OSM 202

If the simple correlation coefficient between two independent variables is greater than .90, then ______________________ is considered to be severe.

multicollinearity

Dependent (or response variable) variable

variable we wish to understand or predict

The range for r^2 is between 0 and 1, and the range for r is between

−1 and 1

The range of feasible values for the multiple coefficient of determination is from

0 to 1

A multiple regression analysis with 20 observations on each of three independent variables and the dependent variable would yield ______ and _______ degrees of freedom, respectively, for regression (explaineD) and error.

3 and 16

If it is desired to include marital status in a multiple regression model by using the categories single, married, separated, divorced, and widowed, what will be the effect on the model?

Four more independent variables will be included.

Regression analysis

a statistical technique that uses observed data to relate the dependent variable to one or more independent variables

The ____________________ is the proportion of the total variation in the dependent variable explained by the regression model.

coefficient of determination

When the constant variance assumption holds, a plot of the residual versus x

forms a horizontal band pattern

In a multiple regression model, the residuals were plotted against the values of one of the independent variables. The plot exhibited a funneling out pattern of residuals. This means that as the value of the independent variable increases, the error terms tend to ___________ and the model assumption of __________ is violated.

increase, constant variance

The following results were obtained as part of a simple regression analysis. r^2 = .9162 F statistic from F table = 3.59 Calculated value of F from the ANOVA table = 81.87 α = .05 p-value = .000 The null hypothesis of no linear relationship between the dependent variable and the independent variable

is rejected

The _________ regression method is used when the response variable is a qualitative or a categorical variable.

logistic

An investigator hired by a client suing for sex discrimination has developed a multiple regression model for employee salaries for the company in question. In this multiple regression model, the salaries are in thousands of dollars. For example, a data entry of 35 for the dependent variable indicates a salary of $35,000. The indicator (dummy) variable for gender is coded as X1 = 0 if male and X1 = 1 if female. The computer output of this multiple regression model shows that the coefficient for this variable (X1) is −4.2. The t test showed that X1 was significant at α= 0.1. This result implies that for male and female workers of the company,

on the average, females earn $4,200 less.

β0 and β1 are called

regression parameters

In simple regression analysis, the quantity that gives the amount by which Y (dependent variable) changes for a unit change in X (independent variable) is called the

slope of the regression line

After plotting the data points on a scatter diagram, we have observed an inverse relationship between the independent variable (X) and the dependent variable (Y). Therefore, we can expect both the sample ___________ and the sample _____________ to be negative values.

slope, correlation coefficient

The least squares regression line minimizes the sum of the

squared differences between actual and predicted Y values

The _____ distribution is used for testing the significance of the slope term.

t

In simple regression analysis, the sum of (y_hat -y_bar)^2 is called

the explained sum of squares

Independent (or predictor) variable

the variable we will use to understand or predict the dependent variable