Deck 10: Correlation and Regression

Question 1

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. Two different tests are designed to measure employee productivity and dexterity. Several employees
Are randomly selected and tested with these results.

Answer 1

B

Question 2

Use computer software to find the multiple regression equation. Can the equation be used for prediction? An anti-smoking group used data in the table to relate the carbon monoxide (CO) of various brands of cigarettes to
Their tar and nicotine (NIC) content.

Answer 2

B

Question 3

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

Answer 3

B

Question 4

Question 5

Find the unexplained variation for the paired data. The equation of the regression line for the paired data below is

A) 14.25
B) 10.00
C) 78.75
D) 88.75

Question 6

A 0.05 significance level is being used to test a correlation between two variables. If the linear correlation coefficient r is found to be 0.591 and the critical values are 878, what can you conclude?

A) There is sufficient evidence to support the claim of a linear correlation between the two variables.
B) There is not sufficient evidence to support the claim of a linear correlation between the two variables.

Question 7

Determine which plot shows the strongest linear correlation.

Question 8

The residual is the difference between the ________ and the ________.

A) observed value of x; predicted value of y
B) observed value of y; predicted value of y
C) predicted value of x; observed value of x
D) predicted value of y; observed value of y

Question 9

A(n) ________ is a point lying far away from other data points on a scatterplot.

A) residual point
B) least-squares point
C) outlier
D) marginal point

Question 10

Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical value(s) of r given that

Question 11

Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of pairs of data n and the
Significance level

Question 12

Use computer software to find the multiple regression equation. Can the equation be used for prediction? A wildlife analyst gathered the data in the table to develop an equation to predict the weights of bears. He used
WEIGHT as the dependent variable and CHEST, LENGTH, and SEX as the independent variables. For SEX, he
Used male = 1 and female = 2.

Question 13

Use the given information to find the coefficient of determination. A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711, the explained variation is 18.592, and the
Unexplained variation is 2.119.

A) 0.114
B) 1.114
C) 0.898
D) 0.102

Question 14

Find the indicated multiple regression equation. Below are performance and attitude ratings of employees. Managers also rate the same employees according to adaptability, and below are the results that correspond to those given above.

Question 15

A) 0.873
B) 0.913
C) 0.985
D) 0.990

Question 16

Find the value of the linear correlation coefficient r. The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands).

A) 0.708
B) -0.071
C) 0.246
D) 0.235

Question 17

Based on the scatterplot, select the most likely value of the linear correlation coefficient r.

A) 0
B) -0.5
C) 1
D) -1

Question 18

Find the value of the linear correlation coefficient r. The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters).

A) 0.196
B) -0.210
C) 0.256
D) 0

Question 19

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of
0)05.
R = 0.543, n = 25

Question 20

Find the explained variation for the paired data. The equation of the regression line for the paired data below is

A) 6421.83
B) 6544.86
C) 13.479
D) 6531.37

Question 21

Which of the following statements concerning the linear correlation coefficient are true? I: If the linear correlation coefficient for two variables is zero, then there is no relationship between the variables.
II: If the slope of the regression line is negative, then the linear correlation coefficient is negative.
III: The value of the linear correlation coefficient always lies between -1 and 1.
IV: A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a linear correlation coefficient of
-0)82.

A) III and IV
B) I and IV
C) II and III
D) I and II

Question 22

Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.

Question 23

Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical value(s) of r given that n = 15 and

Question 24

Provide an appropriate response. For the data below, determine the logarithmic equation, that best fits the data. Hint: Begin by replacing each x-value with ln x then use the usual methods to find the equation of
The least squares regression line.

Question 25

Find the coefficient of determination, given that the value of the linear correlation coefficient, r, is 0.738.

A) 0.262
B) 0.738
C) 0.455
D) 0.545

Question 26

A regression equation is obtained for a set of data. After examining a scatter diagram, the researcher notices a
data point that is potentially an influential point. How could she confirm that this data point is indeed an
influential point?

