# Statistics Multiple Choice Question and Answer

1

Ali says that when many people observe an accident, the victim is less likely to receive assistance. Ali believes that there is a _____ correlation between these variables.

A. small

B. large

C. negative

D. positive.

2

A politician makes the following claim in a speech: "Correlation analysis research has clearly shown that a lack of education causes people to turn to a life of drugs." What is wrong with this politician's claim?

A. Correlation analysis does not prove that one variable causes another.

B. The data to which the politician referred was based on a small sample size.

C. The politician misinterpreted the direction of the correlation.

D. It would be unethical to conduct correlation analysis on people's drug use.

3

"r squared" is the mathematical notation for:

A. The Coefficient of Determination

B. The Coefficient of Variation

C. Spearman's Coefficient of Rank Correlation

D. Pearson's Coefficient of Correlation

4

What is the range of the Pearson Correlation Coefficient?

A. -1 to 1

B. -1 to 0

C. 0 to 1

D. none of the above

5

If both x and y increase together, the Pearson Correlation Coefficient will be

A. negative

B. positive

C. neutral

D. none of the above

6

If the sample correlation coefficient is r = 1 then it means the correlation is

A. Positive strong linear correlation

B. Negative linear correlation

C. no- linear correlation

D. undetermined

E. None of the above

7

Define the coefficient of determination (r squared).

A. measure of the proportion of variation in y using x as the explanatory variable

B. measure of direction of association between dependent and independent variables

C. a and b

D. none of the above

8

The variable being predicted is called the:

A. y variable.

B. dependent variable or x.

C. x.

D. explanatory variable.

9

In simple linear correlation analysis

A. there is only one variable in the model.

B. could be several linear independent variables in the model.

C. there is only one nonlinear term in the model.

D. dependent and independent variables are quantitative.

E. None of the above

10

In simple linear association model, if there is a very strong correlation between the independent and dependent variables, then the correlation coefficient should be

A. close to-1.

B. close to +1.

C. close to either -1 or +l.

D. close to zero.

11

The correlation coefficient r was computed to be -0.60. This indicates that

A. there is almost no relationship between the two variables

B. 60 percent of the variation in the independent variable is accounted for by the variation in the dependent variable.

C. the coefficient of determination is 40%.

D. Slope of the linear association is negative.

E. none of the above

12

A researcher claims that the yield in bushels per acre is related to the average temperature. Interpret the outcome if he collects data on 6 different regions and computed value of the correlation coefficient is 0.98.

A. There is a moderate correlation between temperature and yield.

B. There is a perfect correlation between temperature and yield.

C. 2% of changes of temperature is associated with yield.

D. 98% of changes of yield is associated with temperature.

E. There is a strong positive association between temperature and yield.

13

A researcher claims that the yield in bushes per acre is related to the average temperature. Interpret the coefficient of determination if he collects data on 6 different regions and computed value of the correlation coefficient is 0.98.

A. 98% of the yield is associated with temperature.

B. 2% of the yield is associated with temperature.

C. 4% of changes of temperature is not associated with the region.

D. 96% of regions have yield.

E. 96% of changes of yield are associated with changes of temperature.

F. None of the above

14

Assuming a linear regression of y = 2.1 + 0.8X between temperature and yield, if average temperature is 15 degree, the value of yield in bushes per acre is

A. 33.5

B. 17.1

C. 14.1

D. None of the above

15

Assuming a linear regression of y = 2.1 + 0.8X between temperature and yield, interpret the value of 2.1.

A. It shows strength of association between yield and temperature.

B. Yield is 2.1 times of temperature.

C. At zero temperature, yield is 2.1.

D. Yield and temperature go up together.

E. None of the above.

16

Assuming a linear regression of y = 2.1 + 0.8X between temperature and yield, interpret the value of +0.8.

