Stats 351

Order the steps in developing a hypothesis in order from the first to second to third step.

1. Identify the relevant population parameter of interest 2. Determine whether it is one- or two-tailed test 3. Include some form of the equality sign in the null hypothesis and use the alternative hypothesis to establish a claim

In the presence of correlated observations, the OLS estimators are unbiased, but their estimated standard errors are inappropriate. Which of the following could happen as a result? Multiple choice question. The t test may suggest that the predictor variables are individually and jointly significant when this is not true The model looks better than it really is with a spuriously high R2 All of the answers are correct The F test may suggest that the predictor variables are individually and jointly significant when this is not tru

All of the answers are correct

The degrees of freedom determine the extent of the broadness of the tails of the distribution; If there are fewer degrees of freedom, the tail of the distribution is more: Multiple choice question. Narrow Complicated Furry Broad

Broad : The degrees of freedom determine the extent of the broadness of the tails of the distribution; the fewer the degrees of freedom, the broader the tails.

Which of the following is an example of a Type II Error? Multiple choice question. Is a correct decision Occurs when we reject the null hypothesis Can occur when the null hypothesis is false Can occur when the null hypothesis is true

Can occur when the null hypothesis is false: a Type II error is made when we do not reject the null hypothesis when the null hypothesis is actually false

Which of the following is an example of a Type II Error? Multiple choice question. Occurs when we reject the null hypothesis Can occur when the null hypothesis is true Can occur when the null hypothesis is false Is a correct decision

Can occur when the null hypothesis is false: a Type II error is made when we do not reject the null hypothesis when the null hypothesis is actually false

The assumption of constant variability of observations often breaks down in studies with cross-sectional data. Consider the model y = β0 + β1x + ɛ, where y is a household's consumption expenditure and x is its disposable income. It may be unreasonable to assume that the variability of consumption is the same across a cross-section of household incomes. This violation is called: Multiple choice question. Multicollinearity Nonlinear Patterns Correlated Observations Changing variability

Changing variability

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

If one or more of the relevant predictor variables are excluded, then the resulting OLS estimators are biased. The extent of the bias depends on the degree of the " " between the included and the excluded predictor variables.

Correlation

We can use residual plots to gauge changing variability. The residuals are generally plotted against each predictor variable xj. There is a violation if the variability increases or " " over the values of xj.

Decreases

We are conducting a hypothesis test using α = 0.05. H0:Do not build brick-and-mortar store. HA:Build brick-and-mortar store. We determine that the p-value is .20. What is our decision? Multiple choice question. Do not reject the null hypothesis Reject the null hypothesis Collect more data Re-evaluate the alpha

Do not reject the null hypothesis: Do not reject the null hypothesis if the p-value ≥ α.

What is a good solution when confronted with multicollinearity? Multiple select question. Drop one of the collinear variables Obtain more data because the sample correlation may get weaker Obtain more data because a bigger sample is always better Add another variable

Drop one of the collinear variables Obtain more data because the sample correlation may get weaker

What are some measures that summarize how well the sample regression equation fits the data?

Goodness-of-fit

The detection methods for multicollinearity are mostly informal. Which of the following indicate a potential multicollinearity issue?

High R2 and significant F statistic coupled with insignificant predictor variables

Select all that apply Often it is more in-formative to provide a range of values—an interval—rather than a single point estimate for the unknown population parameter. What two terms are used for this range of values called? Multiple select question. Interval estimate Hypothesis test Population range Confidence interval

Interval estimate Confidence interval

What is the term used in a confidence interval that accounts for the standard error of the estimator and the desired confidence level of the interval? Multiple choice question. Sample proportion Estimate error Margin of error Point estimate

Margin of error

Select all that apply Which of the following summarizes the two correct decisions related to Type I and Type II errors? Multiple select question. Not rejecting the null hypothesis when the null hypothesis is true Not rejecting the null hypothesis when the null hypothesis is false Rejecting the null hypothesis when the null hypothesis is true Rejecting the null hypothesis when the null hypothesis is false

Not rejecting the null hypothesis when the null hypothesis is true Rejecting the null hypothesis when the null hypothesis is false

When confronted with multicollinearity, the best approach may be to do " " if the estimated model yields a high R2,

Nothing

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).

