QA 2 Final

In the general multiple regression equation, which of the following variables represents the Y-intercept?

"a"

independent variable

(X) provides the basis for estimation, the predictor variable

dependent variable

(Y) the variable being predicted or estimated

coefficient of determination

(r squared) a measure of the amount of variation in the dependent variable about its mean that is explained by the regression equation

Moderate correlation range

0.26-0.50

strong positive correlation range

0.51 - 0.75

The coefficient of determination is the square root of the coefficient of correlation.

False

The multiple coefficient of determination, R2, reports the proportion of the variation in Y that is not explained by the variation in the set of independent variables

False

The strength of the correlation between two variables depends on the sign of the coefficient of correlation.

False

Interaction occurs when the relationship between an independent variable and a dependent variable is affected by another independent variable.

True

Stepwise regression analysis is a method that assists in selecting the most significant variables for a multiple regression equation

True

scatter diagram

a graph that shows the degree and direction of relationship between two variables

standard error of estimate

a measure of the accuracy of predictions made with a regression line

In the regression equation, what does the letter "a" represent?

y-intercept

What is the chart called when the paired data (the dependent and independent variables) are plotted?

a scatter diagram

What is the general form of the regression equation?

y=a+(bx)

global test

used to investigate whether any of the independent variables have significant coefficients

When does multicollinearity occur in a multiple regression analysis?

when the independent variables are highly correlated

Which value of r indicates a stronger correlation than 0.40?

-.80

What is the range of values for a coefficient of correlation?

-1 to 1 inclusive

Multicollinearity

-exists when independent variables (X's) are correlated -makes it difficult to make inferences about the individual regression coefficients and their effects on the dependent variable (Y). -Do not affect a multiple regression equation's ability to predict the dependent variable

coefficient of correlation

-measures the strength of the linear relationship between x and y -"r" must be between -1 and 1 where -1 and +1 indicates perfect inverse and perfect direct linear relationships -0 indicates no linear relationship

individual regression coefficient test

-used to determine which independent variables have nonzero regression coefficients -variables with zero regression coefficients are usually dropped

What does the coefficient of determination equal if r = 0.89?

.7921

If all the plots on a scatter diagram lie on a straight line, what is the standard error of estimate?

0

What is the range of values for the coefficient of determination?

0% to 100% inclusive

When expressed as a percentage, what is the range of values for multiple R2?

0% to 100% inclusive

Weak correlation range

0-0.25

very strong correlation range

0.76-1.00

stepwise regression

1. Correlation Matrix 2. Regression 3. Global Test 4. Test of Hypotheses 5. Run regression again 6. Write your new regression equation 7. Examine residual charts 8. Examine normal probability plot

If the coefficient of multiple determination is 0.81, what percent of variation is not explained?

19%

Given the least squares regression equation, Ŷ = 1,202 + 1,133X, when X = 3, what does Ŷ equal?

4601

If the coefficient of determination is 0.94, what can we say about the relationship between two variables?

94% of the variation of the dependent variable is explained by the independent variable

Approximately ________% of the observations lies within two standard errors of the regression line. Enter the number

95

correlation analysis

A measure that depicts the strength and nature of the relationship between two variables

Least Squares Principle

Determining a regression equation by minimizing the sum of the squares of the vertical distances between the actual Y values and the predicted values of Y.

An example of a dummy variable is "time to product's first repair" in years

False

In multiple regression analysis, a residual is the difference between the value of an independent variable and its corresponding dependent variable value.

False

In regression analysis, error is defined as .

False

Multiple regression analysis is used when one independent variable is used to predict values of two or more dependent variables.

False

One assumption underlying linear regression is that the X values are normally distributed.

False

Stepwise regression analysis involves removing all of the independent variables at once whose p-values are not less than alpha.

False

A correlation matrix can be used to assess multicollinearity between independent variables.

True

A correlation matrix shows individual correlation coefficients for all pairs of variables.

True

A scatter diagram is a graph that portrays the correlation between a dependent variable and an independent variable.

True

An economist is interested in predicting the unemployment rate based on gross domestic product. Since the economist is interested in predicting unemployment, the independent variable is gross domestic product

True

Because the coefficient of determination is expressed as a percent, its value is between 0% and 100%.

True

Correlation analysis is a statistical technique used to measure the strength of the relationship between two variables.

True

In multiple regression analysis, an F-statistic is used to test the global hypothesis, H0: All Bi=0

True

The coefficient of determination is the proportion of total variation in Y that is explained by X.

True

The least squares technique minimizes the sum of the squares of the vertical distances between the actual Y values and the predicted values of Y.

True

The regression equation is used to estimate a value of the dependent variable Y based on a selected value of the independent variable X.

True

The values of a and b in the regression equation are called the regression coefficients.

True

regression analysis

Use X to estimate Y -relationship is linear -both variables must be at least in interval scale -the least squares principle is used to determine the equation

In multiple regression analysis, testing the global null hypothesis that all regression coefficients are zero is based on ________.

a F statistic

In multiple regression analysis, how is the degree of association between a set of independent variables and a dependent variable measured?

a coefficient of multiple determination

spurious correlation

accident, an apparent but false relationship between two (or more) variables that is caused by some other variable

Which of the following are true assumptions underlying linear regression? (1) For each value of X, there is a group of Y values that is normally distributed. (2) The means of these normal distributions of Y values all lie on the regression line. (3) The standard deviations of these normal distributions are equal.

all of these are correct

In the regression equation, what does the letter "Y" represent?

dependent variable

In regression analysis, what is the predictor variable called?

independent variable

In the regression equation, what does the letter "X" represent?

independent variable

Which of the following is true about the standard error of estimate?

is a measure of the accuracy of the prediction

regression equation

models a linear relationship between two variables

inverse relationship

number is negative; a relationship in which one variable decreases when another variable increases

direct relationship

number is positive; a relationship in which one variable increases with an increase in another variable

Based on the regression equation, we can ________

predict the value of the dependent variable given a value of the independent variable

If there are four independent variables in a multiple regression equation, there are also four ________.

regression coefficients

To evaluate the assumption of linearity, a multiple regression analysis should include ________.

scatter diagrams of the dependent variable plotted as a function of each independent variable

If the correlation between two variables is close to one, the association between the variables is ________.

strong

What is the test statistic to test the significance of the slope in a regression equation?

t-statistic

What does a coefficient of correlation of 0.70 infer?

the coefficient of determination is .49

residual

the difference between an observed y-value and its predicted y-value on a regression line

A valid multiple regression analysis assumes or requires that ________.

the independent variables and the dependent variable have a linear relationship

In the regression equation, what does the letter "b" represent?

the slope of the line

If the correlation coefficient between two variables, X and Y, equals zero, what can be said of the variables X and Y?

the variables are not related

In multiple regression analysis, residual analysis is used to test the requirement that ________.

the variation in the residuals is the same for all predicted values of Y