A. It shows strength of association between yield and temperature.

B. Yield is 0.8 times of temperature.

C. Yield changes 0.8 in each region.

D. For every extra yield there is 0.8 extra temperatures.

E. None of the above.

17

In simple linear regression model with x representing the independent variable and y representing the dependent variable, linear regression analysis is used to

A. find sample size.

B. find the y intercept and slope of the line of association between X and Y.

C. measure the strength of the linear relationship between x and y, as well as the direction of association.

D. draw a scatter plot

18

If through some analysis, one can conclude that the slope of the line of best fit is not equal to zero, then the simple linear regression model indicates that there is

A. a positive relationship between the independent and dependent variables.

B. a negative relationship between the independent and dependent variables.

C. a positive or negative relationship between the independent and dependent variables.

D. no relationship between the independent and dependent variables.

19

Which of the following is associated with correlation and regression analysis?

A. Least-squares

B. Correlation coefficient

C. Coefficient of determination

D. All of the above

20

For simple linear regression model, if the unit for the dependent variable is square feet, then the unit for the independent variable

A. must be square feet.

B. can be some unit of square measurement.

C. can be any unit.

D. cannot be a unit of square measurement.

21

The slope of the line is called:

A. a and is the point where the regression line cuts the vertical axis.

B. b and gives us a measure of how much y changes as x changes.

C. a correlation coefficient and indicates the variability of the points around the regression line in the scatter plot.

D. none of the above.

22

We have a negative relationship between number of drinks consumed and number of marks in a driving test. One individual scores 3 on number of drinks consumed, another individual scores 5 on number of drinks consumed. What will be their respective scores on the driving test if the intercept is 18 and the slope -3?

A. Driving test scores (y-axis) will be 27 [individual who scored 3 on drink consumption] and 33 [individual who scored 5 on drink consumption].

B. It is not possible to predict from negative relationships.

C. Driving test scores (y-axis) will be 9 [individual who scored 3 on drink consumption] and 3 [individual who scored 5 on drink consumption].

D. Driving test scores (y-axis) will be 51 and 87 [individual who scored 5 on drink consumption].

23

If b = 0 the line of best fit will conventionally be drawn

A. as vertical.

B. as horizontal.

C. as provides the best fit to the scores.

D. through the middle of the data points.

24

On a scatterplot, the regression line

A. is drawn parallel to the horizontal axis.

B. is always perpendicular to the vertical axis.

C. comes as close as possible to touching every score.

D. touches at least half of the scores.

25

A perfect association between variables can be seen on a scatter plot when

A. all dots lie an equal distance from the regression line.

B. all dots lie on the regression line.

C. the regression line forms a right angle at its intersection with the X axis.

D. the regression line is parallel to the X axis.

26

If the regression line showing association between "years of education" and "income" has a slope of 1000,

A. the variables are not related.

B. every year of education increases income by 1000.

C. every change in education increases income.

D. the Y intercept would be 1.00.

27

A study found that parenting classes were closely related to a child's performance in school. Each week of parenting classes taken by a child's parents raised their high school GPA by 0.23 points. With an intercept of 1.68, what could parents who attended 8 weeks of classes expect to see in their child's subsequent GPA?

A. 2.52

B. 3.21

C. 3.52

D. 3.79

28

A research project found that in studying the effects of days spent in drug rehabilitation and number of subsequent arrests, that the slope was -0.59 and the intercept was 6.13. If a person spends 3 days in rehabilitation, what would be their predicted number of future arrests?

A. 2.37

B. 4.36

C. 6.32

D. 7.90

29

A researcher asked a sample of dual career families about the percentage of the family budget contributed by the wife's job (Y) and the total number of children (X). Pearson's r for this relationship is -0.34. Which of the following is an appropriate interpretation of these results?

A. For every dollar contributed by the wife, the number of children increases by .34.

B. For every additional child, the wife must work longer hours.

C. Every additional child lowers the economic wellbeing of the family.

D. As number of children increase, the percentage of the budget contributed by the wife decreases.

30

A study of traffic safety shows a correlation of 0.57 between average speed of traffic and number of fatal accidents for a particular stretch of highway. This means that

A. drivers should speed up to get through this area as quickly as possible.

B. as speed increases, fatalities decrease.

C. fatalities tend to increase as average speed increases.

D. every 1 mile per hour increase in average speed increases the number of traffic fatalities by .57.

31

In a study of the relationship between geographical mobility (number of times a person has changed residences) and number of friends, Pearson's coefficient of determination (is reported as .40. Which of the following would be a correct interpretation?

