Deck 27: Exploring Relationships Among Variables

Question 1

Use the following to answer the question(s) below.
A large pharmaceutical company selected a random sample of new hires and obtained their job performance ratings based on their first six months with the company. These data were used to build a multiple regression model to predict the job performance of new hires based on age, GPA and gender (female = 1 and male = 0). The results of the analysis are shown below.
How much of the variability in Job Performance is explained by the regression model?

A) 30.33%
B) 77.7%
C) 5.56%
D) 60.76%
E) 30.99%

Answer 1

77.7%

Question 2

Which statement about residuals plot is true?

A) A pattern of increasing spread indicates the predicted values become less reliable as the explanatory variable increases.
B) If all of the residuals are very small, the model will not predict accurately.
C) High-leverage points always have large residuals.
D) The outliers always deserve special attention because they produce small residuals.
E) Residuals reveal data that behave differently. The plot provides clues for fixing the regression model.

Answer 2

Residuals reveal data that behave differently. The plot provides clues for fixing the regression model.

Question 3

Use the following to answer the question(s) below.
For many countries tourism is an important source of revenue. Data are collected on the number of foreign visitors to a country (in millions) and total tourism revenue (in billions of dollars) for a sample of 10 countries. Below is the regression analysis output with tourism revenue as the dependent variable.
If we were interested in predicting the tourism revenue for a particular country that had 30 million foreign visitors

A) we should construct a confidence interval using the equation Tourism = 0.295 + 21.5 Visitors.
B) we should construct a prediction interval using the equation Tourism = 21.5 + 0.295 Visitors.
C) we should use the equation Tourism = 0.295 + 21.5 Visitors.
D) we should use the coefficient R2 = 0.634.
E) we should use the correlation coefficient r = = 0.796.

Answer 3

we should construct a prediction interval using the equation Tourism = 21.5 + 0.295 Visitors.

Question 4

Use the following to answer the question(s) below.
For many countries tourism is an important source of revenue. Data are collected on the number of foreign visitors to a country (in millions) and total tourism revenue (in billions of dollars) for a sample of 10 countries. Below is the regression analysis output with tourism revenue as the dependent variable.
The standard error of the slope for this estimated regression equation is

A) 2.58307.
B) 3.462.
C) 0.07917.
D) 6.672.
E) 0.29497.

Question 5

Use the following to answer the question(s) below.
In order to examine if there is a relationship between the size of cash bonuses and pay scale, data were obtained on the average annual cash bonus and the average annual pay for a sample of 20 companies. Below is the regression analysis output with annual cash bonus as the dependent variable.
At 5% significance level, which of the following statements is true about the correlation between average annual cash bonus and average annual pay?

A) It is not significantly different from zero.
B) It is negative but not significantly different from zero.
C) It is positive and significantly different from zero.
D) It is negative and significantly different from zero.
E) We fail to reject the null hypothesis Hο : ρ = 0.

Question 6

Below is the plot of residuals versus fitted values for this regression model. Based on the plot, which assumption/condition is definitely violated?

A) Equal Variance
B) Linearity
C) Normality
D) Independence
E) Randomization

Question 7

Which of the following is not true about the best regression models?

A) They definitely have more predictors than the regular models.
B) They have a relatively high R2 value.
C) They have predictors that are reliably measured and relatively unrelated to each other.
D) They have no cases with extraordinarily high leverage that might dominate and alter the model.
E) They have relatively small P-values for the F- and t-statistics.

Question 8

Use the following to answer the question(s) below.
Weekly commodity prices for heating oil (in cents) were obtained and regressed against time. Below is the regression output and residual plots from fitting a linear model.
Which of the following statement is true?

A) The normal probability plot shows no bend and indicates that Independence assumption is satisfied.
B) The residual plot has no pattern and indicates that Independence assumption is satisfied.
C) The histogram is relatively bell-shaped and indicates that Independence assumption is satisfied.
D) The t-test for the regression slope indicates that Independence assumption is satisfied.
E) The histogram and plots show that not all assumptions and conditions for regression inference are met. It looks like data are highly correlated over time. So, we should test the model for autocorrelation.

