Deck 10: Correlation and Regression

Question 1

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

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

Answer 1

0.990

Question 2

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=10 and

A)
B)
C)
D) r=0.632

Answer 2

Question 3

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 3

-1

Question 4

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 5

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
B) 0.196
C) -0.210
D) 0.256

Question 6

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.

A) WEIGHT =196+2.35 CHEST +3.40 LENGTH +25 SEX; Yes, because the R2 is high.
B) WEIGHT =-320+10.6 CHEST +7.3 LENGTH -10.7SEX ; Yes, because the P -value is high.
C) WEIGHT =-442.6+12.1 CHES +3.6 LENGTH -23.8SEX ; Yes, because the adjusted R2 is high.
D) WEIGHT =442.6+12.1 CHEST +4.2 LENGTH-21SEX ; Yes, because the P -value is low.

Question 7

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 8

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
n=12,

A) r=0.708
B)r=±0.708
C)r=±0.576
D) r=0.735

Question 9

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 10

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.

A)CO = 1.37=5.50TAR - 1.38NIC; Yes, becouse the P- is high
B)CO = 1.37=5.53TAR - 1.3NIC; Yes, becouse the R² is high
C)CO = 1.25=5.55TAR - 5.79NIC; Yes, becouse the P- value is too low/
D)CO = 1.3=5.5TAR - 1.3NIC; Yes, becouse the adjust R² is high

Question 11

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.

A)
B)
C)
D)

Question 12

Determine which plot shows the strongest linear correlation.

A)
B)
C)
D)

Question 13

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 14

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 15

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 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

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

A)
B)
C)
D)

Question 18

Find the unexplained variation for the paired data. The equation of the regression line for the paired data below is y=3x.

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

Question 19

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) 0.246
C) −0.071
D) 0.235

Question 20

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

A) Critical values: r=±0.487 , no significant linear correlation
B) Critical values: r=±0.396 , no significant linear correlation
C) Critical values: r=±0.487 , significant linear correlation
D) Critical values: r=±0.396 , significant linear correlation

Question 21

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=-0.816, n=5

A) Critical values: r= 0.878 , significant linear correlation
B) Critical values: r= 0.878 , no significant linear correlation
C) Critical values: r=0.950 , significant linear correlation
D) Critical values: r= 0.950 , no significant linear correlation

Question 22

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 23

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 24

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 25

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

Question 26

Provide an appropriate response. For the data below, determine the logarithmic equation, y=a+b ln x 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.

A)
B)
C)
D)

Question 27

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
n=14,

A) r=0.661
B) r=0.684
C)
D)

Question 28

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 29

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.

A)
B)
C)
D)

Question 30

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 31

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) 0.844
B) 0.144
C) 0.88
D) 0.856

Question 32

Construct a scatterplot for the given data.

A)
B)
C)
D)

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

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 35

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

A) y=150.7-6.8 x
B) y=-140.4+6.2 x
C) y=-150.7+6.8 x
D) y=140.4-6.2 x

Question 36

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 37

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.

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

A)
B)
C)
D)

Question 38

Use computer software to obtain the multiple regression equation and identify adjusted R and the P -value. An anti-smoking group used data in the table to relate the carbon monoxid (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 39

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 Also, What is the best predicted value of y for x=2 ?

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

Question 40

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=0.767, n=25

A) Critical values: r= ±0.487 , significant linear correlation
B) Critical values: r= ±0.396 , no significant linear correlation
C) Critical values: r= ±0.396 , significant linear correlation
D) Critical values: r= ±0.487 , no significant linear correlation

Question 41

Define the terms predictor variable and response variable.

Question 42

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 43

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 44

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 45

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

Question 46

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 47

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 48

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 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: 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

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 51

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

Question 52

The table lists the value y (in dollars) of $100 desposit (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 53

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 54

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 55

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

Question 56

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

Question 57

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 58

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

Question 59

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 60

When testing to determine if correlation is significant, we use the hypotheses p=0 , What does the symbol represent? Explain the meaning of the null and alternative hypotheses.