Deck 10: Correlation and Regression

Question 1

A regression line was calculated as .The slope of this line is -3.2.

Answer 1

True

Question 2

The standard error of estimate is the standard deviation of the observed x-values about the predicted values.

Answer 2

False

Question 3

With enough variables, it is possible to get an value close to 1, even if the variables have no particular
meaning in the model.

Answer 3

True

Question 4

The range of the correlation coefficient is from 0 to 1.

Question 5

A positive relationship exists when both variables increase or decrease at the same time.

Question 6

A correlation coefficient of 0.96 would mean that the values of x increase as the values of y decrease.

Question 7

When the x-axis and y-axis have been truncated, the y-intercept can be used to graph the regression
line.

Question 8

Using a regression line of , a value of x = 3.6 would result in a predicted value of .

Question 9

If one found that the sum of the residuals from a regression line (with an intercept) was a large negative
value, one could conclude that there is a negative relationship between the independent and dependent
variables.
There must have been a calculation error since the residuals sum to 0 (apart from rounding error).

Question 10

The standard error of estimate is the square root of the unexplained variation.

Question 11

The symbol used for the multiple correlation coefficient is R.

Question 12

If there are three independent variables available, then the value of for a multiple
regression of y using will always be smaller than the value of for a multiple regression of y
using just

Question 13

The two variables in a scatter plot are called the

A)Independent variable and dependent variable
B)Relative frequency and relative proportion
C)Spread and pattern
D)Lines and points

Question 14

The possible relationship between pairs of data values could be examined from a

A)Histogram
B)Scatter plot
C)Pareto graph
D)Pie chart

Question 15

Regression is a statistical method used to describe the nature of the relationship between variables.

Question 16

A positive linear relationship exists when the points in a Pareto graph fall approximately in an ascending
straight line.

Question 17

The population correlation coefficient is computed by using all possible pairs of data values x, y taken
from a population.

Question 18

If the correlation between two variables is computed to be 0.012, one can conclude that there is
essentially no relation between the two variables.

Question 19

The rounding rule for the correlation coefficient uses two decimal places.

Question 20

A regression line can be used to show trends in data.

Question 21

Compute the correlation coefficient for the data below

A)0.942
B)-0.347
C)-0.496
D)-0.992

Question 22

Test the significance of the correlation coefficient r at for the data below.

A)
B)
C)
D)

Question 23

A study was conducted to determine if there was a relationship between the prices a non-member of a club paid for various publications and the prices that a member paid for the same publications.The data
Gathered are shown below.What is the value of the correlation coefficient?

A)0.762
B)0.857
C)0.679
D)0.932

Question 24

The western city wishes to see if there is a relationship between the summer temperature and the amount
of electricity used (in kilowatts).
If a correlation coefficient calculated for n = 14 and is found to be r = 0.856, what is the test value for the t - test?

A)4.059
B)5.736
C)2.851
D)6.374

Question 25

A study was conducted to determine if there was a relationship between the prices a non-member of a club paid for various publications and the prices that a member paid for the same publications.The data
Collected is shown below.Determine the value of

A)13,251
B)93,624
C)19,712
D)9349

Question 26

Daniel Wiseman, a scientist for Gres-Trans Corp., wants to determine if the flow rate of a particular material changes with different changes in temperature.The data is plotted in the figure
Below.What type of relationship exists between the flow rate and the change in temperature?

A)negative
B)positive
C)There is no relationship.
D)curvilinear

Question 27

Compute the correlation coefficient for the data below

A)-0.484
B)0.235
C)0.000
D)-0.323

Question 28

Compute the correlation coefficient for the data below

A)0.521
B)0.368
C)-0.271
D)-0.058

Question 29

Which of the following does not explain a possible relationship between variables when the null hypothesis is rejected?

A)direct cause-and-effect
B)reverse cause-and-effect
C)caused by a third variable
D)negative effect

Question 30

If r = -0.879 and n = 6, test the significance of the correlation coefficient at

A)
B)
C)
D)

Question 31

Determine the type of relationship shown in the figure below.

A)positive
B)negative
C)multiple
D)There is no relationship.

Question 32

The equation of a regression line is .What is the intercept of this line?

