Deck 4: Linear Regression

Question 1

The procedure of using sample data to find the estimated regression equation is better known as _____.

A) point estimation
B) interval estimation
C) the least squares method
D) extrapolation

Answer 1

the least squares method

Question 2

A linear regression analysis for which any one unit change in the independent variable is assumed to:

A) have the same change in the dependent variable.
B) have no change in the dependent variable.
C) have an inverse effect on the dependent variable
D) have a nullifying effect on the dependent variable.

Answer 2

have the same change in the dependent variable.

Question 3

The process of making conjecture about the value of a population parameter, collecting sample data that can be used to assess this conjecture, measuring the strength of the evidence against the conjecture that is provided by the sample, and using these results to draw a conclusion about the conjecture is better known as:

A) postulation.
B) hypothesis testing.
C) statistical inference.
D) empirical research.

Answer 3

hypothesis testing.

Question 4

In the simple linear regression model, the _____ accounts for the variability in the dependent variable that cannot be explained by the linear relationship between the variables.

A) constant term
B) error term
C) model parameter
D) residual

Question 5

A _____ is used to visualize sample data graphically and to draw preliminary conclusions about the possible relationship between the variables.

A) contingency table
B) scatter chart
C) Gantt chart
D) pie chart

Question 6

The _____ is a measure of the error in using the estimated regression equation to predict the values of the dependent variable in a sample.

A) sum of squares due to regression (SSR)
B) error term
C) sum of squares due to error (SSE)
D) residual

Question 7

In the graph of the simple linear regression equation, the parameter βo represents the _____ of the regression line.

A) slope
B) x-intercept
C) y-intercept
D) end-point

Question 8

What would be the value of the sum of squares due to regression (SSR) if the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89?

A) 31.89
B) 19.32
C) 18.43
D) 15.32

Question 9

The coefficient of determination:

A) takes values between -1 to +1.
B) is equal to zero for a perfect fit.
C) is equal to one for the poorest fit.
D) is used to evaluate the goodness of fit.

Question 10

_____ is a statistical procedure used to develop an equation showing how two variables are related.

A) Regression analysis
B) Data mining
C) Time series analysis
D) Factor analysis

Question 11

The graph of the simple linear regression equation is a(n) _____.

A) ellipse
B) hyperbola
C) parabola
D) straight line

Question 12

The _____ is the range of values of the independent variables in the data used to estimate the regression model.

A) confidence interval
B) codomain
C) experimental region
D) validation set

Question 13

In the graph of the simple linear regression equation, the parameter β1 is the _____ of the regression line.

A) slope
B) x-intercept
C) y-intercept
D) end-point

Question 14

The process of making estimates and drawing conclusions about one or more characteristics of a population through analysis of sample data drawn from the population is known as _____.

A) inductive inference
B) deductive inference
C) statistical inference
D) Bayesian inference

Question 15

What would be the coefficient of determination if the total sum of squares (SST) is 23.29 and the sum of squares due to regression (SSR) is 10.03?

A) 2.32
B) 0.43
C) 13.26
D) 0.89

Question 16

Prediction of the value of the dependent variable outside the experimental region is called _____.

A) interpolation
B) forecasting
C) averaging
D) extrapolation

Question 17

A(n) _____ refers to a measurable factor that defines a characteristic of a population, process, or system.

A) random variable
B) expectation
C) parameter
D) residual

Question 18

The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is known as the _____.

A) constant term
B) error term
C) residual
D) model parameter

Question 19

When the mean value of the dependent variable is independent of variation in the independent variable, the slope of the regression line is _____.

A) positive
B) zero
C) negative
D) infinite

Question 20

A regression analysis involving one independent variable and one dependent variable is referred to as a _____.

A) factor analysis
B) time series analysis
C) simple regression
D) data mining

Question 21

What would be the mean square due to regression (MSR) in this case?

A) 15.48
B) 10
C) 5.9
D) 3.87

Question 22

Which of the following inferences can be drawn from the scatter chart given below?

