Question 1

The restricted model is a reduced model where the coefficients that are restricted under the null hypothesis are estimated.

Accepted Answer

The restricted model is a reduced model where the coefficients that are restricted under the null hypothesis are set to specific values (often zero), not estimated.

Question 2

One of the required assumptions of regression analysis states that the error term has a(an) ________ value of zero.

Accepted Answer

expected

Question 3

The test statistic for a test of individual significance is assumed to have a t distribution with n - k - 2 degrees of freedom, where n is the sample size and k is the number of explanatory variables.

Accepted Answer

The correct degrees of freedom for a test statistic in regression analysis, when testing for individual significance, is typically n - k - 1, where n is the sample size and k is the number of explanatory variables (not including the constant term).

Question 4

It is common to refer to the interval estimate for an individual value of y as the ________ interval.

Accepted Answer

The answer of It is common to refer to the...

Question 5

Consider the following simple linear regression model: y = β₀ + β₁x + ε. When determining whether there is a one-to-one relationship between x and y, the null hypothesis takes the form ________. A) H₀: β₁ = 0 B) H₀: β₁ = 1 C) H₀: b₁ = 0 D) H₀: b₁ = 1

Accepted Answer

The answer of Consider the following simple linear regression model:...

Question 6

Consider the following simple linear regression model: y = β₀ + β₁x + ε. When determining whether there is a positive linear relationship between x and y, the alternative hypothesis takes the form ________. A) H_A: β₁ = 0 B) H_A: β₁ > 0 C) H_A: β₁ < 0 D) H_A: b₁ > 1

Accepted Answer

The alternative hypothesis takes the form of a positive relationship between x and y, which means that as x increases, y also increases. This is represented by β₁ > 0.

Question 7

If the residuals are correlated, then the residuals should show no pattern around the horizontal axis.

Accepted Answer

If the residuals are correlated, they will show a pattern around the horizontal axis, indicating a relationship between the dependent and independent variables that has not been accounted for in the model. This pattern may take the form of a curve or slope, and can be detected through various methods such as plotting the residuals or running diagnostic tests.

Question 8

The term BLUE stands for Best Linear Unbiased Estimator.

Accepted Answer

The term BLUE stands for Best Linear Unbiased Estimator and is a commonly used term in statistics.

Question 9

A crucial assumption in a regression model is that the error term is not correlated with any of the explanatory variables.

Accepted Answer

This assumption is known as the assumption of no autocorrelation or, more commonly, the assumption of no correlation between the error term and the independent variables. This is important because if this assumption is violated, it can lead to biased and inconsistent estimates of the regression coefficients, and can also affect statistical inference and prediction.

Question 10

With the partial F test, we basically analyze the ratio of (SSE_R- SSE_U) to ________.

Accepted Answer

The answer of With the partial F test, we basically...

Question 11

If in the multiple linear model the slope coefficient β_i is negative, it suggests an inverse (negative) relationship between the explanatory variable x_i and the response variable y holding the other explanatory variables constant.

Accepted Answer

A negative slope coefficient indicates that as the value of the explanatory variable x decreases, the value of the response variable y also decreases, holding all other variables constant. This is commonly referred to as an inverse (negative) relationship between x and y.

Question 12

Consider the following simple linear regression model: y = β₀ + β₁x + ε. When determining whether x significantly influences y, the null hypothesis takes the form ________. A) H₀: β₁ = 0 B) H₀: β₁ = 1 C) H₀: b₁ = 0 D) H₀: b₁ = 1

Accepted Answer

The null hypothesis in a simple linear regression model when testing whether x significantly influences y is typically that the coefficient on x (β) is equal to 0 (i.e. there is no significant relationship between x and y). Therefore, choice A is the correct answer as it specifies the null hypothesis in this form. Choices B and D are incorrect as they state that the coefficient on x is equal to 1, which is not the null hypothesis. Choice C is also incorrect as it uses the estimate of the coefficient (b) rather than the true parameter (β) in the null hypothesis.

Question 13

The term multicollinearity refers to the condition when the variance of the error term, conditional on x₁, x₂, …, x_n, is the same for all observations.

Accepted Answer

The definition given for multicollinearity is incorrect. Multicollinearity refers to the condition when there is a high correlation between two or more predictor variables in a regression model. It can lead to inflated standard errors, unstable coefficients, and unreliable hypothesis tests.

