Question 1

What would be the mean square due to regression (MSR) in this case?
A) 15.48
B) 10
C) 5.9
D) 3.87

Accepted Answer

The MSR is given by the formula (SSR/q). Substituting the given values, we get MSR=3.87.

Question 2

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.

Accepted Answer

The variation in the residuals e increases as the value of the independent variable x increases, suggesting that the residuals do not have a constant variance.

Question 3

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

Accepted Answer

The confidence level 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.

Question 4

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)

Accepted Answer

The residuals are positive for small and large values of the independent variable x but are negative for the remaining values of the independent variable. This pattern suggests that the linear relationships in the regression model underpredicts the value of dependent variable for small and large values of the independent variable and overpredicts the value of the dependent variable for intermediate values of the independent variable. In this case, the regression model does not adequately capture the relationship between the independent variable x and the dependent variable y.

Question 5

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)

Accepted Answer

In this figure, connected consecutive residuals allow us to see a distinct pattern across every set of four residuals; the second residual is consistently larger than the first and smaller than the third, whereas the fourth residual is consistently the smallest. This pattern, which occurs consistently over each set of four consecutive residuals in the chart, suggests that the residuals generated by this model are not independent.

Question 6

_____ 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

Accepted Answer

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

Question 7

_____ is the data set used to build the candidate models.
A) Range
B) Codomain
C) Validation set
D) Training set

Accepted Answer

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

Question 8

_____ 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

Accepted Answer

Interval estimation 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.

Question 9

What would be the mean square error (MSE) in this case?
A) 0.59
B) 0.01
C) 1.26
D) 545

Accepted Answer

The MSE is given by the formula (SSE/ n-q-1). Substituting the given values, we get SSE=0.0097, which is approximated to 0.01.

Question 10

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

Accepted Answer

The principle of using the simplest meaningful model possible without sacrificing accuracy is referred to as Ockham's razor.
Problems

Question 11

_____ refers to the degree of correlation among independent variables in a regression model.
A) Multicollinearity
B) Tolerance
C) Rank
D) Confidence level

Accepted Answer

Multicollinearity is the degree of correlation among independent variables in a regression model.

Question 12

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)

Accepted Answer

The residuals in the given figure are not symmetrically distributed around zero; many of the negative residuals are relatively close to zero, while the relatively few positive residuals tend to be far from zero. This skewness suggests that the residuals are not normally distributed.

Question 13

_____ 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

Accepted Answer

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

Question 14

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

Accepted Answer

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 knot or breakpoint.

Question 15

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.

Accepted Answer

The practical implication of normally distributed errors with a mean of zero and a constant variation for any given combination of values of x₁, x₂, . . . , xq is that the regression estimates are unbiased, possess consistent accuracy, and tend to err in small amounts rather than in large amounts.

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

What would be the F test statistic in this case?
A) 396.46
B) 400
C) 350.32
D) 298.55

Accepted Answer

The F test statistic is given by the formula MSR / MSE. Substituting the given values, we get F=396.46.

Question 19

_____ 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

Accepted Answer

Interaction 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.

Question 20

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

Accepted Answer

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

Quiz 4: Linear Regression

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

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

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.

The following scatter chart would help conclude that:

The following scatter chart would help conclude that:

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

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

_____ 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.

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

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

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

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

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

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 normally distributed error term with mean of zero would:

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

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

What would be the F test statistic in this case?

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