Econometrics Questions

For the linear regression model, y = β0 + β1x1 + β2x2 + . . . + βkxk + ɛ, which of the following are the competing hypotheses used for a test of joint significance? Choose both the correct test for the null and alternative hypotheses.Multiple select question.H0:β1=β2=... =βk=0HA:At least one βi≠0H0: βj =βj0HA: βj ≠βj0

Consider the following linear regression model, which links the response variable y with k predictor variables x1, x2,..., xk:y=β0+β1x1+β2x2+... +βkxk+ε. If, for example, the slope coefficient β1 equals zero, then the predictor variable x1 does what and implies what? Choose all that answer the 'does what?' and 'Implies what?' questions!-Implying that x1 does not influence y-Drops out of the equation-Then x1 influences y-Does not drop out of the equation

Which of the following are the assumptions that underlie the classical linear regression model? Please select all that apply!Multiple select question.-The regression model given by y = β0 + β1x1 + β2x2 +... + βkxk + ɛ is linear in the parameters β0, β1,..., βk.-There is an exact linear relationship among the predictor variables; or, in statistical terminology, there is no perfect multicollinearity.-Conditional on x1, x2,.., xk, the error term ɛ is uncorrelated across observations; or, in statistical terminology, there is no serial correlation.-The error term ɛ is correlated with any of the predictor variables x1, x2,..., xk

What is the condition called when two or more predictor variables have an exact linear relationship?Model inadequaciesNonzero slope coefficientNonlinear violationPerfect multicollinearity

The variance inflation factor (VIF) is another measure that can detect a high correlation between three or more predictor variables even if no pair of predictor variables has a particularly high correlation. What is the smallest possible value of VIF? (absence of multicollinearity).ZeroVIF exceeds 5 or 10VIF does not exceed 5 or 10One

If the linear regression model includes an intercept, the number of dummy variables representing a categorical variable should be one less than the number of categories of the variable. This solution helps avoid which problem?-Categorical variables-This is not an issue-Dummy variable trap-Category sum trap

'______________________' plots are used to detect some of the common violations to the regression model assumptions. These graphical plots are easy to use and provide informal analysis of the estimated regression models.

When we assess a linear regression model, there are several tests we can use. What is the test called that determines whether the predictor variables x1, x2,..., xk have a joint statistical influence on y?Test for nonzero slope coefficientTest of joint significanceTest for goodness of fitTest of individual significance

The simple linear regression model y = β0 + β1x + ɛ implies that if x goes up by one unit, we expect y to change by how much? (irrespective of the value of x),ɛβ1xβ0

True or false: R2 can decrease as we add more predictor variables to the linear regression modelTrueFalse

We use analysis of variance (ANOVA) in the context of the linear regression model to derive R2.We denote the total variation in y as Σ(yi−y ̄)2, which is the numerator in the formula for the variance of y. What is this total variation called?Total sum of squaresTotal errorSquared errorRegression error

If we include as many dummy variables as there are categories, then their sum will equal '__________________'.

What is used to evaluate how well the sample regression equation fits the data?The standard error of the estimateThe goodness-of-fit measureThe coefficient of determination, R²The dispersion of residuals

In order to select the preferred model, we examine several goodness-of-fit measures: Select all goodness-of-fit measures examined!Multiple select question.The standard coefficientThe coefficient of determinationThe adjusted coefficient of determinationThe standard error of the estimate

In the case of a dummy variable categorizing a person's gender, we can define 1 for male and 0 for female. In this case, what would the reference category be?§ Male§ 1§ Female§ 0

The nonzero slope coefficient test is used for a renowned financial application referred to as the capital asset pricing model (CAPM).The model y = α + βx + ɛ, is essentially a simple linear regression model that uses α and β, in place of the usual β0 and β1, to represent the intercept and the slope coefficients, respectively. Which of the following is true about the slope coefficient β, called the stock's beta? Select that apply!Multiple select question.-When β equals 0, any change in the market return leads to an identical change in the given stock return.-A stock for which β > 1 is considered more "aggressive" or riskier than the market-Measures how sensitive the stock's return is to changes in the level of the overall market-When β equals 1, any change in the market return leads to an identical change in the given stock return.

In order to avoid the possibility of R2 creating a false impression, virtually all software packages include adjusted R2. Unlike R2, adjusted R2 explicitly accounts for what?The number of samples takenMulticollinearityThe sample size nThe number of predictor variables k

A simple linear regression model and is represented as y = β0 + β1x1 + ɛ,; What do β0and β1 (the Greek letters read as betas) represent? (They must be shown in the correct order!)1. Intercept, slope2. Dependent, independent3. Slope, intercept4. Slope, dependent

What are some measures that summarize how well the sample regression equation fits the data?Goodness-of-fitPredictor variablesDummy variablesRegression

When comparing models with the same response variable, we prefer the model with a smaller se. A smaller se implies that there is '_________________' dispersion of the observed values from the predicted values.