Question 9

A forester would like to estimate the diameter of maple trees based on age. She gathers data from trees that have been cut and plots their diameters (in inches) against their ages (in years). She fits a linear model and both the scatterplot and residual plots are shown below. Which of the following is true?

A) If we used this model to predict the diameter of a maple tree that is 50 years old, the predicted value would be too low.
B) If we used this model to predict the diameter of a maple tree that is 50 years old, the predicted value would be quite reliable.
C) Re-expressing these data by taking the logarithm of age would not improve this model.
D) The residual plot shows no bend. We should not consider transforming data.
E) If we used this model to predict the diameter of a maple tree that is 50 years old, the predicted value would be too high; furthermore, re-expressing these data by taking the logarithm of age would improve this model.

Question 10

Use the following to answer the question(s) below.
For many countries tourism is an important source of revenue. Data are collected on the number of foreign visitors to a country (in millions) and total tourism revenue (in billions of dollars) for a sample of 10 countries. Below is the regression analysis output with tourism revenue as the dependent variable.
How much of the variability in tourism revenue is accounted for by the number of foreign visitors?

A) 63.4%
B) 13.8%
C) 2.58 billion $
D) 21.464%
E) 3.73 billion $

Question 11

Use the following to answer the question(s) below.
In order to examine if there is a relationship between the size of cash bonuses and pay scale, data were obtained on the average annual cash bonus and the average annual pay for a sample of 20 companies. Below is the regression analysis output with annual cash bonus as the dependent variable.
What is the correlation between average annual cash bonus and average annual pay?

A) -0.223
B) 0.472
C) 0.108
D) -0.540
E) 0.245

Question 12

The residual plot for a linear regression model is shown below. Which of the following is true?

A) The linear model is okay because approximately the same number of points is above the line as below it.
B) The linear model is okay because the association between the two variables is fairly strong.
C) The linear model is okay because there is no extreme outlier.
D) The linear model is okay because there is no pattern.
E) The linear model is not good because of the curve in the residuals.

Question 13

Use the following to answer the question(s) below.
For many countries tourism is an important source of revenue. Data are collected on the number of foreign visitors to a country (in millions) and total tourism revenue (in billions of dollars) for a sample of 10 countries. Below is the regression analysis output with tourism revenue as the dependent variable.
At the 0.05 level of significance,

A) we reject the alternative hypothesis.
B) we do not reject the null hypothesis.
C) we conclude that the number of foreign visitors is not significant in explaining tourism revenue.
D) we reject the null hypothesis, and we conclude that the number of foreign visitors is significant in explaining tourism revenue.
E) we support the null hypothesis and we conclude that the number of foreign visitors and tourism revenue are not related.

Question 14

Use the following to answer the question(s) below.
A large pharmaceutical company selected a random sample of new hires and obtained their job performance ratings based on their first six months with the company. These data were used to build a multiple regression model to predict the job performance of new hires based on age, GPA and gender (female = 1 and male = 0). The results of the analysis are shown below.
Based on the F-statistic and associated P-value, we can conclude that at α = 0.05

A) the regression model is not significant overall.
B) all independent variables in the model are significant.
C) the regression model is significant overall.
D) none of the independent variables in the model are significant.
E) only GPA variable in the model is significant.

Question 15

Use the following to answer the question(s) below.
Weekly commodity prices for heating oil (in cents) were obtained and regressed against time. Below is the regression output and residual plots from fitting a linear model.
Based on the output and plots, which of the following statements is not true?

A) The t-test for the regression slope indicates that it is significantly different from zero. However, histogram shows that the distribution is skewed to the right.
B) According to the regression output, the model explains 71.9% of the variability in heating oil prices. However, the residual plot shows a clear pattern and curvature.
C) The normal probability plot shows some bend and indicates that we probably cannot proceed with regression inference.
D) The residual plot suggests that the Independence assumption might be violated.
E) The histogram and plots show that all assumptions and conditions for regression inference are met.

Question 16

The Durbin-Watson statistic indicates

A) that there is evidence of positive autocorrelation.
B) that there is evidence of negative autocorrelation.
C) that there is no evidence of positive autocorrelation.
D) that there is no evidence of negative autocorrelation.
E) Since the Durbin-Watson statistic falls between the critical values, the test is inconclusive.

