Deck 9: Correlation and Regression

Question 1

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

Answer 1

True

Question 2

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

Answer 2

True

Question 3

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

Answer 3

True

Question 4

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 5

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 6

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 7

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

Question 8

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

The symbol used for the multiple correlation coefficient is R.

Question 15

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

Question 16

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

Question 17

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

Question 18

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 19

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

Question 20

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

Question 21

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

Question 22

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 23

Question 24

A) Do not reject -= 0 because -4.31 < 3.18
B) Reject -= 0 because -3.99 > 3.18
C) Do not reject -= 0 because -3.99 > -4.30
D) Reject -= 0 because -4.31 > 2.78

Question 25

Compute the test value for the data in the table.

A) 8.329
B) 6.785
C) 5.919
D) 9.648

Question 26

Question 27

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 28

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

Question 29

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

Question 30

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

Question 31

Question 32

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 33

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

Question 34

Question 35

A) 0.123
B) 10.857
C) 0.001
D) 0.082

Question 36

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

Question 37

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

Question 38

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 39

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

Question 40

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

Question 41

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 42

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

Question 43

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

Question 44

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 45

If the correlation coefficient is 0.93, what is the unexplained variation?

A) 7%
B) 93%
C) 13.5%
D) 86.5%

Question 46

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

Question 47

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 48

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 49

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 50

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

Question 51

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 52

What is the value of when x = 3, if the equation of the regression line is

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

Question 53

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 54

Question 55

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

Question 56

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

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

Question 57

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 58

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

Question 59

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

Question 60

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

Question 61

Two researchers run identical experiments, except researcher A collects twice as many points as researcher B. For a specific value of x, researcher A estimates a y value of
, and researcher B
Estimates a y value of
. We would expect that researcher A's 95% prediction interval around
to be,
In general,

A) wider than researcher B's 95% prediction interval around
B) narrower than researcher B's 95% prediction interval around
C) the same as researcher B's 95% prediction interval around
D) wider than researcher B's 95% prediction interval around or narrower than researcher B's 95%
) prediction interval around
, with equal probability

Question 62

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

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

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

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

Question 66

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 the correlation coefficient would be

Question 67

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

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

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

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

Question 70

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 71

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

Question 72

Question 73

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 . 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 the slope of the
Regression line would be

Question 74

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

Question 75

Question 76

In a __________ relationship, as one variable increases, the other variable decreases, and vice versa.
________________________________________

Question 77

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

Question 78

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 79

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 80

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