Chapter 4
The adjusted r2 will always increase as additional variables are added to the model.
FALSE
The multiple regression model includes several dependent variables.
FALSE
The multiple regression model includes several intercept terms.
FALSE
The null hypothesis in the F-test is that there is a linear relationship between the X and Y variables.
FALSE
Suppose that you believe that a cubic relationship exists between the independent variable (of time) and the dependent variable Y. Which of the following would represent a valid linear regression model? A) Y = b0 + b1 X, where X = time3 B) Y = b0 + b1 X3, where X = time C) Y = b0 + 3b1 X, where X = time3 D) Y = b0 + 3b1 X, where X = time E) Y = b0 + b1 X, where X = time1/3
A
The sum of the squares total (SST) A) measures the total variability in Y about the mean. B) measures the total variability in X about the mean. C) measures the variability in Y about the regression line. D) measures the variability in X about the regression line. E) indicates how much of the total variability in Y is explained by the regression model.
A
Which of the following is an assumption of the regression model? A) The errors are independent. B) The errors are not normally distributed. C) The errors have a standard deviation of zero. D) The errors have an irregular variance. E) The errors follow a cone pattern.
A
The random error in a regression equation A) is the predicted error. B) includes both positive and negative terms. C) will sum to a large positive number. D) is used to estimate the accuracy of the slope. E) is maximized in a least squares regression model.
B
Which of the following statements is true regarding a scatter diagram? A) It provides very little information about the relationship between the regression variables. B) It is a plot of the independent and dependent variables. C) It is a line chart of the independent and dependent variables. D) It has a value between -1 and +1. E) It gives the percent of variation in the dependent variable that is explained by the independent variable.
B
Which of the following statements is/are not true about regression models? A) Estimates of the slope are found from sample data. B) The regression line minimizes the sum of the squared errors. C) The error is found by subtracting the actual data value from the predicted data value. D) The dependent variable is the explanatory variable. E) The intercept coefficient is not typically interpreted.
C, D
Which of the following conditions can be detected from residual analysis? A) Nonlinearity Nonconstant variance B) Multicollinearity C) A and B D) A, B, and C
D
Which of the following is true regarding a regression model with multicollinearity, a high r2 value, and a low F-test significance level? A) The model is not a good prediction model. B) The high value of r2 is due to the multicollinearity. C) The interpretation of the coefficients is valuable. D) The significance level tests for the coefficients are not valid. E) The significance level for the F-test is not valid.
D
Estimates of the slope, intercept, and error of a regression model are found from sample data.
FALSE
If the assumptions of regression have been met, errors plotted against the independent variable will typically show patterns.
FALSE
If the significance level for the F-test is high enough, there is a relationship between the dependent and independent variables.
FALSE
In a scatter diagram, the dependent variable is typically plotted on the horizontal axis.
FALSE
In regression, a dependent variable is sometimes called a predictor variable.
FALSE
In regression, an independent variable is sometimes called a response variable.
FALSE
In regression, there is random error that can be predicted.
FALSE
If multicollinearity exists, then individual interpretation of the variables is questionable, but the overall model is still good for prediction purposes.
TRUE
Summing the error values in a regression model is misleading because negative errors cancel out positive errors.
TRUE
The regression line minimizes the sum of the squared errors.
TRUE
The variable to be predicted is the dependent variable.
TRUE