A. Mobility explains 16% of the variation in number of friends.

B. There is a strong positive relationship between number of friends and mobility.

C. As mobility increases, number of friends decreases.

D. Mobility explains 40% of the variation in number of friends.

32

At Middletown High, a coefficient of correlation of -0.60 was found between the number of high-school activities offered and the number of drug-related suspensions. What percent of drug-related suspensions is explained by factors other than high-school activities?

A. 36%

B. 40%

C. 60%

D. 64%

33

Correlation coefficient of the relationship between unemployment and crime rates is calculated for 4 different cities. Which city shows the strongest relationship between these two variables?

A. City A, r = +1.7

B. City B, r = - 0.6

C. City C, r = +0.11

D. City D, r = +0.588

34

Which correlation coefficient best presents association between hours of studying and grade?

A. -0.4

B. +0.3

C. +1.0

D. +0.8

35

Scatter plot can be used to study

A. direction of association between gender and income

B. percentage variation of association between gender and income

C. strength and direction of association between minutes doing exercise and body fat percentage

D. All of the above

36

In a government study of the relationship between the number of passengers on an aircraft and the total weight in kg of luggage stored in the aircraft's baggage compartment, the coefficient of correlation is computed to be 0.8. We can, therefore, conclude that

A. 80% of the variation in the weight of luggage is explained by the number of passengers

B. 20% of the variation in the weight of luggage is explained by the number of passengers

C. 64% of the variation in the weight of luggage is explained by the number of passengers

D. 36% of the variation in the weight of luggage is explained by the number of passengers

37

Which of the following is not a possible value of correlation coefficient?

A. +1

B. -1

C. 0.011

D. 1.1.

38

For the simple linear correlation model, if all the points on a scatter plot lie on a straight line then the correlation coefficient can be:

A. -1.

B. +1.

C. positive or negative.

D. All of the above

39

What does a -0.8 correlation coefficient between the dependent variable y and the independent variable x indicate?

A. There is strong negative correlation between these two variables.

B. There is almost no correlation between these two variables.

C. Changes of variable y is strongly caused by changes of variable x.

D. None of the above

40

What does linear correlation analysis show?

A. Strength of association between the dependent variable y and the independent variable x

B. Percent of the variation in dependent variable associated with the variation in the independent variable.

C. Direction of association between dependent and independent variables.

D. All of the above

41

Simple Linear Correlation analysis is used to:

A. study cause and effect relationship between variables.

B. study changes of independent variable.

C. study growth of variables.

D. study relationship between two variables.

E. none of the above.

42

You are given the attached set of observations for the independent variable x and the dependent variable y. The correlation coefficient is

x 3 1 2 3

y 8 4 5 5

A. -1.0.

B. -0.7.

C. 0.8.

D. 0.7.

43

You are given the attached set of observations for the independent variable x and the dependent variable y. The data set shows that:

x 3 1 2 3

y 8 4 5 5

A. There is strong negative correlation between these two variables.

B. There is no correlation between these two variables.

C. There is weak positive correlation between these two variables.

D. None of the above

44

You are given the attached set of observations for the independent variable x and the dependent variable y. What does it show?

x 2 1 4 5 5

y 6 4 3 2 2

A. There is no correlation between the two variables

B. There is a positive correlation between the two variables

C. There is a negative correlation between the two variables

D. None of the above

45

The yield in bushes per acre is related to the average temperature. The attached sample data was obtained in a recent study. The least-square regression equation for yield in bushes and the average temperature is

Region Temperature Yield (in bushes per acre)

1 4 3

2 8 7

3 10 8

4 12 10

5 9 8

6 6 4

A. y = 1.3 + 1.1X

B. y = 2.1 + 0.9 X

C. y = -0.8 + 0.9 X

D. y = -1.3 + 1.1X

46

Which correlation coefficient best presents the attached graph?

