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Q:
In regression model: , then the value of y is expected to increase with x until x reaches a certain point after which the value of y is expected to decrease.
Q:
Interaction terms and polynomial terms should not be included in the same multiple regression model.
Q:
A multiple regression model of the form = B0+ B1x + B2x2 + B3x3+ ε is called an expanded second-order polynomial since it contains all the terms up to x3in the model at one time.
Q:
In curvilinear regression modeling, a composite model is one that contains either the basic terms or the interactive terms but not both.
Q:
In a second-order polynomial regression model, the regression coefficient, B2, will be positive if the parabola opens downward and negative when the parabola opens upward.
Q:
A multiple regression model of the form is called a second-degree polynomial model.
Q:
The following output is for a second-order polynomial regression model where the independent variables are x and x2(x^2 in output). Some of the output has been omitted.Considering the above information, it is clear that the second-order polynomial model will be a more effective regression model for explaining the variation in the y variable than would a linear regression model involving only one independent variable, x.
Q:
If a polynomial model has a larger R-square than a linear model for the same set of data, this is one indication that the polynomial model fits the data better than the linear model.
Q:
When a regression equation includes a term such as x1x2where two independent variables are multiplied, this is an interaction term.
Q:
Consider the following scatter plot:Given the apparent relationship between the x and y variable, a possible curvilinear regression model to consider would be a second-order polynomial model.
Q:
If one independent variable affects the relationship between a second independent variable and the dependent variable, it is said that there is interaction between the two independent variables.
Q:
Consider the following regression model: , then the parabola will open downward and if B2< 0, then the parabola will open downward.
Q:
A complete polynomial model contains terms of all orders less than or equal to the pthorder.
Q:
A regression model of the form: = B0+ B1x1+ B2+ B3+ ε is called a 3rdorder polynomial model.
Q:
To describe variable credit status that has three levels: Excellent, Good, and Poor, we need to use two different dummy variables.
Q:
If given a choice in collecting data on age for use as an independent variable in a regression model, a decision maker would generally prefer to record the actual age rather than an age category so as to avoid using dummy variables.
Q:
You should not include more than one categorical variable in a multiple regression because the use of two or more will cause misleading results.
Q:
In a study of employees at a local company, the human resource manager wants to develop a multiple regression model to explain the difference in employee wage rates. She is thinking of including a variable, degree status, in which the following categories exist: no degree, H.S. degree, junior college degree, bachelor degree, graduate degree. Two other variables are being considered; Age and Years With the Company. Given this, the appropriate number of variables in the model will be six.
Q:
A regression equation that predicts the price of homes in thousands of dollars is = 24.6 + 0.055x1 - 3.6x2, where x2is a dummy variable that represents whether the house is on a busy street or not. Here
x2= 1 means the house is on a busy street and x2= 0 means it is not. From this we can conclude that on average homes that are on busy streets are worth $3600 more than homes that are not on busy streets.
Q:
A study has recently been conducted by a major computer magazine publisher in which the objective was to develop a multiple regression model to explain the variation in price of personal computers. Three quantitative independent variables were used along with one qualitative variable. The qualitative variable was coded 1 if the computer included a monitor, 0 otherwise. The following computer printout shows the final output.Based on this information, given the other variables in the model, whether or not a monitor is included has a significant impact on the price of the personal computer.
Q:
Consider the following regression equation: = 356 + 180x1- 2.5x2. The x1variable is a quantitative variable and the x2variable is a dummy with values 1 and 0. Given this, we can interpret the slope coefficient on variable x2 as follows: Holding x1constant, if the value of x2 is changed from 0 to 1, the average value of y will decrease by 2.5 units.
Q:
On a survey there is a question that asks whether someone lives in a house, apartment, or condominium. These three responses could be coded in a dummy variable using value 0, 1, and 2.
Q:
One of the variables that are being considered for inclusion in a multiple regression model is marital status of the customer. There are four possible responses listed for this variable. Based on this, four dummy variables will need to be created and incorporated into the regression model.
Q:
The method used in regression analysis for incorporating a categorical variable into the model is by organizing the categorical variable into one or more dummy variables.
Q:
A dummy variable is a dependent variable whose value is set at either zero or one.
Q:
Models can be specified as linear or nonlinear.
Q:
A major car magazine has recently collected data on 30 leading cars in the U.S. market. It is interested in building a multiple regression model to explain the variation in highway miles. The following correlation matrix has been computed from the data collected: mileage, highwaymileage, cityCurb WeightcylindersHorsepowermileage, highway1 mileage, city0.8575505981 Curb Weight-0.739110566-0.707651041 cylinders-0.694837149-0.8661350560.5964757111 Horsepower-0.549172956-0.6841991970.2932023850.8403472191 The analysts also produced the following multiple regression output using curb weight, cylinders, and horsepower as the three independent variables. Note, a number of the output fields are missing, but can be determined from the information provided.Based on the information provided, the 95 percent confidence interval estimate for regression slope coefficient for horsepower is approximately - 0.041 to 0.009 and since this interval crosses zero, we are unable to conclude that the regression slope coefficient for this variable is different from zero.
Q:
The variance inflation factor (VIF) provides a measure for each independent variable of how much multicollinearity is associated with that particular independent variable.
Q:
In a multiple regression analysis with three independent variables the null hypothesis for conducting the test of the overall model is:
H0: β0= β1= β2= β3= 0.
Q:
The variance inflation factor is an indication of how much multicollinearity there is in the regression model.
Q:
If the R-square for a multiple regression model with two independent variables is .64, the correlation between the two independent variables will be .80
Q:
Based on the correlations below: Y X1
0.8 X2
0.7 we could say that x1accounts for 64 percent of the variation in y and x2accounts for 49 percent of the variation in y. So if both xs are included in a multiple regression model, then the resulting R-square = 1.13.
Q:
In a multiple regression model, the adjusted R-square value measures the explained variation in the dependent variable after taking into account the relationship between the sample size and the number of independent variables in the model.
Q:
When an independent variable, that has a positive correlation with the dependent variable, receives a negative slope in a multiple regression, this is probably caused by multicollinearity.
Q:
In a multiple regression model where three independent variables are included in the model, the percentage of explained variation will be equal to the square of the sum of the correlations between the independent variables and the dependent variable.
Q:
The adjusted R2value can be larger or smaller that the R2values depending on the data set.
Q:
If a decision maker has several potential independent variables to select from in building a regression model, the variable that, by itself, will always be the most effective in explaining the variation in the dependent variable will be the variable that has a correlation closest to positive 1.00.
Q:
A correlation matrix shows the correlation between each independent variable and the dependent variable but gives no information about the potential for multicollinearity problems.
Q:
In the model diagnosis step in regression modeling, we are interested in the sign and size of the regression slope coefficients.
Q:
The correlation matrix is an effective means of determining whether any of the independent variables has a curvilinear relationship with the dependent variable.
Q:
Multicollinearity occurs when one or more independent variables is highly correlated with the dependent variable.
Q:
A model is a representation of an actual system.
Q:
In simple linear regression analysis, the regression model forms a straight line in two-dimensional space through the x,y data points, while a multiple regression model forms a plane through multidimensional space.
Q:
In a multiple regression model, the regression coefficients are calculated such that the quantity, , is minimized.
Q:
In a multiple regression model, it is assumed that the errors or residuals are normally distributed.
Q:
The standard error of the estimate is a term that is used for the standard deviation of the residuals in a multiple regression model.
Q:
In conducting multiple regression analysis, t-tests should be conducted prior to conducting the F-test.
Q:
It is generally suggested that the sample size in developing a multiple regression model should be at least four times the number of independent variables.
Q:
Where there are two independent variables in a multiple regression, the regression equation forms a plane.
Q:
The three components of the regression model-building process are model specification, model fitting, and model diagnosis.
Q:
Residuals are calculated by e = y - .
Q:
In a multiple regression model, each regression slope coefficient measures the average change in the dependent variable for a one-unit change in the independent variable, all other variables held constant.
Q:
The multiple coefficient of determination measures the percentage of variation in the dependent variable that is explained by the independent variables in the model.
Q:
In multiple regression analysis, the model will be developed with one dependent variable and two or more independent variables.
Q:
The multiple coefficient of determination is the average of all the squared correlations of the independent variables.
Q:
In a multiple regression model, R-square can be computed by squaring the highest correlation coefficient between the dependent variable and any independent variable.
Q:
In multiple regression analysis, the residual is the absolute difference between the actual value of y and the predicted value of y.
Q:
The following multiple regression was conducted to attempt to predict the price of yachts based on the independent variables shown.Given this information and your knowledge of multiple regression, determine which, if any, of the four independent variables are statistically significant in explaining the variation in the dependent variable. Use a 0.05 level of significance and use the p-value method.
Q:
Explain the difference between forward stepwise regression (standard stepwise), forward selection, and all possible subsets regression approaches.
Q:
Based on the residual plot below, which of the following is correct?The above residual plot shows:A) linearity and nonconstant variance.B) nonlinearity and constant variance.C) linearity and constant variance.D) nonlinearity and nonconstant variance.
Q:
A standardized residual is:
A) equal to the sum of the residuals divided by n-1.
B) the ratio of each residual divided by an estimate for the standard deviation of the residuals.
D) None of the above
Answer: B
Q:
Consider the following residual plot.Given this plot, what conclusion should be reached?A) There appears to be no basis for concluding that the relationship between the x and y variable is not linear.B) The assumption of constant variance seems to be supported by this plot.C) Both A and B are true.D) Neither A nor B are true.
Q:
If the residuals have a constant variance, which of the following should be evident?
A) The residuals should have a variance equal to zero for all levels of the independent variable.
B) The plot of the residuals against each x variable should show that the spread in the residuals is about the same at all levels of each of the independent variables.
C) The average residual should be about zero and the residual standard deviation should be approximately 1.
D) None of the above
Q:
The assumption that the errors or residuals are independent is best checked by:
A) looking at a normal probability plot of the residuals.
B) looking a scatter plot of each x versus y.
C) looking at a residual plot versus x and checking for curvature.
D) looking at a plot of the residuals versus time and checking for trends.
Q:
To determine the aptness of the model, which of the following would most likely be performed?
A) Check to see whether the residuals have a constant variance
B) Determine whether the residuals are normally distributed
C) Check to determine whether the regression model meets the assumption of linearity
D) All of the above
Q:
The editors of a national automotive magazine recently studied 30 different automobiles sold in the United States with the intent of seeing whether they could develop a multiple regression model to explain the variation in highway miles per gallon. A number of different independent variables were collected. The following regression output is the result of using a forward selection stepwise regression approach.Which of the following might explain why no other independent variables entered the model?A) No other variable had a correlation with the dependent variable that was close to 1.0.B) None of the remaining variables had a positive correlation with y.C) The remaining variables must be nearly perfectly correlated with the two variables already in the model.D) Given the two variables already in the model, none of the others could add significantly to the percentage of variation in the y variable that would be explained by the model.
Q:
Which of the following is an advantage of using stepwise regression compared to just entering all the independent variables at one time?
A) Stepwise will generally produce a model with a larger R-square value.
B) The standard error of the estimate for a model constructed with stepwise regression will be larger than the one generated when all variables are entered at the same time.
C) The stepwise regression allows the decision maker to observe the effects of multicollinearity more easily than when all the variables are entered at one time.
D) There are no advantages of using stepwise regression over entering all variables at one time.
Q:
Which of the following is the difference between forward selection and standard stepwise regression?
A) In the standard stepwise regression, variables that were added at earlier steps can be removed at later steps, which is not the case with forward selection.
B) The standard stepwise approach will generally produce a regression model with a higher R-square value than the forward selection approach.
C) Forward selection begins by selecting the variable with the highest correlation with the dependent variable and then proceeds to select subsequent variables in order of their F-to-enter value, while standard stepwise selects the variables in the order specified by the decision maker and then removes them from the model as needed.
D) There are no appreciable differences between the two methods, just different names for the same technique.
Q:
A decision maker has five potential independent variables with which to build a regression model to explain the variation in the dependent variable. At step 1, variable x3enters the regression model. Which of the following indicates which of the four remaining independent variables will be next to enter the model?
A) The variable that has the next highest correlation with the dependent variable
B) The variable that will provide the next largest value for the slope coefficient
C) The variable with the highest coefficient of partial determination
D) Can't be determined without seeing the correlation matrix.
Q:
Standard stepwise regression
A) is the same as forward selection.
B) involves trying more regressions that the best subsets method.
C) always finds the best regression model.
D) combines attributes of both forward selection and backward elimination.
Q:
Which of the following is not considered to be a stepwise regression technique?
A) Forward selection regression
B) Optimal variable entry and removal regression
C) Backward elimination
D) Standard stepwise regression
Q:
The following model:
y = β0 + β1x1 + β2x2 + β3x1x2+ ε
A) is a linear model with interaction.
B) is a second order polynomial model.
C) is a composite model.
D) is a convex model.
Q:
Second-order polynomial models:
A) always curve upward.
B) always curve downward.
C) can curve upward or downward depending on the data.
D) measure interaction between variables.
Q:
Interaction exists in a multiple regression model when:
A) one independent variable affects the relationship between another independent variable and the dependent variable.
B) multicollinearity is present in a regression model.
C) the regression model is overall insignificant.
D) a polynomial model used.
Q:
The following regression output is from a multiple regression model:The variables t, t2, and t3 represent the t, t-squared, and t-cubed respectively where t is the indicator of time from periods t = 1 to t = 20. Which of the following best describes the type of forecasting model that has been developed?A) A complete third-order polynomial modelB) A tri-variate smoothed regression modelC) A nonlinear trend modelD) A qualitative regression model
Q:
Assume that a time-series plot takes the form of that shown in the following graph:Given this plot, which of the following models would likely give the best fit?
Q:
Which of the following would best describe the situation that a second-degree polynomial regression equation would be used to model?
A) An exponential growth trend
B) A cosine function
C) A parabola
D) It depends on the number of independent variables.
Q:
A forecasting model of the following form was developed:Which of the following best describes the form of this model?A) Quadratic modelB) 3rddegree polynomial modelC) 3rdlevel regression modelD) Tri-slope regression model
Q:
In a multiple regression, the dependent variable is house value (in '000$) and one of the independent variables is a dummy variable, which is defined as 1 if a house has a garage and 0 if not. The coefficient of the dummy variable is found to be 5.4 but the t-test reveals that it is not significant at the 0.05 level. Which of the following is true?
A) A garage increases the house value by $5,400.
B) A garage increases the house value by $5,400, holding all other independent variables constant.
C) The house value remains the same with or without a garage.
D) We need to include other dummy variables.
Q:
A multiple regression was conducted to predict the price of yachts in thousands of dollars. A dummy variable was included to indicate whether or not the yacht has a flying bridge, where 0 means "no" and 1 means "yes."Which of the following statements is correct using the 0.10 level of significance?A) Having a flying bridge significantly increases the price of a yacht by an average of $17.7, given the other variables present.B) Having a flying bridge significantly increases the price of a yacht by an average of $17,708, given the other variables present.C) We can tell that 17 out of 20 yachts have a flying bridge.D) Whether or not the yacht has a flying bridge does not significantly affect the price of a yacht, given the other variables present.