Question 17

Use the following to answer the question(s) below.
A large pharmaceutical company selected a random sample of new hires and obtained their job performance ratings based on their first six months with the company. These data were used to build a multiple regression model to predict the job performance of new hires based on age, GPA and gender (female = 1 and male = 0). The results of the analysis are shown below.
Which of the following is the correct interpretation for the regression coefficient of Gender?

A) The regression coefficient indicates that the job performance score for a female will, on average, be 9.06 points higher than for males of the same age and GPA.
B) The regression coefficient indicates that the job performance score for a female will, on average, be 9.06 points lower than for males of the same age and GPA.
C) The regression coefficient indicates that the job performance score for a female will, on average, be 9.06 times higher than for males.
D) The regression coefficient indicates that the job performance score for a female will, on average, be 9.06 times lower than for males.
E) The regression coefficient indicates that the job performance score for a female will, on average, be 2.314 times lower than for males.

Question 18

Use the following to answer the question(s) below.
A large pharmaceutical company selected a random sample of new hires and obtained their job performance ratings based on their first six months with the company. These data were used to build a multiple regression model to predict the job performance of new hires based on age, GPA and gender (female = 1 and male = 0). The results of the analysis are shown below.
At α = 0.05, we can conclude that

A) Age is not a significant variable in predicting job performance.
B) GPA is a significant variable in predicting job performance.
C) the regression coefficient associated with GPA is significantly different from zero.
D) Gender is a significant variable in predicting job performance.
E) the regression coefficient associated with Age is not significantly different from zero.

Question 19

Use the following to answer the question(s) below.
For many countries tourism is an important source of revenue. Data are collected on the number of foreign visitors to a country (in millions) and total tourism revenue (in billions of dollars) for a sample of 10 countries. Below is the regression analysis output with tourism revenue as the dependent variable.
The calculated t-statistic to test whether the regression slope is significantly different from zero is

A) 6.20.
B) 13.88.
C) 0.07917.
D) 2.58307.
E) 3.73.

Question 20

The model = 12 + 20 Diameter can be used to predict the breaking strength of a rope (in kilograms) from its diameter (in centimetres). According to this model, how much force should a rope one-half centimeter in diameter withstand?

A) 484 kg
B) 16 kg
C) 22 kg
D) 256 kg
E) 4.7 kg

Question 21

Re-expressing these data results in the following model The residuals plotted against the fitted values for this model is shown below. What is true about the predicted concentration level after 10 hours has elapsed?

A) The predicted value is 0.1000 units/cc.
B) This value is considered as a regular one.
C) This value is accurate because R2 = 100.0%.
D) The predicted value is 1.2589 units/cc, and this value is considered an extrapolation.
E) 10 hours falls into the range of the predictor variable Time Elapsed.

Question 22

Use the following to answer the question(s) below.
Data were collected for a sample of 12 pharmacists to determine if years of experience and salary are related. Below are the regression analysis results. The dependent variable is Salary in thousands of dollars.
The calculated t-statistic to test whether the regression slope is significant is

A) 10.99.
B) 47.97.
C) 31.2.
D) 6.93.
E) 5.58485.

Question 23

Use the following to answer the questions below.
The following is output from regression analysis performed to develop a model for predicting a firm's Price-Earnings Ratio (PE) based on Growth Rate, Profit Margin, and whether or not the firm is Green (1 = Yes, 0 = No).
Which of the following is the correct interpretation for the regression coefficient of Green?

A) The regression coefficient indicates that the PE ratio of a firm that is green will, on average, be 2.09 points higher than a firm that is not green with the same profit growth rate and profit margin.
B) The regression coefficient indicates that the PE ratio of a firm that is green will, on average, be 2.09 points lower than a firm that is not green with the same profit growth rate and profit margin.
C) The regression coefficient indicates that the PE ratio of a firm that is green will, on average, be 2.09 times higher than a firm that is not green.
D) The regression coefficient indicates that the PE ratio of a firm that is green will, on average, be 2.09 times lower than a firm that is not green.
E) The regression coefficient is not significantly different from zero.

Question 24

Using the estimated regression equation to predict salary for 10 years of experience gives the following results. Which of the following is true?

