Deck 10: Correlation and Regression

Question 1

Determine which plot shows the strongest linear correlation._

Answer 1

C

Question 2

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

A)0
B)1
C)−1
D)−0.5

Answer 2

C

Question 3

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 https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/.
n=12 ,

A) r=0.708
B)
C)
D) r=0.735

Answer 3

Question 4

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

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

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 7

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 8

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 9

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

Question 10

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 11

For the data below, determine the value of the linear correlation coefficient r between y and X₂.

Question 12

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

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

Question 13

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 14

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 15

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

Question 16

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 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 17

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 18

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

A) 13.479
B) 6,531.37
C) 6,544.86
D) 6,421.83

Question 19

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 20

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 21

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) 7.0
B) 5.0
C) 8.0
D) 17.0

Question 22

Use computer software to obtain the multiple regression equation and identify adjusted and the P -value. 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.

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

Question 23

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

Question 24

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 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 25

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 26

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.
Adaptability : Find the multiple regression equation that expresses performance in terms of attitude and
Adaptability.

Question 27

Below are the productivity, dexterity, and job satisfaction ratings of ten randomly selected_ employees.

Question 28

Provide an appropriate response. For the data below, determine the logarithmic equation, ya=+b lnx 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 29

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 30

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 31

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

A)0
B)1
C)−1
D)−0.5

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

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,

A)
B)
C)
D)

Question 34

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 35

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

Question 36

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

A)
B)
C)
D) r=0.514

Question 37

Construct a scatterplot for the given data._

Question 38

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 39

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 40

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 41

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 42

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 43

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 44

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 45

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: , where x represents the number of years of
study and y represents the grade on the test. Identify the predictor and response variables.

Question 46

Describe the standard error of estimate, se. 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 se is 0?

Question 47

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).

Question 48

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 49

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

Question 50

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.

Question 51

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 52

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 53

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 54

When testing to determine if correlation is significant, we use the hypotheses What does the symbol represent? Explain the meaning of the null and altemative hypotheses.

Question 55

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 = 0.05.

Question 56

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