A)-4.6
B)3.2
C)4.6
D)0

Question 33

Compute the correlation coefficient for the data below

A)0.123
B)10.857

Question 34

A study was conducted to determine if there was a relationship between the prices a non-member of a club paid for various publications and the prices that a member paid for the same publications.The data
Collected are shown below.Find the value of

A)13,251
B)93,624
C)19,712
D)9349

Question 35

Compute the correlation coefficient for the data below

A)0.661
B)-0.437
C)0.467
D)-0.135

Question 36

Ten pairs of points yielded a correlation coefficient r of 0.79.If which of the following statements is correct if (Do not calculate a t-value.)

A)Because 0.79 is greater than 0.632, the null hypothesis is not rejected.
B)Because 0.79 is greater than 0.632, the null hypothesis is rejected.
C)Because 0.79 is greater than 0.602, the null hypothesis is not rejected.
D)There is no correlation between the variables.

Question 37

The western city wishes to see if there is a relationship between the summer temperature and the amount
of electricity used (in kilowatts).
A correlation coefficient computed for n = 18 and is r = 0.692.Using the t -test for the correlation coefficient, what are the critical values?

A)+2.120
B)+2.101
C)+1.734
D)+1.746

Question 38

A study was conducted to determine if there was a relationship between the prices a non-member of a club paid for various publications and the prices that a member paid for the same publications.Which of
The following could not be the value of a correlation coefficient?

A)-0.683
B)0.197
C)1.000
D)-1.369

Question 39

The western city wishes to see if there is a relationship between the summer temperature and the amount
of electricity used (in kilowatts).
Compute the value of the correlation coefficient for the data in the table.

A)0.924
B)0.834
C)0.798
D)0.938

Question 40

Test the significance of the correlation coefficient r at for the data below.

A)
B)
C)
D)

Question 41

If the equation for the regression line is y = -4x + 6, then the slope of this line is

A)12
B)6
C)2
D)-4

Question 42

Compute the standard error of the estimate for the data below.

A)0.66
B)1.02
C)1.49
D)1.79

Question 43

Compute the slope of the regression line for the data below.

A)-1.31
B)-0.43
C)0.93
D)-3.06

Question 44

If the equation for the regression line is y = 7x - 6, then a value of x = 3 will result in a predicted value for y of

A)13
B)25
C)27
D)15

Question 45

Compute the slope of the regression line for the data below.

A)-0.51
B)-1.43
C)1.01
D)-3.37

Question 46

If the equation for the regression line is y = 11x + 2, then a value of x = -3 will result in a predicted value for y of

A)2
B)5
C)-31
D)11

Question 47

Compute the standard error of the estimate for the data below.

A)3.36
B)3.93
C)7.06
D)9.07

Question 48

Compute the intercept of the regression line for the data below.

A)3.54
B)3.87
C)4.15
D)4.87

Question 49

Compute the slope of the regression line for the data below.

A)-1.93
B)-0.93
C)1.36
D)-4.78

Question 50

If the equation for the regression line is y = -8x + 3, then the intercept of this line is

A)6
B)3
C)-5
D)-8

Question 51

If the correlation coefficient r is equal to 0.6, find the coefficient of nondetermination.

A)0.64
B)0.77
C)0.48
D)0.36

Question 52

The following data list ages of cars (in years) and monthly repair cost (in dollars).What is the standard error of estimate?

A)6.36
B)7.34
C)8.75
D)5.49

Question 53

Compute the standard error of the estimate for the data below.

A)11.50
B)3.80
C)14.46
D)7.35

Question 54

Compute the intercept of the regression line for the data below.

A)0.71
B)3.72
C)3.93
D)9.32

Question 55

If the correlation coefficient r is equal to 0.66, find the coefficient of determination.

A)The coefficient of determination is 0.56.
B)The coefficient of determination is 0.81.
C)The coefficient of determination is 0.44.
D)The coefficient of determination is 0.19.

Question 56

What is the value of when x = 3, if the equation of the regression line is = 23.1 - 3.8x?

A)4.73
B)5.29
C)34.5
D)11.7

Question 57

If the correlation coefficient is 0.79, what is the explained variation?

A)37.6%
B)62.4%
C)79%
D)21%

Question 58

Compute the intercept of the regression line for the data below.

A)1.38
B)2.90
C)3.77
D)7.54

Question 59

If the correlation coefficient r is equal to 0.48, find the coefficient of determination.