A) 95% of pharmacists with 10 years of experience earn between $38,960 and $65,130.
B) 95% of pharmacists with 10 years of experience earn between $48,010 and $56,080.
C) We are 95% confident that a particular pharmacist who has 10 years of experience earns between $38,960 and $65,130.
D) We are 95% confident that a particular pharmacist who has 10 years of experience earns between $48,010 and $56,080.
E) 52.05% of pharmacists with 10 years of experience on average earn between $48,010 and $56,080.

Question 25

Use the following to answer the question(s) below.
Data were collected for a sample of 12 pharmacists to determine if years of experience and salary are related. Below are the regression analysis results. The dependent variable is Salary in thousands of dollars.
The standard error of the slope for this estimated regression equation is

A) 3.381.
B) 0.2149.
C) 5.58485.
D) 82.8.
E) 1.4882.

Question 26

The model = 3.30 + 0.235 Speed can be used to predict the stopping distance (in metres) for a car traveling at a specific speed (in kph). According to this model, about how much distance will a car going 65 kph need to stop?

A) 345.0 metres
B) 18.6 metres
C) 27.0 metres
D) 4.3 metres
E) 729.0 metres

Question 27

Use the following to answer the question(s) below.
Stock prices and earnings per share (EPS) data were collected for a sample of 15 companies. Below are the regression results. The dependent variable is Stock Price.
What is the correlation between stock price and EPS?

A) -0.975
B) 0.975
C) 0.906
D) 0.950
E) -0.950

Question 28

Which of the following is/are not correct about the best regression models?

A) They have relatively few predictors.
B) They have a relatively high R2 value.
C) They have predictors that are reliably measured and relatively unrelated to each other.
D) They have no cases with extraordinarily high leverage that might dominate and alter the model.
E) They can be obtained only by stepwise regression method.

Question 29

Which of the following measures is used to check for collinearity when building a multiple regression model?

A) Cook's Distance
B) Variance Inflation Factor
C) Determination Coefficient
D) Standardized Residual
E) Leverage Index

Question 30

Use the following to answer the question(s) below.
Stock prices and earnings per share (EPS) data were collected for a sample of 15 companies. Below are the regression results. The dependent variable is Stock Price.
Which of the following statements is true about the correlation between stock price and EPS?

A) The correlation is negative.
B) The correlation is not significantly different from zero.
C) The correlation is positive and significantly different from zero.
D) We fail to reject the null hypothesis Hο : ρ ≠ 0.
E) As t statistic for the correlation coefficient test equals 15.82 and associated P-value is very small, we fail to support the alternative hypothesis HΑ : ρ ≠ 0.

Question 31

Use the following to answer the question(s) below.
A linear regression model was fit to data representing technology adoption over time. The regression output and residual plot appears below.
It is known that at 1% significance level the critical values for Durbin-Watson statistic are 0.738 and 1.038. The Durbin-Watson statistic indicates

A) that the residuals are positively autocorrelated.
B) that the residuals are negatively autocorrelated.
C) that there is no positive autocorrelation.
D) that there is no negative autocorrelation.
E) that the test is inconclusive as dL < D < dU.

Question 32

Use the following to answer the question(s) below.
Data were collected for a sample of 12 pharmacists to determine if years of experience and salary are related. Below are the regression analysis results. The dependent variable is Salary in thousands of dollars.
How much of the variability in pharmacists' salary is accounted for by years of experience?

A) 82.8%
B) 47.97%
C) 5.58485 thousand dollars
D) 10.99%
E) 98.9%

Question 33

Use the following to answer the question(s) below.
Data were collected for a sample of 12 pharmacists to determine if years of experience and salary are related. Below are the regression analysis results. The dependent variable is Salary in thousands of dollars.
The P-value associated with this statistic is < 0.001. At the 0.05 level of significance

A) we reject the alternative hypothesis.
B) we fail to reject the null hypothesis.
C) there is no evidence that the number of years of experience is significant in explaining pharmacists' salary.
D) we reject the null hypothesis, and we conclude that there is strong evidence of an association between years of experience and pharmacists' salary.
E) we support the null hypothesis, and we conclude that years of experience and pharmacists' salary are not related.