Question 14

The ________ model is a complete model that imposes no restrictions on the coefficients.

Accepted Answer

The answer of The ________ model is a complete model...

Question 15

If the confidence interval does not contain the value zero, then the ________ variable associated with the regression coefficient is significant.

Accepted Answer

The answer of If the confidence interval does not contain...

Question 16

The F test can be applied for any number of linear restrictions; the resulting test is often referred to as the ________ F test.

Accepted Answer

The answer of The F test can be applied for...

Question 17

When some explanatory variables of a regression model are strongly correlated, this phenomenon is called serial correlation.

Accepted Answer

Serial correlation refers to the correlation between error terms in a time series data, not the correlation between explanatory variables in a regression model. When explanatory variables in a regression model are strongly correlated, it is called multicollinearity.

Question 18

________ plots can be used to detect common violations, and they can be used to detect outliers.

Accepted Answer

The answer of ________ plots can be used to detect...

Question 19

Conditional on x₁, x₂, ..., x_k, the error term ε is ________ distributed.

Accepted Answer

The answer of Conditional on x₁, x₂, ..., x_k, the...

Question 20

The alternative hypothesis for the test of joint significance is specified as: H_A: At least two β_j ≠ 0.

Accepted Answer

The alternative hypothesis for the test of joint significance is that at least one β_j ≠ 0, not necessarily two or more.

Quiz 15: Inference With Regression Models

The restricted model is a reduced model where the coefficients that are restricted under the null hypothesis are estimated.

One of the required assumptions of regression analysis states that the error term has a(an) ________ value of zero.

The test statistic for a test of individual significance is assumed to have a t distribution with n - k - 2 degrees of freedom, where n is the sample size and k is the number of explanatory variables.

It is common to refer to the interval estimate for an individual value of y as the ________ interval.

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether there is a one-to-one relationship between x and y, the null hypothesis takes the form ________.

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether there is a positive linear relationship between x and y, the alternative hypothesis takes the form ________.

If the residuals are correlated, then the residuals should show no pattern around the horizontal axis.

The term BLUE stands for Best Linear Unbiased Estimator.

A crucial assumption in a regression model is that the error term is not correlated with any of the explanatory variables.

With the partial F test, we basically analyze the ratio of (SSER - SSEU) to ________.

If in the multiple linear model the slope coefficient βi is negative, it suggests an inverse (negative) relationship between the explanatory variable xi and the response variable y holding the other explanatory variables constant.

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether x significantly influences y, the null hypothesis takes the form ________.

The term multicollinearity refers to the condition when the variance of the error term, conditional on x1, x2, …, xn, is the same for all observations.

The ________ model is a complete model that imposes no restrictions on the coefficients.

If the confidence interval does not contain the value zero, then the ________ variable associated with the regression coefficient is significant.

The F test can be applied for any number of linear restrictions; the resulting test is often referred to as the ________ F test.

When some explanatory variables of a regression model are strongly correlated, this phenomenon is called serial correlation.

________ plots can be used to detect common violations, and they can be used to detect outliers.

Conditional on x1, x2, ..., xk, the error term ε is ________ distributed.

The alternative hypothesis for the test of joint significance is specified as: HA: At least two βj ≠ 0.

Consider the following simple linear regression model: y = β₀ + β₁x + ε. When determining whether there is a one-to-one relationship between x and y, the null hypothesis takes the form ________.

Consider the following simple linear regression model: y = β₀ + β₁x + ε. When determining whether there is a positive linear relationship between x and y, the alternative hypothesis takes the form ________.

With the partial F test, we basically analyze the ratio of (SSE_R- SSE_U) to ________.

If in the multiple linear model the slope coefficient β_i is negative, it suggests an inverse (negative) relationship between the explanatory variable x_i and the response variable y holding the other explanatory variables constant.

Consider the following simple linear regression model: y = β₀ + β₁x + ε. When determining whether x significantly influences y, the null hypothesis takes the form ________.

The term multicollinearity refers to the condition when the variance of the error term, conditional on x₁, x₂, …, x_n, is the same for all observations.

Conditional on x₁, x₂, ..., x_k, the error term ε is ________ distributed.

The alternative hypothesis for the test of joint significance is specified as: H_A: At least two β_j ≠ 0.