Deck 10: Correlation and Regression

Question 1

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) 1.114
B) 0.102
C) 0.898
D) 0.114

Answer 1

C

Question 2

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

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

Answer 2

A

Question 3

Answer 3

B

Question 4

Question 5

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 6

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).

Question 7

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

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

Question 8

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).

Question 9

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.

Question 10

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 11

Question 12

The residual is the difference between the ____________________ and the ___________________.

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

Question 13

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

Question 14

Question 15

Question 16

Question 17

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 18

Determine which plot shows the strongest linear correlation.

Question 19

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

Question 20

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.

Question 21

Question 22

Question 23

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

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

Question 24

Question 25

Question 26

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

Question 27

Question 28

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

Question 29

Question 30

Question 31

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

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

Question 32

Question 33

Find the indicated multiple regression equation. Below are performance and attitude ratings of employees.

Question 34

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

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

Question 35

Question 36

Question 37

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

Question 38

Question 39

Construct a scatterplot for the given data.

Question 40

Question 41

The table below shows the population of a city (in millions)in each year during the

Question 42

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 43

The results for several randomly selected students for test 1 and test 2 grades are given
below.

Question 44

Question 45

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 46

Question 47

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

Question 48

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 49

Question 50

Question 51

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 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 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 54

Question 55

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

Question 56

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

Question 57

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

Question 58

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

Question 59

Question 60