Question 27

A 0.01 significance level is being used to test a correlation between two variables. If the linear correlation coefficient r is found to be 0.591 and the critical values are r = ±0.590 what can you conclude?

A) There is sufficient evidence to support the claim of a linear correlation between the two variables.
B) There is not sufficient evidence to support the claim of a linear correlation between the two variables.

Question 28

A quadratic regression model is fit to a set of sample data consisting of 6 pairs of data. Given that the sum of squares of residuals is 29.73 and that the y-values are 11, 14, 19, 22, 26, 27, find

A) 0.144
B) 0.88
C) 0.856
D) 0.844

Question 29

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of
0)05.

Question 30

Based on the scatterplot, select the most likely value of the linear correlation coefficient r.

A) 1
B) -1
C) -0.5
D) 0

Question 31

A(n) ________ is a point that strongly affects the graph of the regression line.

A) least squares point
B) residual point
C) influential point
D) marginal point

Question 32

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of
0)05.

Question 33

A) 0.931, 0.902, 0.000
B) 0.976, 0.921, 0.002
C) 0.861, 0.900, 0.015
D) 0.943, 0.934, 0.000

Question 34

Use the given data to find the best predicted value of the response variable. Ten pairs of data yield r = 0.003 and the regression equation . What is the best predicted value of y for x = 2?

A) 8.0
B) 17.0
C) 7.0
D) 5.0

Question 35

Construct a scatterplot for the given data.

Question 36

Find the value of the linear correlation coefficient r. The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands):

A) 0.235
B) 0.246
C) -0.071
D) 0.708

Question 37

Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of pairs of data n and the
Significance level

Question 38

The residual is the ________ the observed value of y and the predicted value of y.

A) quotient of
B) product of
C) sum of
D) difference between

Question 39

Use computer software to find the best multiple regression equation to explain the variation in the dependent variable, Y, in terms of the independent variables,

Question 40

Below are the productivity, dexterity, and job satisfaction ratings of ten randomly selected employees. Find the multiple regression equation that expresses the job satisfaction scores in terms of the productivity and dexterity scores.

Question 41

The results for several randomly selected students for test 1 and test 2 grades are given below. Is there sufficient evidence to suggest that there is a linear correlation between test 1 and test 2 grades? Construct a
scatterplot, and find the value of the linear correlation coefficient r. Also, find the P-value or the critical value(s) of r
using

Question 42

Applicants for a particular job, which involves extensive travel in Spanish speaking countries must take a
proficiency test in Spanish. The sample data below were obtained in a study of the relationship between the
numbers of years applicants have studied Spanish (x) and their score on the test (y). The regression equation , was obtained. Construct a residual plot for the data.

Question 43

Define the terms predictor variable and response variable. Give examples for each.

Question 44

Suppose there is significant correlation between two variables. Describe two cases under which it might be
inappropriate to use the linear regression equation for prediction. Give examples to support these cases.

Question 45

The table lists the value y (in dollars) of $100 deposited in a certificate of deposit (CD) at a bank after y years. Construct a scatterplot and identify the mathematical model that best fits the given data. Assume that the model
is to be used only for the scope of the given data, and consider only linear, quadratic, logarithmic, exponential,
and power models. Include the type of model and the equation for the model you find.

Question 46

For each of 200 randomly selected cities, Pete recorded the number of churches in the city (x) and the number of
homicides in the past decade (y). He calculated the linear correlation coefficient and was surprised to find a
strong positive linear correlation for the two variables. Does this suggest that building new churches causes an
increase in the number of homicides? Why do you think that a strong positive linear correlation coefficient was
obtained? Explain your answer with reference to the term lurking variable.

Question 47

The following table gives the US domestic oil production rates (excluding Alaska) from 1987 to 2002. A
regression equation was fit to the data and the residual plot is shown below. Does the residual plot suggest that the regression equation is a bad model? Why or why not?

Question 48

Question 49

A set of data consists of the number of years that applicants for foreign service jobs have studied German and
the grades that they received on a proficiency test. The following regression equation is obtained: ^y = 31.6 +
10.9x, where x represents the number of years of study and y represents the grade on the test. Identify the
predictor and response variables.