Question 34

A least squares estimated regression line has been fitted to a set of data and the resulting residual plot is shown. Which is true?

A) The linear model seems appropriate.
B) The linear model is poor because some residuals are large.
C) The linear model is poor because there is a pattern.
D) The plot shows a bend, thus a curved model would be more appropriate.
E) There is one extreme outlier, a transformation of the data is recommended.

Question 35

Which statement about re-expressing data is true?

A) To make unimodal distribution that is skewed to the left more symmetric we should take the square root of the variable.
B) Transforming data cannot make a scatterplot and residual plot less spread out.
C) Transforming data is based only on the logarithmic function of the response variable.
D) One goal of re-expressing may be to make the variability of the response variable more uniform.
E) Re-expressing data by the logarithms should be used only when we want make the form of the scatterplot more nearly linear.

Question 36

Use the following to answer the questions below.
The following is output from regression analysis performed to develop a model for predicting a firm's Price-Earnings Ratio (PE) based on Growth Rate, Profit Margin, and whether or not the firm is Green (1 = Yes, 0 = No).
Based on the F-statistic and associated P-value, we can conclude at α = 0.05 that

A) the regression model is not significant overall.
B) all independent variables in the model are significant.
C) the regression model is significant overall.
D) none of the independent variables in the model are significant.
E) only Profit Margin variable in the model is significant.

Question 37

Use the following to answer the questions below.
The following is output from regression analysis performed to develop a model for predicting a firm's Price-Earnings Ratio (PE) based on Growth Rate, Profit Margin, and whether or not the firm is Green (1 = Yes, 0 = No).
At α = 0.05, we can conclude that

A) Growth Rate is not a significant variable in predicting a firm's PE ratio.
B) Profit Margin is a significant variable in predicting a firm's PE ratio.
C) the regression coefficient associated with Growth Rate is not significantly different from zero.
D) whether or not a firm is Green is significant in predicting its PE ratio.
E) the regression coefficient associated with whether or not a firm is Green is not significantly different from zero.

Question 38

Use the following to answer the question(s) below.
A newly developed drug is tested to determine absorption levels in a patient's bloodstream. A patient is injected with the drug and the concentration (units/cc) in the patient's blood is measured every hour for seven hours. Below is the output from fitting a linear regression model.
Which of the following is true?

A) The linear model is absolutely perfect for estimation of the concentration level after 10 hours. The scatterplot shows no bend.
B) This model will probably underestimate the concentration level after 10 hours. The scatterplot shows some bend and suggests that the linear model is not appropriate.
C) This model will definitely overestimate the concentration level after 10 hours, as the scatterplot shows two extreme outliers.
D) The linear model is appropriate for estimation of the concentration level after 10 hours. It explains 89.21% of the variability in blood concentration levels of the drug.
E) The linear model is not appropriate because it explains only 4.72% of the variability in blood concentration levels of the drug.

Question 39

Use the following to answer the question(s) below.
A linear regression model was fit to data representing technology adoption over time. The regression output and residual plot appears below.
Based on the output and plot, which of the following statements is not true?

A) According to the regression output, the model explains 82.5% of the variability in Technology Adoption. However, the residual plot shows a pattern and curvature.
B) The scatter plot of the residuals against the predicted values shows a pattern. A regression model applied to the data is questionable.
C) The t-test for the regression slope indicates that it is significantly different from zero, but the residual scatter plot shows that Equal Variance assumption is violated.
D) The regression model is applied to the time series data. The residual plot suggests that the Independence assumption might be violated. We have to use Durbin-Watson statistic to detect autocorrelation.
E) The plot shows that all assumptions and conditions for regression inference are met. R2 and P-value report that there is strong correlation between Technology Adoption and Time.

Question 40

Below are residual plots for this regression model. Based on these plots, which of the following statements is true?

A) The scatterplot of the residuals against the predicted values shows patter.
B) The scatterplot of residuals against the predicted values shows no possible outlier.
C) The histogram is bell-shaped. The Nearly Normal condition is reasonably satisfied.
D) The histogram indicates that the Independence assumption is violated.
E) The normal probability plot shows no bend.