary, teacher: years of experience

2)

_______

A)

Teacher: weekly salary: both

Teacher: years of experience: explanatory

B)

Teacher: weekly salary: explanatory

Teacher: years of experience: response

C)

Teacher: weekly salary: response

Teacher: years of experience: explanatory

D)

Teacher: weekly salary: both

Teacher: years of experience: both

E)

Teacher: weekly salary: explanatory

Teacher: years of experience: both

Suppose you are to form a scatterplot by collecting data for the given pair of variables. Determine the likely direction, form, and strength.

3)

Depth, water pressure

3)

_______

A)

Positive, no form, strong

B)

Positive, nonlinear, moderate

C)

Negative, nonlinear, moderate

D)

Negative, straight, moderate

E)

Positive, straight, strong

4)

Student: grade point average, student: height (feet)

4)

_______

A)

No direction, linear, moderate

B)

Negative, straight, moderate

C)

No direction, no form, very weak

D)

No direction, no form, strong

E)

Positive, no form, very weak

Find the correlation.

5)

Two different tests are designed to measure employee productivity and dexterity. Several employees are randomly selected and tested with these results.

[pic]

36 75

5)

_______

A)

-0.280

B)

0.471

C)

0.115

D)

0.986

E)

0.159

Solve the problem.

6)

A science instructor assigns a group of students to investigate the relationship between the pH of the water of a river and its water's hardness (measured in grains). Some students wrote these conclusions: "there was a very strong correlation of 1.47 between pH of the water and water's hardness." Is the calculation of the correlation appropriate?

6)

_______

A)

Yes: the pH and the hardness of the water are data collected from the same river.

B)

Yes: correlation can be greater than 1.

C)

No: there is little or no association.

D)

No: correlation must be equal to 1.

E)

No: correlation cannot be greater than 1.

7)

A science instructor assigns a group of students to investigate the linear relationship between the pH of the water of a river and its water's hardness (measured in grains). Some students wrote these conclusions: "My correlation of -0.94 shows that there is almost no association between pH of the water and water's hardness." Is the interpretation of the correlation appropriate?

7)

_______

A)

No: a correlation of -0.94 shows a strong relation in a negative direction.

B)

No: correlation is always positive.

C)

Yes: pH and hardness of water do not have the same units.

D)

Yes: a correlation of -0.94 shows a weak relation in a negative direction.

E)

No: the pH and the hardness of the water are data collected from the same river.

8)

A science instructor assigns a group of students to investigate the relationship between the pH of the water of a river and its water's hardness (measured in grains). Some students wrote these conclusions: "there was a very strong correlation of 0.917 [pic] between pH of the water and water's hardness." Is the calculation of the correlation appropriate?

8)

_______

A)

No: correlation has no units.

B)

No: pH and hardness of water have different units.

C)

Yes: the pH and the hardness of the water are data collected from the same river.

D)

Yes: correlation is less than 1.

E)

No: there is little or no association.

Tell what the residual plot indicates about the appropriateness of the linear model that was fit to the data.

9)

[pic]

9)

_______

A)

Model is not appropriate. The relationship is nonlinear.

B)

Model may not be appropriate. The spread is changing.

C)

Model is appropriate.

10)

[pic]

10)

______

A)

Model is appropriate.

B)

Model is not appropriate. The relationship is nonlinear.

C)

Model may not be appropriate. The spread is changing.

Answer the question appropriately.

11)

A random sample of records of electricity usage of homes gives the amount of electricity used and size (in square feet) of 135 homes. A regression to predict the amount of electricity used (in kilowatt-hours) from size has an R-squared of 71.8%. The residuals plot indicated that a linear model is appropriate. Write a sentence summarizing what [pic] says about this regression.

11)

______

A)

Size differences explain 71.8% of the variation in electricity usage.

B)

Differences in electricity usage explain 28.2% of the variation in the number of house.

C)

Differences in electricity usage explain 71.8% of the variation in the size of house.

D)

Size differences explain 71.8% of the variation in the number of homes.

E)

Size differences explain 28.2% of the variation in electricity usage.

12)

The relationship between the number of games won by a minor league baseball team and the average attendance at their home games is analyzed. A regression to predict the average attendance from the number of games won has an [pic] = 29.9%. The residuals plot indicated that a linear model is appropriate. What is the correlation between the average attendance and the number of games won.

12)

______

A)

0.547

B)

0.837

C)

0.701

D)

0.089

E)

0.299

Use the model to make the appropriate prediction.

13)

A random sample of records of electricity usage of homes in the month of July gives the amount of electricity used and size (in square feet) of 135 homes. A regression was done to predict the amount of electricity used (in kilowatt-hours) from size. The residuals plot indicated that a linear model is appropriate. The model is [pic] size. How much electricity would you predict would be used in a house that is 2273 square feet?

13)

______

A)

3477.6 kilowatt-hours

B)

1363.8 kilowatt-hours

C)

1781.67 kilowatt-hours

D)

159.8 kilowatt-hours

E)

2567.8 kilowatt-hours

Answer the question appropriately.

14)

A correlation of zero between two quantitative variables means that

14)

______

A)

re-expressing the data will guarantee a linear association between the two variables.

B)

there is no association between the two variables.

C)

None of the above.

D)

there is no linear association between the two variables.

E)

we have done something wrong in our calculation of r.

Part II:

For each of the problems please do the following:

A) Write down the line of regression with context

B) Write down the correlation coefficient ( r value) with context

C) Write down the coefficient of determination (r2 )

1) 2)

2) The population of the city of Jackson for the past ten years is listed in the chart below.

a) What is the least square regression equation with context

____________________________________

b) What would the population be of Jackson when it is 60 years old?________

c) What would the population be of Jackson when it is 100 years old? ____________

d) How old would Jackson be if the population was 27,486.8?

3.dasdf

The table above shows the years of experience for eight technicians at Lewis Techomatic and the hourly rate of pay each technician earns.

A) What is the least square regression line?

B) Predict the hourly rate of pay for a person who has 7years of experience.

C) How about for a person who has 12 years experience.

1)

E

2)

C

3)

E

4)

C

5)

D

6)

E

7)

A

8)

A

9)

C

10)

B

11)

A

12)

A

13)

E

14)

D

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