The deviations of observed responses around the conditional means _y|x are called...

averages.

errors.

mistakes.

corrections.

The equation for the group coded as 0 in the dummy variable forms a baseline for comparison.

True

False

The adjusted R-squared takes account of...

the number of explanatory variables and the number of observations.

the number of outliers.

the number of observations.

the number of explanatory variables.

Which of the following are conditions for two-sample inferences?

1. the data are simple random samples (SRS)
2. no lurking variable that explains the differences
3. groups have similar variances
4. each sample meets the sample size condition

I, II, and IV

I, II, and III

I, II, III, and IV

I, III, and IV

The multiple regression model (MRM) models the association in the population between multiple explanatory variables and response.

True

False

The square of any correlation can be interpreted as the r² of the regression of one variable on the other.

True

False

In regression analysis, the associated variable...

defines the x-axis and is called the explanatory variable or predictor.

defines the z-axis and is called the lurking variable.

defines the y-axis and is called the response.

none of the above.

Failure to reject H₀ shows that B₁ might be zero, not that it is zero.

True

False

Deviations of the residuals from normality may suggest an important omitted variable.

True

False

The intercept and slope for the group coded as 0 in the dummy variable are the intercept and slope of the explanatory variable in the multiple regression.

True

False

The slope of the dummy variable is the sum of estimated intercepts.

True

False

Which of the following are improvements that help refine a model's fit to the data?

Transformations

Removing outliers

All of these are correct

Added explanatory variables

One should remove variables one at a time to make sure that you don't omit a useful variable that was disguised by collinearity.

True

False

The standard deviation of the residuals measures how much the residuals vary around the fitted line.

True

False

The product of two explanatory variables in a regression model is called...

variability.

covariance.

dependence.

interaction.

The squared correlation r², or r-squared, determines the fraction of the variation accounted for by the least-squares regression line.

True

False

Which of the following are remedies for collinearity?

All of these are correct.

Remove redundant explanatory variables.

Do nothing.

Re-express the explanatory variables.

Attaching measurement units to b₀ and b₁ is a key initial step in interpreting these estimates.

True

False

The job of the standard error is to...

predict the sample to sample variation.

estimate the sample to sample variation.

predict the sample to sample variation.

estimate the mean-variance.

We use a scatterplot matrix to identify possible explanatory variables to add.

True

False

The horizontal deviations from the data points to the line are called residuals.

True

False

Failing to reject H₀: B₁ = 0

proves B₁ > 0

proves B₁ = 0

proves B₁ < 0

does not prove B₁ = 0

In regression analysis, the variable that we are trying to describe or predict...

defines the z-axis and is called the lurking variable.

defines the x-axis and is called the explanatory variable or predictor.

none of the above.

defines the y-axis and is called the response.

Which of the following are assumptions the SRM makes about errors?

All of these are correct

Equal variance

Normal

Independent

Which of the following are conditions for simple regression?

Random residual variation

All of these

No obvious lurking variable

Linear

Which of the following are reasons for removing an interaction that is not statistically significant?

1. simplicity
2. collinearity
3. covariance

II and III

I and II

I, II, and III

I and III

A scatterplot matrix allows us to determine visually how strong the association is among the different pairs of variables.

True

False

The slope of the interaction is the difference between estimated slopes in the simple regressions.

True

False

A variable is a confounding variable if it is correlated with the response and the two groups differ with respect to this variable.

True

False

The formula for the residual degrees of freedom in a multiple regression is...

k - 1

n - k

n - k - 1

n - 1