A. -0.4

B. -0.9

C. -1.0

D. +0.8

https://brainmass.com/statistics/simple-linear-regression/statistics-multiple-choice-question-and-answer-642721

#### Solution Preview

1

Ali says that when many people observe an accident, the victim is less likely to receive assistance. Ali believes that there is a _____ correlation between these variables.

A. small

B. large

C. negative

D. positive.

Answer: C. As the number of people to observe the accident increases, the likelihood that the victim will receive assistance decreases.

2

A politician makes the following claim in a speech: "Correlation analysis research has clearly shown that a lack of education causes people to turn to a life of drugs." What is wrong with this politician's claim?

A. Correlation analysis does not prove that one variable causes another.

B. The data to which the politician referred was based on a small sample size.

C. The politician misinterpreted the direction of the correlation.

D. It would be unethical to conduct correlation analysis on people's drug use.

Answer: A. The politician said the correlation analysis showed cause when that isn't the purpose of correlation analysis.

3

"r squared" is the mathematical notation for:

A. The Coefficient of Determination

B. The Coefficient of Variation

C. Spearman's Coefficient of Rank Correlation

D. Pearson's Coefficient of Correlation

Answer: A. r^2 is known as the Coefficient of Determination.

4

What is the range of the Pearson Correlation Coefficient?

A. -1 to 1

B. -1 to 0

C. 0 to 1

D. none of the above

Answer: A. The lowest value is -1 while the highest value is 1.

5

If both x and y increase together, the Pearson Correlation Coefficient will be

A. negative

B. positive

C. neutral

D. none of the above

Answer: B. When both x and y increase together, there is a positive correlation between the variables.

6

If the sample correlation coefficient is r = 1 then it means the correlation is

A. Positive strong linear correlation

B. Negative linear correlation

C. no- linear correlation

D. undetermined

E. None of the above

Answer: A. 1 is a positive number.

7

Define the coefficient of determination (r squared).

A. measure of the proportion of variation in y using x as the explanatory variable

B. measure of direction of association between dependent and independent variables

C. a and b

D. none of the above

Answer: A

8

The variable being predicted is called the:

A. y variable.

B. dependent variable or x.

C. x.

D. explanatory variable.

Answer: B

9

In simple linear correlation analysis

A. there is only one variable in the model.

B. could be several linear independent variables in the model.

C. there is only one nonlinear term in the model.

D. dependent and independent variables are quantitative.

E. None of the above

Answer: D. Both variables need to have numerical values.

10

In simple linear association model, if there is a very strong correlation between the independent and dependent variables, then the correlation coefficient should be

A. close to-1.

B. close to +1.

C. close to either -1 or +l.

D. close to zero.

Answer: C

11

The correlation coefficient r was computed to be -0.60. This indicates that

A. there is almost no relationship between the two variables

B. 60 percent of the variation in the independent variable is accounted for by the variation in the dependent variable.

C. the coefficient of determination is 40%.

D. Slope of the linear association is negative.

E. none of the above

Answer: D. -0.60 is a negative number. When r is negative, the slope of the linear association is also negative.

12

A researcher claims that the yield in bushels per acre is related to the average temperature. Interpret the outcome if he collects data on 6 different regions and computed value of the correlation coefficient is 0.98.

A. There is a moderate correlation between temperature and yield.

B. There is a perfect correlation between temperature and yield.

C. 2% of changes of temperature is associated with yield.

D. 98% of changes of yield is associated with temperature.

E. There is a strong positive association between temperature and yield.

Answer: E. 0.98 is close to +1.

13

A researcher claims that the yield in bushes per acre is related to the average temperature. Interpret the coefficient of determination if he collects data on 6 different regions and computed value of the correlation coefficient is 0.98.

A. 98% of the yield is associated with temperature.

B. 2% of the yield is associated with temperature.

C. 4% of changes of temperature is not associated with the region.

D. 96% of regions have yield.

E. 96% of changes of yield are associated with changes of temperature.

F. None of the above

Answer: E, ...

#### Solution Summary

The solutions are available in Word format as well as in text format. The Excel file contains computations for selected problems.