Question 50

Give an example of a pair of variables which you would expect to have a negative linear correlation coefficient
and explain why.

Question 51

The table below shows the population of a city (in millions) in each year during the period 2010-2015. Using the
number of years since 2010 as the independent variable, find the regression equation of the best model. Assume
that the model is to be used only for the scope of the given data, and consider only linear, quadratic,
logarithmic, exponential, and power models. Include the type of model and the equation for the model you find.

Question 52

Sketch an example of a residual plot that suggests that a regression equation is not a good model. Be sure to
include at least 10 points in your example.

Question 53

The table below lists weights (carats) and prices (dollars) for randomly selected diamonds. Find the regression
equation, letting the weight be the predictor variable. Find the best predicted price for a diamond with a weight
of 1.50 carats. What is wrong with predicting the price of a 1.50-carat diamond?

Question 54

Question 55

Describe the standard error of estimate, . How do smaller values of se relate to the dispersion of data points
about the line determined by the linear regression equation? What does it mean when is 0?

Question 56

The following residual plot is obtained after a regression equation is determined for a set of data. Does the
residual plot suggest that the regression equation is a bad model? Why or why not?

Question 57

Sketch a sample scatterplot of at least 5 points that would have a linear correlation coefficient equal to -1.

Question 58

Give an example of a pair of variables whose linear correlation coefficient is likely to be close to zero.

Question 59

The table below lists weights (carats) and prices (dollars) for randomly selected diamonds. Is there sufficient
evidence to suggest that there is a linear correlation between weights and prices? Construct a scatterplot, and
find the value of the linear correlation coefficient r.
Also find the P-value or the critical values of r using

Question 60

Describe what scatterplots are and discuss the importance of creating scatterplots.

Question 61

Find the value of the linear correlation coefficient r.
The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test.

A) -0.678
B) 0.678
C) 0.224
D) -0.224

Question 62

Construct a scatterplot for the given data.

Question 63

Find the value of the linear correlation coefficient r.

A) 0.156
B) -0.175
C) 0
D) 0.175

Question 64

Find the value of the linear correlation coefficient r.
Two separate tests are designed to measure a student's ability to solve problems. Several students are randomly selected to take both tests and the results are shown below.

A) 0.548
B) 0.867
C) 0.109
D) 0.714

Question 65

Construct a scatterplot for the given data.

Question 66

Determine which scatterplot shows the strongest linear correlation.
Which shows the strongest linear correlation?

Question 67

Find the value of the linear correlation coefficient r.
Two different tests are designed to measure employee productivity and dexterity. Several employees are randomly selected and tested with these results.

A) 0.115
B) 0.471
C) 0.986
D) -0.280

Question 68

Question 69

Find the value of the linear correlation coefficient r.

A) 0.214
B) -0.078
C) 0.109
D) -0.054

Question 70

Question 71

Construct a scatterplot for the given data.

Question 72

Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear
correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance
level

Question 73

Determine which scatterplot shows the strongest linear correlation.
Which shows the strongest linear correlation?

Question 74

Find the value of the linear correlation coefficient r.

A) -0.775
B) -0.081
C) 0.754
D) 0

Question 75

Find the value of the linear correlation coefficient r.
A study was conducted to compare the average time spent in the lab each week versus course grade for computer programming students. The results are recorded in the table below.

A) -0.284
B) 0.462
C) -0.335
D) 0.017

Question 76

Question 77

Find the value of the linear correlation coefficient r.
Managers rate employees according to job performance and attitude. The results for several randomly selected employees are given below.

A) 0.916
B) 0.729
C) 0.863
D) 0.610

Question 78

Construct a scatterplot for the given data.

Question 79

Find the value of the linear correlation coefficient r.
The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands):

A) 0.246
B) -0.071
C) 0.235
D) 0.708

Question 80

Find the value of the linear correlation coefficient r.
The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters):

A) 0.256
B) 0
C) 0.196
D) -0.210