Deck 15: Multiple Regression Analysis and Model Building

Question 1

The correlation matrix is an effective means of determining whether any of the independent variables has a curvilinear relationship with the dependent variable.

Answer 1

False

Question 2

The multiple coefficient of determination is the average of all the squared correlations of the independent variables.

Answer 2

False

Question 3

In multiple regression analysis,the model will be developed with one dependent variable and two or more independent variables.

Answer 3

True

Question 4

In multiple regression analysis,the residual is the absolute difference between the actual value of y and the predicted value of y.

Question 5

In a multiple regression model,R-square can be computed by squaring the highest correlation coefficient between the dependent variable and any independent variable.

Question 6

Multicollinearity occurs when one or more independent variables is highly correlated with the dependent variable.

Question 7

In a multiple regression model,it is assumed that the errors or residuals are normally distributed.

Question 8

The three components of the regression model building process are model specification,model fitting,and model diagnosis.

Question 9

In a multiple regression model,the regression slope coefficients measure the average change in the dependent variable for a one-unit change in the independent variable,all other variables held constant.

Question 10

The standard error of the estimate is a term that is used for the standard deviation of the residuals in a multiple regression model.

Question 11

In a multiple regression model,the regression coefficients are calculated such that the quantity, ,is minimized.

Question 12

In conducting multiple regression analysis,t-tests should be conducted prior to conducting the F-test.

Question 13

A correlation matrix shows the correlation between each independent variable and the dependent variable but gives no information about the potential for multicollinearity problems.

Question 14

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.

Question 15

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.

Question 16

Residuals are calculated by e = y - .

Question 17

Where there are two independent variables in a multiple regression,the regression equation forms a plane.

Question 18

In the model diagnosis step in regression modeling,we are interested in the sign and size of the regression slope coefficients.

Question 19

The multiple coefficient of determination measures the percentage of variation in the dependent variable that is explained by the independent variables in the model.

Question 20

A model is a representation of an actual system.

Question 21

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.

Question 22

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.

Question 23

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.

Question 24

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.

Question 25

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: 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 = 17.45.

Question 26

The variance inflation factor (VIF)provides a measure for each independent variable of how much multicollinearity is associated with that particular independent variable.

Question 27

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: 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.

Question 28

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: 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.

Question 29

The adjusted R² value can be larger or smaller that the R² values depending on the data set.

Question 30

The variance inflation factor is an indication of how much multicollinearity there is in the regression model.

Question 31

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.

Question 32

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.

Question 33

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: 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.

Question 34

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: 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.

Question 35

In a multiple regression analysis with three independent variables the null hypothesis for conducting the test of the overall model is:
H_o : β₀ = β₁ = β₂ = β₃ = 0.

Question 36

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: 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.

Question 37

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 x's are included in a multiple regression model,then the resulting R-square = 1.13.

Question 38

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

Question 39

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.

Question 40

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.

Question 41

A dummy variable is a dependent variable whose value is set at either zero or one.

Question 42

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: 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.

Question 43

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.

Question 44

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.

Question 45

A regression model of the form: = + + + + is called a 3^rd order polynomial model.

Question 46

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: 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.

Question 47

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.

Question 48

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.

Question 49

To describe variable credit status that has three levels: Excellent,Good,and Poor,we need to use two different dummy variables.

Question 50

Models can be specified as linear or nonlinear.

Question 51

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.

Question 52

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.

Question 53

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.

Question 54

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.

Question 55

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 PC's in the data set did not have a monitor included.

Question 56

You should not include more than one categorical variable in a multiple regression because the use of two or more will cause misleading results.

Question 57

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.

Question 58

Consider the following regression model: = B₀ + B₁x₁ + + ε.If B₂ > 0,then the parabola will open downward and if B₂ < 0,then the parabola will open downward.

Question 59

A complete polynomial model contains terms of all orders less than or equal to the p^th order.

Question 60

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: 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 DASH 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.

Question 61

Stepwise selection will always find the best regression model.

Question 62

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.

Question 63

The following output is for a second-order polynomial regression model where the independent variables are x and x² (x^2).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.

Question 64

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.

Question 65

Interaction terms and polynomial terms should not be included in the same multiple regression model.

Question 66

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.

Question 67

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.

Question 68

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.

Question 69

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.

Question 70

In regression model: y = β₀ + β₁x₁ + + ε ,if β₂ < 0,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.

Question 71

The following output is for a second-order polynomial regression model where the independent variables are x and x² (x^2).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.

Question 72

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 x³ in the model at one time.

Question 73

When a regression equation includes a term such as x₁x₂ where two independent variables are multiplied,this is an interaction term.

Question 74

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.

Question 75

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.

Question 76

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.

Question 77

In curvilinear regression modeling,a composite model is one that contains either the basic terms or the interactive terms but not both.

Question 78

The following output is for a second-order polynomial regression model where the independent variables are x and x² (x^2).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.

Question 79

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

Question 80

A multiple regression model of the form = B₀ + B₁x + B₂x² + ε is called a second-degree polynomial model.