4302 exam 1

The specification of linear regression models (i.e., the choice of dependent and explanatory variables) is based on... (2)

- Economic/business theories - Logic and intuition

What is Multicollinearity related to?

A high level of correlation between explanatory variables

What factor does increase the estimated value of the variance of 𝛽hat𝑗 ?

A high 𝜎hat^2

In the Gauss Markov Theorem, what does BLUE stand for?

Best Linear Unbiased Estimators

Data on the 2019 spring semester GPA at TTU for each of the students enrolled in AAEC 4302 in Summer II corresponds to:

Cross sectional data

T/F Econometric models such as the simple and multiple linear regression models are only used by academic researchers at universities and research institutions. There are no applications of these models in private businesses

False

What are the maximum and minimum values for R2?

Minimum = 0; maximum=1

The least square estimators 𝛽̂hat0 and 𝛽̂hat1 are unbiased estimators for 𝛽0 and 𝛽1 since:

On average, they are equal to the true population values (i.e., E[𝛽̂hat0] = 𝛽0 𝑎𝑛𝑑 E[𝛽̂hat1] = 𝛽1)

In the simple linear regression model 𝑦 = 𝛽0 + 𝛽1𝑥 + 𝜇, the linear relation implied by the model is between: a) The average value of y and 𝑥 b) The average value of x and 𝑦 c) y and x d) y and 𝜇

The average value of y and 𝑥

In the simple linear regression model 𝑦 = 𝛽0 + 𝛽1𝑥 + 𝜇 , what are the estimators for 𝛽0 and 𝛽1:

The formulas we use to estimate the coefficients using sample values for y and x

T/F In both the SLR model and the MLR model the residuals or predicted errors are calculated as the difference between the observed value of y and the predicted value of y.

True

T/F In the simple linear regression model 𝑦 = 𝛽0 + 𝛽1𝑥 + 𝜇 , use of the least squares estimators for 𝛽0 and 𝛽1, 𝛽̂hat0 and 𝛽̂hat1, result in different estimated values when different samples are used:

True

T/F Multicollinearity is a problem because it results in estimates of Var(𝛽̂hat𝑖 ) that are larger (i.e., less precise)

True

T/F One of the main reasons behind the development of Econometric as a branch of Economics is the need for statistical procedures that account for the nonexperimental (i.e., observational) nature of the data used in Economics

True

T/F Random sampling means that each individual in the population has the same probability of being selected in the sample

True

T/F The Simple Linear Assumption 1 (SLR1) refers to the validity of the assumption that y = β 0 + β1x + u is the correct model

True

Data on variables for one individual (e.g., a country) observed multiple times correspond to: a) Cross sectional data b) Time series data c) Panel data d) None of the above

b) Time series data

In the simple linear regression model 𝑦 = 𝛽0 + 𝛽1𝑥 + 𝜇 : a) 𝛽0 + 𝛽1𝑥1 is the systematic component (model for the mean) b) 𝜇 is the random or unsystematic component c) a) and b) d) None of the above

c) a) and b)

Econometric models can be used only to: a) To estimate economic relationships b) To test economic theories c) To evaluate policies d) All of the above

d) All of the above

What of the following is a similarity between the simple linear regression (SLR) models and the multiple linear regression (MLR) model? a) In both cases the estimated beta coefficients minimize the sum of residuals. b) In both cases the R2 measures the proportion of the variability in the explanatory variables that is explained by the model. c) Both cases assume a linear relationship between the explanatory variable(s) and the average value of the error term. d) None of the above

d) None of the above

T/F It possible to estimate 𝛽hat0 and 𝛽hat1 using a unique value of x as long as we have several values of the dependent variable y.

false

T/F The R2 measures the percentage of total variability in the independent variable (x) that is explained by the model.

false

T/F The expression E[y] means the estimated value of y:

false

T/F The formulas to calculate Var(𝛽̂ 1) in the SLR and the MLR models are exactly the same

false

T/F Rj^2 is the R^2 of a regression of xj as the dependent variable and all other x's as explanatory variables.

true

T/F The hat (^) used in coefficients is used to differentiate the true unknown population values (for example, β0) from the coefficient obtained using sample data (for example, 𝛽̂hat 0).

true

What does VIF stand for?

variance inflation factor

The least square estimator 𝛽̂hat 1 is said to be an unbiased estimator for β1 because

𝐸[𝛽̂hat 1] = β1

The simple linear regression model: y = β 0 + β1x + u implies a linear relationship between

𝑥 and the average value of y (which is E[y])