A) The residuals have a varying variance.
B) The model captures the relationship between the variables accurately.
C) The regression model follows the F probability distribution.
D) The residual distribution is consistently scattered about zero.

Question 23

The _____ is an indication of how frequently interval estimates based on samples of the same size taken from the same population using identical sampling techniques will contain the true value of the parameter we are estimating.

A) residual
B) tolerance factor
C) confidence level
D) accuracy level

Question 24

The following scatter chart would help conclude that:

A) the residuals have a constant variance.
B) the model fails to capture the relationship between the variables accurately.
C) the model underpredicts the value of the dependent variable for intermediate values of the independent variable.
D) the residual is normally distributeD)

Question 25

The following scatter chart would help conclude that:

A) the model is time-invariant.
B) the model captures the relationship between the variables accurately.
C) the residuals are interdependent.
D) the residuals are normally distributeD)

Question 26

_____ refers to the data set used to compare model forecasts and ultimately pick a model for predicting values of the dependent variable.

A) Codomain
B) Training set
C) Validation set
D) Range

Question 27

_____ is the data set used to build the candidate models.

A) Range
B) Codomain
C) Validation set
D) Training set

Question 28

_____ refers to the use of sample data to calculate a range of values that is believed to include the unknown value of a population parameter.

A) Interval estimation
B) Hypothesis testing
C) Statistical inference
D) Point estimation

Question 29

What would be the mean square error (MSE) in this case?

A) 0.59
B) 0.01
C) 1.26
D) 545

Question 30

The principle of using the simplest meaningful model possible without sacrificing accuracy is referred to as_____.

A) Engel's law
B) KISS principle
C) Murphy's law
D) Ockham's razor

Question 31

_____ refers to the degree of correlation among independent variables in a regression model.

A) Multicollinearity
B) Tolerance
C) Rank
D) Confidence level

Question 32

Which of the following inferences can be drawn from the scatter chart given below?

A) The residuals have a constant variance.
B) The model captures the relationship between the variables accurately.
C) The model underpredicts the value of the dependent variable for intermediate values of the independent variable.
D) The residual distribution is not normally distributeD)

Question 33

_____ is used to test the hypothesis that the values of the regression parameters β1, β2, . . . , βq are all zero.

A) An F test
B) A t test
C) The least squares method
D) Extrapolation

Question 34

The prespecified value of the independent variable at which its relationship with the dependent variable changes in a piecewise linear regression model is referred to as the _____.

A) milestone
B) breakpoint
C) tipping point
D) watchpoint

Question 35

A normally distributed error term with mean of zero would:

A) have values that are symmetric about the variance.
B) allow more accurate modelling.
C) yield biased regression estimates.
D) be a hyperbolic curve.

Question 36

Assessing the regression model on data other than the sample data that was used to generate the model is known as _____.

A) approximation
B) cross-validation
C) graphical validation
D) postulation

Question 37

Fitting a model too closely to sample data, resulting in a model that does not accurately reflect the population is termed as _____.

A) approximation
B) hypothesizing
C) overfitting
D) postulating

Question 38

What would be the F test statistic in this case?

A) 396.46
B) 400
C) 350.32
D) 298.55

Question 39

_____ refers to the scenario in which the relationship between the dependent variable and one independent variable is different at different values of a second independent variable.

A) Interaction
B) Multicollinearity
C) Autocorrelation
D) Covariance

Question 40

A variable used to model the effect of categorical independent variables in a regression model is known as a _____.

A) dependent variable
B) response
C) dummy variable
D) predictor variable

Question 41

The data shown below are the average personal income and personal consumption expenditures based on the survey conducted in the year 1995 to 2009 in U.S.
a. Develop a scatter chart for the above data. What does this chart indicate about the relationship between average personal income and personal consumption expenditure?
b. Develop an estimated regression equation showing how personal consumption expenditure is related personal income.
c. What proportion of variation in the sample values of proportion of personal consumption expenditure does this model explain?

