Question 1

The graph of the prediction equation obtained from the model  is a(n)
A)Line
B)Plane
C)Parabola
D)Exponential curve

Accepted Answer

C

Question 2

When the quadratic regression model y = ₀ + ₁x + ₂x² + $\varepsilon$ is used the term ₁ shows the rate of curvature of the parabola.

Accepted Answer

True

Question 3

The standard error decreases if and only if the adjusted multiple coefficient of determination decreases.

Accepted Answer

The standard error and the adjusted multiple coefficient of determination are not directly related. It is possible for one to decrease while the other increases or remains unchanged.

Question 4

If we increase the number of independent variables in a multiple regression model,the F statistic will always increase.

Accepted Answer

The F statistic may not always increase with more independent variables because it depends on the overall fit of the model and the significance of the added variables. Adding variables that do not improve the model's fit can lead to a decrease or no change in the F statistic.

Question 5

In the quadratic regression model the ₁ term represents the: A)Rate of curvature of the parabola. B)Value of Y when X is zero. C)Shift parameter of the parabola. D)Y-intercept of the parabola.

Accepted Answer

The answer of In the quadratic regression model  the...

Question 6

An independent variable dropped during an iteration of the backward elimination process may be added back to the regression model during a later iteration of the process.

Accepted Answer

In backward elimination, once an independent variable is removed, it is not reconsidered in later iterations.

Question 7

In multiple regression analysis,if the simple correlation coefficient between the dependent variable and one of the independent variables is .95,then this indicates that the problem of multicollinearity exists.

Accepted Answer

The answer of In multiple regression analysis,if the simple correlation...

Question 8

As we increase the number of independent variables in a multiple regression model,the F statistic will _____ increase.
A)Always
B)Sometimes
C)Never

Accepted Answer

The answer of As we increase the number of independent...

Question 9

The general form of the quadratic multiple regression models is: A)y =β₁X₁ + β₂X₂ + ε B)y =β₀+β₁X₁ +ε C)y =β₀ + ₁X₁ +β₂X₂² +ε D)y =β₀ + β₂X₂² +ε E)y =β₀ +β₁X₂² +ε

Accepted Answer

₀ + ₁X₁ + ₂X₂² +

Question 10

In the quadratic regression model if the term ₂ is ______ zero,then the parabola opens __________. A)Less than,upward B)Greater than,upward C)Greater than,either upward or downward D)Less than,either upward or downward E)Equal to,downward

Accepted Answer

The answer of In the quadratic regression model  if...

Question 11

In comparing regression models,the regression model with the largest R² will also have the smallest standard error(s).

Accepted Answer

Standard error only decreases if the adjusted R² increases. So if comparing regression models, you should use adjusted R² rather than R².

Question 12

One way to identify outliers with respect to their x values is to calculate their leverage values.

Accepted Answer

Leverage values can be used to identify outliers with respect to their x values. A data point with a high leverage value means that its x value is far away from the other x values in the data set, making it an outlier in terms of its x value.

Question 13

When there are indications of autocorrelation,first an investigation should be conducted to determine whether one or more independent variables that might explain the autocorrelation have been omitted from the model.

Accepted Answer

Autocorrelation can be caused by omitted variables that are related to both the dependent and independent variables in the model. Therefore, the first step when autocorrelation is detected is to investigate whether any relevant independent variables have been left out of the model.

Question 14

Multicollinearity hinders the regression model's ability to predict the dependent variable on the basis of a combination of values of the independent variable in the experimental region.

Accepted Answer

The answer of Multicollinearity hinders the regression model's ability to...

Question 15

If a particular multiple regression model has a small value of the C statistic and C for this model is less than k + 1,where k is the number of independent variables in the model,then the model should be considered biased and therefore undesirable.

Accepted Answer

If these conditions exist, the model should be considered desirable.

Question 16

In a multiple regression mode if the largest VIF is 21.6,then it can be concluded that there are indications of multicollinearity.

Accepted Answer

A VIF (variance inflation factor) value of 21.6 indicates that there is a high degree of correlation between one or more independent variables in the model. This high level of correlation suggests multicollinearity, which can affect the accuracy and reliability of the regression coefficients and prediction results.

Question 17

The variance inflation factor measures the relationship between the dependent variable and the rest of the independent variables in the regression model.

Accepted Answer

The variance inflation factor (VIF) measures the degree of multicollinearity between independent variables in a regression model, not the relationship between the dependent variable and independent variables.

Question 18

Even when an unimportant variable is added to a regression model,the explained variation will increase.

