Chapters 14 and 15

In a multiple regression model, the error term ε is assumed to have a mean of:

0.

Which of the following statements is false?

Regression analysis can be interpreted as a procedure for establishing a cause-and-effect relationship between variables.

The mathematical equation relating the expected value of the dependent variable to the value of the independent variables, which has the form of E(y)=Bo+B1..+bpxp , is called:

a multiple regression equation.

The mathematical equation that explains how the dependent variable y is related to several independent variables and has the form y=Bo+Bixi...Bpxp..+E is called:

a multiple regression model.

If the coefficient of determination is a positive value, then the coefficient of correlation:

can be either negative or positive.

The value of the coefficient of correlation (r):

can be equal to the value of the coefficient of determination (r2).

The coefficient of determination:

cannot be negative.

If a significant relationship exists between x and y and the coefficient of determination shows that the fit is good, the estimated regression equation should be useful for:

estimation and prediction.

Observations with extreme values for the independent variables are called:

high leverage points.

The tests of significance in regression analysis are based on assumptions about the error term ɛ. One such assumption is that the error term follows ɛ a(n) _____ distribution for all values of x.

normal

A graph of the standardized residuals plotted against values of the normal scores that helps to determine whether the assumption that the error term has a normal probability distribution appears to be valid is called a:

normal probability plot.

In a multiple regression model, the values of the error term, ε, are assumed to be:

normally distributed.

When we conduct significance tests for a multiple regression relationship, the F test will be used as the test for:

overall significance.

Graphical representation of the residuals that can be used to determine whether the assumptions made about the regression model appear to be valid is called a:

residual plot.

The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is called a(n):

residual.

Since the multiple regression equation generates a plane or surface, its graph is called a:

response surface.

An F test, based on the F probability distribution, can be used to test for:

significance in regression.

When constructing a confidence or a prediction interval to quantify the relationship between two quantitative variables, what distribution do confidence and prediction intervals follow?

t distribution

If a residual plot of x versus the residuals, y - ŷ, shows a non-linear pattern, then we should conclude that:

the regression model is not an adequate representation of the relationship between the variables.

The tests of significance in regression analysis are based on assumptions about the error term ɛ . One such assumption is that the variance of ɛ, denoted by 𝝈2, is:

the same for all values of x.

In a multiple regression model, the variance of the error term, ε, is assumed to be:

the same for all values of x1, x2,..., xp.

In a regression analysis, an outlier will always increase:

the value of the correlation.

In multiple regression analysis:

there can be several independent variables, but only one dependent variable.

Which of the following variables is categorical?

Gender

Influential observations always:

None of the above are correct.

The multiple regression equation based on the sample data, which has the form of y=b0..+bpxp , is called:

an estimated multiple regression equation.

When working with regression analysis, an outlier is:

any observation that does not fit the trend shown by the remaining data.

Suppose a residual plot of x verses the residuals, y - ŷ, shows a nonconstant variance. In particular, as the values of x increase, suppose that the values of the residuals also increase. This means that:

as the values of x get larger, the ability to predict y becomes less accurate.

When we use the estimated regression equation to develop an interval that can be used to predict the mean for ALL units that meet a particular set of given criteria, that interval is called a(n):

confidence interval.

In regression analysis, the variable that is being predicted is the:

dependent variable.

A variable used to model the effect of categorical independent variables is called a(n):

dummy variable.

The term in the multiple regression model that accounts for the variability in y that cannot be explained by the linear effect of the p independent variables is the:

error term,E

The model developed from sample data that has the form y= bo+b1x is known as the:

estimated regression equation.

In general, R2 always _____ as independent variables are added to the regression model.

increases

In a multiple regression model, the values of the error term, ε, are assumed to be:

independent of each other.

The tests of significance in regression analysis are based on assumptions about the error term ɛ. One such assumption is that the values of ɛ are:

independent.

When we conduct significance tests for a multiple regression relationship, the t test can be conducted for each of the independent variables in the model. Each of those tests are called tests for:

individual significance.

An observation that has a strong influence or effect on the regression results is called a(n):

influential observation.

If a categorical variable has k levels, then:

k - 1 dummy variables are needed.

Larger values of r2 imply that the observations are more closely grouped about the:

least squares line.

The method used to develop the estimated regression equation that minimizes the sum of squared residuals is called the:

least squares method.

The tests of significance in regression analysis are based on several assumptions about the error term ɛ. Additionally, we make an assumption about the form of the relationship between x and y. We assume that the relationship between x and y is:

linear.

The term used to describe the case when the independent variables in a multiple regression model are correlated is:

multicollinearity.

The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is called the:

multiple coefficient of determination.

The study of how a dependent variable y is related to two or more independent variables is called:

multiple regression analysis.

When constructing a confidence or a prediction interval to quantify the relationship between two quantitative variables, the appropriate degrees of freedom are:

n - 2.

All things held constant, which interval will be wider: a confidence interval or a prediction interval?

prediction interval

When studying the relationship between two quantitative variables, whenever we want to predict an individual value of y for a new observation corresponding to a given value of x, we should use a(n):

prediction interval.

When we use the estimated regression equation to develop an interval that can be used to predict the mean for a specific unit that meets a particular set of given criteria, that interval is called a(n):

prediction interval.

The mathematical equation relating the independent variable to the expected value of the dependent variable, E(y)= Bo+B1x , is known as the:

regression equation.

In regression analysis, the equation in the form y = 𝛽0 + 𝛽1x + ε is called the:

regression model.

Dummy variables must always have:

values of either 0 or 1.

In a regression analysis, the error term ε is a random variable with a mean or expected value of

zero.