One

What is the condition called when two or more predictor variables have an exact linear relationship? Multiple choice question. Nonlinear violation Model inadequacies Nonzero slope coefficient Perfect multicollinearity

Perfect multicollinearity

What is the condition called when two or more predictor variables have an exact linear relationship? Multiple choice question. Perfect multicollinearity Nonlinear violation Nonzero slope coefficient Model inadequacies

Perfect multicollinearity

In the presence of changing variability, the estimated standard errors of the OLS estimators are inappropriate. What does this imply about using standard testing? Multiple choice question. We should use F tests only We should use standard t tests only Standard t or F tests are not valid as they are based on these estimated standard errors. Use standard t or F tests

Standard t or F tests are not valid as they are based on these estimated standard errors.

Another standardized statistic, which uses the estimator S in place of σ, is computed as T= ̄X−μ/S/√n. Which distribution does the random variable T follow?

T distribution: The random variable T follows the Student's t distribution, more commonly known as the t distribution.

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 coefficient of determination The standard coefficient The standard error of the estimate The adjusted coefficient of determination

The coefficient of determination The standard error of the estimate The adjusted coefficient of determination

What is used to evaluate how well the sample regression equation fits the data? Multiple select question. The goodness-of-fit measure The dispersion of residuals The coefficient of determination, R² The standard error of the estimate

The coefficient of determination, R² The standard error of the estimate

We can use residual plots to gauge changing variability.The residuals are generally plotted against each predictor variable xj Which of the following indicates there is no violation? Multiple choice question. The residuals are NOT randomly dispersed across the values of xj The predictor variable is randomly dispersed across the residuals There is no way to indicate no violation The residuals are randomly dispersed across the values of xj

The residuals are randomly dispersed across the values of xj

We can plot the residuals sequentially over time to look for correlated observations. If there is no violation, then what would you see? Multiple choice question. The residuals should show no pattern around the horizontal axis. The residuals should show no pattern around the vertical axis. The residuals should show a normal pattern around the vertical axis. The residuals should show a normal pattern around the horizontal axis.

The residuals should show no pattern around the horizontal axis.

Instead of se2,we generally report the standard deviation of the residual, denoted se, more commonly referred to as

The standard error of the estimate

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? Multiple choice question. Regression error Squared error Total error Total sum of squares

Total sum of squares

True or false: In most applications, we require some form of the equality sign in the null hypothesis

True

True or false: Linearity is justified if the residuals are randomly dispersed across the values of a predictor variable.

True

In the presence of changing variability, the OLS estimators are " ", but their estimated standard errors are inappropriate.

Unbiased

An important first step before running a regression model is to compile a comprehensive list of potential predictor variables. How can we reduce the list to a smaller list of predictor variables? Multiple choice question. We use R to make the necessary correction Use the adjusted R2 criterion to reduce the list The best approach may be to do nothing We must include all relevant variables

Use the adjusted R2 criterion to reduce the list

A crucial assumption in a linear regression model is that the error term is not correlated with the predictor variables. In general, when does this assumption break down?

When important predictor variables are excluded.

We can plot the residuals sequentially over time to look for correlated observations. How are violations indicated?

When positive residuals and negative residuals alternate over a few periods, sometimes positive or negative for a couple of periods.

We use hypothesis testing to resolve conflicts between two competing hypotheses on a particular population parameter of interest. Which of the following corresponds to the null hypothesis? contradicts the default state or status quo denoted H0 corresponding to a presumed default state of nature or status quo denoted HA

denoted H0 corresponding to a presumed default state of nature or status quo

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.

less

If sample evidence is inconsistent with the null hypothesis, we " " the null hypothesis.

reject

" " 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.

residual

If residual plots exhibit strong nonlinear patterns, the inferences made by a linear regression model can be quite misleading. In such instances, we should employ nonlinear regression methods based on simple transformations of the " " and the predictor variables.

response

The basic principle of hypothesis testing is to first assume that the null hypothesis is " " and then determine if sample evidence contradicts this assumption.

true

For the 99% confidence interval, what is α/2? Multiple choice question. .015 .005 .05 .10

α/2 = 0.01/2 = 0.005

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),

β1