Question 42

A student is interested in studying the impact of number of books referred by students on a statistics course and the number of lectures they attended on the final grade on the course. A sample of 25 students is selected and the data is given below.
a. Develop an estimated regression equation using number of books referred and the number of lectures attended to predict the final grade on the course.
b. Joseph referred 4 books and attended 19 lectures. What is his predicted final score on the course?

Question 43

A research center is interested in investigating about height and age of children who are between 5 to 9 years old. In order to do this, a sample of 15 children is selected and the data is given below.
a. Develop a scatter chart with age as the independent variable. What does the scatter chart indicate about the relationship between the height and age of children?
b. Use the data to develop an estimated regression equation that could be used to estimate the height based on the age. What is the estimated regression model?
c. How much of the variation in the sample values of height does the model estimated in part b explain?

A) Develop a scatter chart with age as the independent variable. What does the scatter chart indicate about the relationship between the height and age of children?
B) Use the data to develop an estimated regression equation that could be used to estimate the height based on the age. What is the estimated regression model?
C) How much of the variation in the sample values of height does the model estimated in part b explain?

Question 44

A survey is conducted to determine whether the age of car influences the annual maintenance cost. A sample of 10 cars is selected and the data is shown below.
a. Test whether each of the regression parameters β0 and β1 is equal to zero at a 0.05 level of significance.
b. Interpret the estimated regression parameters? Are these interpretations reasonable?

Question 45

A production company is studying the relationship between the average cost/unit and number of units produced in a batch. A sample of 10 batches is selected and the data is given below.

a. Develop an estimated quadratic regression equation for the data. How much variation in the sample values of cost/unit does this regression model explain?
b. Is the overall regression relationship significant at a 0.05 level of significance? If so, then test the relationship between the independent variable and the dependent variable at a 0.05 level of significance.

Question 46

A company's sales in the period 2000 to 2011 along with the national income of the country, where the business is set up, are as below.

Test whether each of the regression parameters β₀ and β₁ is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters?

Question 47

The data shown below are the average personal income and personal consumption expenditures based on the survey conducted in the year 1995 to 2009 in U.S.
a. What is the 95 percent confidence interval for the regression parameter β1? Based on this interval, what conclusion can you make about the hypotheses that the regression parameter β1 is equal to zero?
d. What is the 95 percent confidence interval for the regression parameter β0? Based on this interval, what conclusion can you make about the hypotheses that the regression parameter β0 is equal to zero?

Question 48

A survey conducted by a research team was to investigate how the education level, tenure in current employment, and age, are related to annual income. A sample 20 employees is selected and the data is given below.
a. Check if the F test leads to conclude that an overall regression relationship exists. If yes, use the t test to determine the significance of each independent variable. What is the conclusion for each test at the 0.05 level of significance?
b. Remove all independent variables that are not significant at the 0.05 level of significance from the estimated regression equation. What is your estimated regression equation in this case?

Question 49

A student is interested in studying the impact of number of books referred by students on a statistics course and the number of lectures they attended on the final grade on the course. A sample of 25 students is selected and the data is given below.
a. Use the F test to determine the overall significance of the relationship. What is your conclusion at the 0.05 level of significance? Use the t test to determine the significance of each independent variable? What are your conclusions at the 0.05 level of significance?
b. How much of the variation in the final grade does the model in part (a) explain?

Question 50

A research team in at the Gonzaga University is interested in predicting a student's overall university GPA if his/her high school GPA is known. Assume that a random sample of 20 students is selected and the data is given below.
a. Develop a scatter chart for these data with High School GPA as the independent variable. What does the scatter chart indicate about the relationship between high school GPAs and overall university GPA?
b. Develop an estimated regression equation showing how high school GPA is related to overall university GPA. What is the estimated regression model?
c. What is the predicted overall university GPA of Sophia, a student who has been admitted to Gonzaga University, with 3.40 high school GPA?

Question 51

The data on profit and market capitalization for a sample of 15 different firms in U.S are as below.
a. Develop a scatter chart for the above data. What does this chart indicate about the relationship between market capitalization and profit?
b. Use the data to develop an estimated regression equation that could be used to estimate a firm's profit based on its market capitalization. What is the estimated regression model?
c. What is the predicted profit for the market capitalization of 70721.3 ($ million)?