Accepted Answer

Adding any variable to a regression model will increase the total variance explained by the model, even if the variable is not important or has no significant effect on the outcome variable. This is because the total variance explained is a function of both the variance explained by the predictors as well as any unexplained variance.

Question 19

In the quadratic regression model ,the v₂ term represents the: A)Rate of curvature of the parabola. B)Value of Y when X is zero. C)Shift parameter of the parabola. D)Y-intercept of the parabola.

Accepted Answer

The answer of In the quadratic regression model  ,the...

Question 20

Cook's distance is a way to determine whether an observation is influential.

Accepted Answer

Cook's distance is a commonly used method to assess the impact of individual observations on fitted regression models. It assesses how much the model coefficients change when the ith observation is removed from the data set. The larger the Cook's distance value, the greater the influence that observation has on the fitted regression model.

Quiz 15: Model Building and Model Diagnostics

The graph of the prediction equation obtained from the model is a(n)

The standard error decreases if and only if the adjusted multiple coefficient of determination decreases.

If we increase the number of independent variables in a multiple regression model,the F statistic will always increase.

In the quadratic regression model the ₁ term represents the:

An independent variable dropped during an iteration of the backward elimination process may be added back to the regression model during a later iteration of the process.

In multiple regression analysis,if the simple correlation coefficient between the dependent variable and one of the independent variables is .95,then this indicates that the problem of multicollinearity exists.

As we increase the number of independent variables in a multiple regression model,the F statistic will _____ increase.

The general form of the quadratic multiple regression models is:

In the quadratic regression model if the term ₂ is zero,then the parabola opens ____.

In comparing regression models,the regression model with the largest R² will also have the smallest standard error(s).

One way to identify outliers with respect to their x values is to calculate their leverage values.

When there are indications of autocorrelation,first an investigation should be conducted to determine whether one or more independent variables that might explain the autocorrelation have been omitted from the model.

Multicollinearity hinders the regression model's ability to predict the dependent variable on the basis of a combination of values of the independent variable in the experimental region.

If a particular multiple regression model has a small value of the C statistic and C for this model is less than k + 1,where k is the number of independent variables in the model,then the model should be considered biased and therefore undesirable.

In a multiple regression mode if the largest VIF is 21.6,then it can be concluded that there are indications of multicollinearity.

The variance inflation factor measures the relationship between the dependent variable and the rest of the independent variables in the regression model.

Even when an unimportant variable is added to a regression model,the explained variation will increase.

In the quadratic regression model ,the v₂ term represents the:

Cook's distance is a way to determine whether an observation is influential.

Quiz 15: Model Building and Model Diagnostics

The graph of the prediction equation obtained from the model is a(n)

When the quadratic regression model y = 0 + 1x + 2x2 + ε\varepsilonε is used the term 1 shows the rate of curvature of the parabola.

The standard error decreases if and only if the adjusted multiple coefficient of determination decreases.

If we increase the number of independent variables in a multiple regression model,the F statistic will always increase.

In the quadratic regression model the 1 term represents the:

An independent variable dropped during an iteration of the backward elimination process may be added back to the regression model during a later iteration of the process.

In multiple regression analysis,if the simple correlation coefficient between the dependent variable and one of the independent variables is .95,then this indicates that the problem of multicollinearity exists.

As we increase the number of independent variables in a multiple regression model,the F statistic will _____ increase.

The general form of the quadratic multiple regression models is:

In the quadratic regression model if the term 2 is ______ zero,then the parabola opens __________.

In comparing regression models,the regression model with the largest R2 will also have the smallest standard error(s).

One way to identify outliers with respect to their x values is to calculate their leverage values.

When there are indications of autocorrelation,first an investigation should be conducted to determine whether one or more independent variables that might explain the autocorrelation have been omitted from the model.

Multicollinearity hinders the regression model's ability to predict the dependent variable on the basis of a combination of values of the independent variable in the experimental region.

If a particular multiple regression model has a small value of the C statistic and C for this model is less than k + 1,where k is the number of independent variables in the model,then the model should be considered biased and therefore undesirable.

In a multiple regression mode if the largest VIF is 21.6,then it can be concluded that there are indications of multicollinearity.

The variance inflation factor measures the relationship between the dependent variable and the rest of the independent variables in the regression model.

Even when an unimportant variable is added to a regression model,the explained variation will increase.

In the quadratic regression model ,the v2 term represents the:

Cook's distance is a way to determine whether an observation is influential.

In the quadratic regression model the ₁ term represents the:

In the quadratic regression model if the term ₂ is zero,then the parabola opens ____.

In comparing regression models,the regression model with the largest R² will also have the smallest standard error(s).

In the quadratic regression model ,the v₂ term represents the: