Q&A Hero

Q: A useful method for determining whether a linear function is the appropriate function to describe the relationship between the x and y variable is a residual plot in which the residuals are plotted on the vertical axis and the independent variable is on the horizontal axis.

Q: When we say that we wish to determine the aptness of a regression model, we are actually saying that we wish to check to see whether the resulting model meets the basic assumptions of regression analysis.

Q: The best subsets method will involve trying fewer different regression models than stepwise regression.

Q: If a stepwise regression approach is used to enter, one at a time, four variables into a regression model, the resulting regression equation may differ from the regression equation that occurs when all four of the variables are entered at one step.

Q: Standard stepwise regression is a good way of identifying potential multicollinearity problems since we are able to see the impact on the model at each step that occurs when a new variable is added to the model. For instance, if bringing in a new variable causes the sign to change on a previously entered variable, we have evidence of multicollinearity.

Q: The forward selection method and the backward elimination method will always lead to choosing the same final regression model.

Q: One reason for examining the adjusted R-square value in a multiple regression analysis is that the R-square value will increase just by adding additional independent variables to the model, whereas the adjusted R-square accounts for the relationship between the number of independent variables and the sample size and may actually decline if inappropriate independent variables are included in the model.

Q: When the best subsets approach is used in a regression application, one method for determining which of the many possible models to select for potential use is called the Cp statistic.

Q: In the best subsets approach to regression analysis, if we start with 4 independent variables, a total of 33 different regression models will actually be computed for possible selection as the best model to use.

Q: It is possible for the standard error of the estimate to actually increase if variables are added to the model that do not aid in explaining the variation in the dependent variable.

Q: Standard stepwise regression combines attributes of both forward selection and backward elimination.

Q: In a forward stepwise regression process, it is actually possible for the R-square value to decline if variables are added to the regression model that do not help to explain the variation in the dependent variable.

Q: Stepwise selection will always find the best regression model.

Q: In a forward selection stepwise regression process, the second variable to be selected from the list of potential independent variables is always the one that has the second highest correlation with the dependent variable.

Q: In a forward selection stepwise regression process, the first variable to be selected will be the variable that can, by itself, do the most to explain the variation in the dependent variable. This will be the variable that provided the highest possible R-square value by itself.

Q: A decision maker is considering constructing a multiple regression model with two independent variables. The correlation between x1 and y is 0.70, and the correlation between variable x2 and y is 0.50. Based on this, the regression model containing both independent variables will explain 74 percent of the variation in the dependent variable.

Q: Stepwise regression is the approach that is always taken when developing a regression model to fit a curvilinear relationship between the dependent and potential independent variables.

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 + is called an expanded second-order polynomial since it contains all the terms up to x3 in 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: 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, both independent variables in the model are considered statistically significant at the alpha = 0.05 level.

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: 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, the model explains approximately 56.7 percent of the variation in the y variable.

Q: When a regression equation includes a term such as x1x2 where 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:. If B2 > 0, 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 pth order.

Q: A regression model of the form: is called a 3rd order 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: 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. One appropriate approach for including this variable is to code the categories 1, 2, 3, 4, and 5.

Q: A regression equation that predicts the price of homes in thousands of dollars is = 24.6 + 0.055x1 - 3.6x2, where x2 is 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: 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, it is possible to determine that 4 of the PCs in the data set did not have a monitor included.

Q: Consider the following regression equation: = 356 + 180x1 - 2.5x2. The x1 variable is a quantitative variable and the x2 variable is a dummy with values 1 and 0. Given this, we can interpret the slope coefficient on variable x2 as follows: Holding x1 constant, 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, highway mileage, city Curb Weight cylinders Horsepower mileage, highway 1 mileage, city 0.857550598 1 Curb Weight -0.739110566 -0.70765104 1 cylinders -0.694837149 -0.866135056 0.596475711 1 Horsepower -0.549172956 -0.684199197 0.293202385 0.840347219 1 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: 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, highway mileage, city Curb Weight cylinders Horsepower mileage, highway 1 mileage, city 0.857550598 1 Curb Weight -0.739110566 -0.70765104 1 cylinders -0.694837149 -0.866135056 0.596475711 1 Horsepower -0.549172956 -0.684199197 0.293202385 0.840347219 1 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, using a 0.05 level of statistical significance, both curb weight and horsepower are statistically significant variables in explaining the variation in the dependent variable when they are included in the model along with cylinders.

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 correltion matrix has been computed from the data collected: mileage, highway mileage, city Curb Weight cylinders Horsepower mileage, highway 1 mileage, city 0.857550598 1 Curb Weight -0.739110566 -0.70765104 1 cylinders -0.694837149 -0.866135056 0.596475711 1 Horsepower -0.549172956 -0.684199197 0.293202385 0.840347219 1 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, holding the other variables constant, increasing horsepower by one unit results in an average decrease in highway mileage by 0.016 miles per gallon.

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, highway mileage, city Curb Weight cylinders Horsepower mileage, highway 1 mileage, city 0.857550598 1 Curb Weight -0.739110566 -0.70765104 1 cylinders -0.694837149 -0.866135056 0.596475711 1 Horsepower -0.549172956 -0.684199197 0.293202385 0.840347219 1 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 above information, the test statistic for testing whether the overall model is statistically significant is approximately F = 17.4

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-0.549172956-0.6841991970.2932023850.8403472191The 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.If the analysts are interested in testing whether the overall regression model is statistically significant, the appropriate null and alternative hypotheses are:

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, highway mileage, city Curb Weight cylinders Horsepower mileage, highway 1 mileage, city 0.857550598 1 Curb Weight -0.739110566 -0.70765104 1 cylinders -0.694837149 -0.866135056 0.596475711 1 Horsepower -0.549172956 -0.684199197 0.293202385 0.840347219 1 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 this information, the standard error of the estimate for the regression model is approximately 6.46 miles per gallon.

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: 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 independent variables were used. The following computer printout shows the final output. However, several values are omitted from the printout. Given this information, using an alpha = .05 level, you can conclude that the overall regression model is statistically significant.

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 independent variables were used. The following computer printout shows the final output. However, several values are omitted from the printout. Given this information, the calculated test statistic for the regression slope coefficient on the variable RAM, is approximately 1.54.

Q: In a multiple regression analysis with three independent variables the null hypothesis for conducting the test of the overall model is:

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 independent variables were used. The following computer printout shows the final output. However, several values are omitted from the printout. Given this information, the regression model explains just under 70 percent of the variation in the price of personal computers.

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 x1 accounts for 64 percent of the variation in y and x2 accounts 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: 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, highway mileage, city Curb Weight cylinders Horsepower mileage, highway 1 mileage, city 0.857550598 1 Curb Weight -0.739110566 -0.70765104 1 cylinders -0.694837149 -0.866135056 0.596475711 1 Horsepower -0.549172956 -0.684199197 0.293202385 0.840347219 1 The analysts also produced the following multiple regression output using curb weight, cylinders, and horsepower as the three independent variables. Note that a number of the output fields are missing, but can be determined from the information provided. Based on the information provided, the three independent variables explain approximately 67 percent of the variation in the highway mileage among these 30 cars.

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: 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, highway mileage, city Curb Weight cylinders Horsepower mileage, highway 1 mileage, city 0.857550598 1 Curb Weight -0.739110566 -0.70765104 1 cylinders -0.694837149 -0.866135056 0.596475711 1 Horsepower -0.549172956 -0.684199197 0.293202385 0.840347219 1 If the independent variables, curb weight, cylinders, and horsepower are used together in a multiple regression model, there may be a potential problem with multicollinearity since horsepower and cylinders are highly correlated.

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, highway mileage, city Curb Weight cylinders Horsepower mileage, highway 1 mileage, city 0.857550598 1 Curb Weight -0.739110566 -0.70765104 1 cylinders -0.694837149 -0.866135056 0.596475711 1 Horsepower -0.549172956 -0.684199197 0.293202385 0.840347219 1 If only one independent variable (ignoring city mileage) is to be used in explaining the dependent variable in a regression model, the percentage of variation that will be explained will be nearly 74 percent.

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, highway mileage, city Curb Weight cylinders Horsepower mileage, highway 1 mileage, city 0.857550598 1 Curb Weight -0.739110566 -0.70765104 1 cylinders -0.694837149 -0.866135056 0.596475711 1 Horsepower -0.549172956 -0.684199197 0.293202385 0.840347219 1 Based on this information, if we test using a 0.05 level of significance, the critical value for testing whether any of the independent variables are significantly correlated with the dependent variable is t = 2.0484.

Q: The adjusted R2 value can be larger or smaller that the R2 values 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.