A) Develop a scatter chart for the above datA) What does this chart indicate about the relationship between market capitalization and profit?
B) Use the data to develop an estimated regression equation that could be used to estimate a firm's profit based on its market capitalization. What is the estimated regression model?
C) What is the predicted profit for the market capitalization of 70721.3 ($ million)?

Question 52

A production company is studying the relationship between the average cost/unit and number of units produced in a batch. A sample of 10 batches is selected and the data is given below.

a. Develop a scatter chart for these data. What does the scatter chart indicate about the relationship between average cost/unit and number of units produced?
b. Develop an estimated simple linear regression equation for the data. How much variation in the sample values of cost/unit is explained by this regression model?

Question 53

A researcher wanted to study effect of two factors, x₁ and x₂, on yield (y). The observations are given below.
a. Develop an estimated linear regression equation with the factor x₁ as the independent variable. Test for a significant relationship between factor x₁ and yield at the 0.05 level of significance.
b. How much of the variation in the sample values of yield does the model in part (a) explain?

Question 54

A survey is conducted to determine whether the age of car influences the annual maintenance cost. A sample of 10 cars is selected and the data is shown below.
a. Develop a scatter chart for these data with age of cars as the independent variable. What does the scatter chart indicate about the relationship between age of a car and the annual maintenance cost?
b. Use the data to develop an estimated regression equation that could be used to predict the annual maintenance cost given the age of the car. What is the estimated regression model?

Question 55

A researcher wanted to study effect of two factors, x₁ and x₂, on yield (y). The observations are given below.
a. Develop an estimated regression equation with both factors x₁ and x₂ as the independent variables. Is the overall regression statistically significant at the 0.05 level of significance? If so, then test whether each of the regression parameters β0, β1, and β2 is equal to zero at a 0.01 level of significance. What are the correct interpretations of the estimated regression parameters?
b. How much of the variation in the sample values of y does the model in part (a) explain?

Question 56

Consider the following data with the dependent variable y, independent variable x, and the dummy variable
a. Develop the estimated regression equation using all of the independent variables included in the data.
b. Test for an overall regression relationship at the 0.05 level of significance. Is there a significant regression relationship?

Question 57

Consider the below data which is based on a company's sales in the period 2000 to 2011 along with the national income of the country, where the business is set up.
a. Develop a scatter chart for these data, treating the national income as the independent variable. Does a simple linear regression model appear to be appropriate?
b. Develop an appropriate estimated regression equation to predict the company's sales, given the national income. How much variation in the sample values of company's sales is explained by this regression model

Question 58

A company's sales in the period 2000 to 2011 along with the national income of the country, where the business is set up, are as below.
a. Develop a scatter chart for the above data. What does this chart indicate about the relationship between the National Income and the Company's sales in the period 2000 to 2011?
b. Use the data to develop an estimated regression equation that could be used to estimate the company's sales based on the national income. What is the estimated regression model?

A) Develop a scatter chart for the above datA) What does this chart indicate about the relationship between the National Income and the Company's sales in the period 2000 to 2011?
B) Use the data to develop an estimated regression equation that could be used to estimate the company's sales based on the national income. What is the estimated regression model?

Question 59

A survey conducted by a research team was to investigate how the education level, tenure in current employment, and age, are related to annual income. A sample 20 employees is selected and the data is given below.
a. Determine the estimated multiple linear regression equation that can be used to predict the annual income given number of years school completed (Education), length of tenure in current employment, and age.
b. Use the F test to determine the overall significance of the regression relationship. What is the conclusion at the 0.05 level of significance?

Question 60

Consider the following data with the dependent variable y, independent variable x, and the dummy variable a. Check if the overall regression relationship exists for the above data. If yes, test the relationship between each independent variable and the dependent variable at the 0.05 level of significance, and interpret the relationship between each of the independent variables and the dependent variable.
b. How much of the variation in the sample values of delay does this estimated regression equation explain?
d.