A)0.77
B)0.69
C)0.36
D)0.23

Question 60

What is the equation for the regression line if ?

A)
B)
C)
D)

Question 61

An experiment is carried out to determine the relationship between the average speed
(rpm) and power (hp) of a mixer.Construct a scatter plot for the data obtained in the
experiment.

Question 62

A psychologist wants to determine if there is a linear relationship between the number of hours a
person goes without sleep and the number of mistakes he/she makes on a simple test.The following
data is recorded.Determine the equation of the regression line and graph the line on a scatter
plot.

Question 63

The standard error of estimate can be used for constructing a(n) __________ interval about a value.
________________________________________

Question 64

When r is not significantly different from 0, the best predictor of y is the mean of the __________ of
y.
________________________________________

Question 65

A study on the oxygen consumption rate (OCR) of sea cucumbers involved random samples of size 3 at each of the temperatures 10, 11, 12, 13, 14, and 15oC A regression model was fit in order to study
The relationship between OCR and temperature.If one of the analysts converted the temperatures to
Fahrenheit (o F = 32 +(9/5) o C ) the correlation coefficient would be

A)increased by a factor 9/5
B)increased by a factor 5/9
C)unaltered
D)decreased by a factor 9/5

Question 66

In a multiple regression model if the value of increases by 6 and the value of x3 decreases by 3, then the predicted value for y will

A)increase by 87
B)decrease by 87
C)increase by 45
D)decrease by 45

Question 67

As a researcher collects more and more data, the 95% prediction intervals in general

A)become narrower and narrower, with the widths getting closer and closer to 0
B)become narrower and narrower, but the widths are always more than approximately 2 times the standard error of the estimate
C)become narrower and narrower, but the widths are always more than approximately 4 times the standard error of the estimate
D)become narrower and narrower, but the widths are always more than approximately 4 times the slope

Question 68

For a prediction value of y' from a specific value x, which of the following contribute to the prediction error?

A)The error in estimating the slope
B)The error in estimating the intercept
C)The standard error of the estimate
D)All of the above

Question 69

An analysis results in a multiple regression equation of We can conclude that

A)The variable x1 is a very significant factor in this model
B)The variable x1 is a moderately significant factor in this model
C)The variable x1 is not a significant factor in this model
D)This is insufficient information to assess the significance of x1

Question 70

In a multiple regression model value changes by 2, then the predicted value for y will change by

A)10
B)32
C)0
D)30

Question 71

If there is a strong negative linear relationship between the variables, the value of __________ will be
close to -1.
________________________________________

Question 72

A study was conducted to determine if there was a linear relationship between a person's age and his/
her peak heart rate.Construct a scatter plot and determine what type of relationship there is between a
person's age and his/her peak heart rate.

Question 73

A multiple regression line was calculated in which was a student's grade point average and was a student's age.The multiple regression line was calculated as .If a student has a grade
Point average of 5.9 and is 20 years old, what is the predicted value of ?

A)387.2
B)400.1
C)421.6
D)615.5

Question 74

A study on the oxygen consumption rate (OCR) of sea cucumbers involved random samples of size 3 at each of the temperatures 10, 11, 12, 13, 14, and 15oC A regression model was fit in order to study
The relationship between OCR and temperature.The degrees of freedom for testing that there is no
Relationship between OCR and temperature would be

A)5
B)8
C)15
D)16

Question 75

Draw a scatter plot for the following data that show the demand for a product (in hundreds) and its price
(in dollars) charged in nine different cities.

Question 76

A correlation coefficient r was calculated to be 0.61.The coefficient of determination would be
approximately __________.
________________________________________

Question 77

__________ is a statistical method used to determine whether a relationship between variables exists.
________________________________________

Question 78

A study on the oxygen consumption rate (OCR) of sea cucumbers involved random samples of size 3 at each of the temperatures 10, 11, 12, 13, 14, and 15oC.A regression model was fit in order to study the
Relationship between OCR and temperature.The slope of the regression line was found to be positive.
If one of the analysts converted the temperatures to Fahrenheit (o F = 32 + (9/5) o C) the slope of the
Regression line would be

A)increased by a factor 9/5
B)increased by a factor 5/9
C)unaltered
D)decreased by a factor 9/5