Exam 4: Regression Models

When the significance level is small enough in the F-test, we can reject the null hypothesis that there is no linear relationship.

List the four assumptions of the regression model.

A large school district is reevaluating its teachers' salaries. They have decided to use regression analysis to predict mean teacher salaries at each elementary school. The research has come up with the following prediction equation: Y = $18012.24 + 1432.37X₁ - 4.07 X₂ where X₁ = Yrs Exp and X₂ = Yrs Exp² (a) If a teacher has 7 years of experience, what is the expected salary? (b) If teacher has 10 years of experience, what is the expected salary?

In regression, the X variable is known as the ________ variable.

Another name for a dummy variable is a binary variable.

Consider the regression model Y = 389.10 - 14.6X. If the r² value is 0.657, what is the correlation coefficient?

With a nonlinear relationship, a ________ is necessary to turn a nonlinear model into a linear model.

The value of r² can never decrease when more variables are added to the model.

Error is the difference in the actual value and the predicted value.

What can be said about a correlation coefficient of +1?

In a good regression model the residual plot shows

A prediction equation for starting salaries (in $1,000s) and SAT scores was performed using simple linear regression. In the regression printout shown below, what can be said about the level of significance for the overall model?

The ________ indicates how much total variability in Y is explained by the regression model.

Errors are also called residuals.

What can be said about a correlation coefficient of -1?

Bob White is conducting research on monthly expenses for medical care, including over the counter medicine. His dependent variable is monthly expenses for medical care while his independent variables are number of family members and insurance type (government funded, private insurance and other). He has coded insurance type as the following: X₂ = 1 if government funded, X₃ = 1 if private insurance Below is his Excel output. (a) What is the prediction equation? (b) Based on the significance F-test, is this model a good prediction equation? (c) What percent of the variation in medical expenses is explained by the independent variables? (d) Based on his model, what are the predicted monthly expenses for a family of four with private insurance? (e) Based on his model, what are the predicted monthly expenses for a family of two with government funded insurance? (f) Based on his model, what are the predicted monthly expenses for a family of five with no insurance?

A large international sales organization has collected data on the number of employees and the annual gross sales during the last 7 years. (a) Develop a scatter diagram. (b) Determine the correlation coefficient. (c) Determine the coefficient of determination. (d) Determine the least squares trend line. (e) Determine the predicted value of sales for 2100 employees.

The errors in a regression model are assumed to have an increasing mean.

What is the formula for r²?

Summing the error values in a regression model is misleading because negative errors cancel out positive errors.