Deck 9: Multiple Regression: Modeling Multivariate Relationships

Question 1

One limitation to regression is that,due to latent variables,it is hard to know what variable should predict what.

Answer 1

True
A latent variable gives rise to two (or more)others that lack an otherwise causal relationship.This leads to mistakenly basing predictions on the wrong variable.

Question 2

Regression is the dominant method of data analysis throughout the natural and social sciences.

Answer 2

True
Regression is the most commonly used method of data analysis.

Question 3

Although regression can verify a relationship between variables,it cannot quantify the nature of that relationship.

Answer 3

False
One of the primary advantages of regression is that it can verify and quantify relationships.

Question 4

A histogram will show if the data points are normally distributed.

Question 5

The Breusch-Pagan test detects whether data is normally distributed.

Question 6

Autocorrelation occurs when the error does not have a constant variance.

Question 7

Nonlinear relationships can be examine with ordinary linear regression through transformation functions such as logs,exponents,squares,square roots,and polynomials.

Question 8

All regression models,including simple linear,binary,ordinal,multinomial logit,rank-ordered,and count,can be viewed as special cases of the general formulation called the General Linear Model.

Question 9

Standardized residuals are useful in seeing whether there are any strong outliers.

Question 10

In regression analysis,the F-test tells you if all of the variables taken together help explain the variation in the dependent variable.

Question 11

Substantial autocorrelation within data can be corrected for with myriad techniques,such as transformations and dummy variables.It should therefore not call into question the regression model itself.

Question 12

Regression,as a general method,is so versatile,through transformations and special cases,that it can never be overused.

Question 13

Each independent coefficient ( $\beta$ )in a regression model will show the impact on the dependent variable of a one-unit change in the corresponding independent variable,if all of the other variables are held constant.

Question 14

One of the limitations of regression is that it can be used only for linear relationships.

Question 15

The problem with heteroscedasticity is that researchers tend to be underconfident,i.e.they must make statements as if the data is worse than it actually is.

Question 16

Regression presumes the following theoretical model for the population:
$$Y = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \ldots + \beta _ { k } X _ { k } + \varepsilon$$
where Y is the dependent variable,the Xs are the independent variables,the ?s are the coefficients of the independent variables,and ? is the error.

Question 17

Of the two main methods underlying nearly all of mathematical reasoning,statistics (particularly regression)is used when dealing with quantities that are certain.

Question 18

One way to correct for heteroscedasticity is to transform either the independent variables or the dependent variable using logarithms.

Question 19

The t-test is the first thing that should be checked in a regression output.If it is not significant,then the entire model is not providing sufficient explanatory power.

Question 20

is the form of a geometric relationship.

Question 21

_______________ occurs when the error does not have a constant variance.

A) Non-normality
B) Heteroscedasticity
C) Autocorrelation
D) Multicollinearity

Question 22

The best way to see if heteroscedasticity is present is to

A) plot the residuals against the dependent variables and examine at them
B) plot the residuals against each of the independent variables and examine them
C) use the Kolmogorov-Smirnov or Shapiro-Wilk test supplied in most computer statistical programs
D) apply a logarithmic transformation

Question 23

Polynomial regression is a robust method that should be among the first transformations to try on nonlinear data.

Question 24

All of the following statements about regression are true except:

A) Regression is a way to put a line through a group of data points.
B) Regression is a method for testing the validity of relationships.
C) Regression is method of verifying causal relationships.
D) Regression is a flexible methodology for measuring how things influence one another.

Question 25

For multiple linear regression,researchers want to examine the r² instead of the adjusted r² because the r² is not as easily fooled by additional independent variables.

Question 26

Due to assumptions in linear regression about the distribution and mean of the error,the only population parameter that will need to be estimated to understand the extent of error is the

A) autocorrelation of the error
B) standard deviation of the error
C) coefficient of determination
D) coefficient of variation

Question 27

Predicting one dependent variable based on many independent variables is called

A) simple linear regression
B) bivariate regression
C) multiple regression
D) multinomial regression

Question 28

For linear regression,the assumption is made that the error term is

A) normally distributed with a mean of 1
B) normally distributed with a mean of 0
C) the sum of the standard deviations of all of the $\beta$ values
D) the sum-of-squares explained by the regression model

Question 29

To determine if the fit of a regression equation is larger than the error,the _______________ is used.

A) F-test
B) t-test
C) chi-square
D) significance level

Question 30

If the error for one data point can help predict the value of the error in nearby data points,then the problem is

A) non-normality
B) heteroscedasticity
C) autocorrelation
D) multicollinearity

Question 31

_______________ occurs when a number of potential predictors in a regression model are highly correlated.

A) Non-normality
B) Multicollinearity
C) Heteroscedasticity
D) Autocorrelation

Question 32

To determine if a regression model is useful,the

A) fit (or prediction) should be bigger, on average, than "error"
B) coefficients (the b's) should be clearly different from zero
C) p value should be greater than the F-test value
D) all of the above
E) both a and b

Question 33

Standardized residuals are used to determine if there are any potential outliers in the data.Data points that are greater that have residuals higher than _______________ in magnitude should be examined,unless the data set is very large.

A) 1
B) 3
C) 5
D) 10

Question 34

The value of r² will always increase when adding additional variables to a multiple linear regression equation.

Question 35

To determine if the regression coefficients (b's)in a regression model are significantly different from zero,the _______________ is used.

A) F-test
B) t-test
C) chi-square
D) significance level

Question 36

If the dependent variable is nominal data,then you would use Poisson regression for the regression analysis

Question 37

All of the following are limitations of regression except

A) regression assumptions are usually violated
B) almost nothing is really linear
C) latent variables may be present
D) insufficient predictor variables

Question 38

_______________ occurs when the error is not normally distributed.

A) Non-normality
B) Heteroscedasticity
C) Autocorrelation
D) Multicollinearity

Question 39

In binary regression,it would be inappropriate to put a line through the observations in a data plot,because the values of the independent variables can only be 0 or 1.

Question 40

Violating the underlying assumptions of regression can lead to all of the following problems except

A) non-normality
B) standardized residuals
C) heteroscedasticity
D) autocorrelation

Question 41

If the dependent variable is a nominal scale,then the proper regression model to use is

A) multinomial regression
B) probit model
C) ordered logit model
D) linear regression after a chi square transformation
E) count regression

Question 42

The model used most often in marketing that includes item-specific information is referred to as the

A) Gumbel Logit model (GLM)
B) Multinomial Logit model (MNL)
C) Guadagni & Little Logit model (GLLM)
D) Kaiser Probit model (KPM)

Question 43

Identifying nonlinear relationships between variables is accomplished by transforming one or more variables and then estimating the fit with

A) linear regression
B) curvilinear regression
C) multicollinearity analysis
D) a close examination of the residuals plot

Question 44

The error term in a binary regression using a logit model is assumed to be a

A) normal distribution
B) Gumbel distribution
C) bivariate distribution
D) Poisson distribution

Question 45

Use the regression output below to answer the following questions.

Which statistics should one look at to determine which of the independent variables are most significant in the regression?

A) r² and adj r²
B) sum of squares and F-test
C) F-test and p
D) t-test and p

Question 46

If the dependent variable is an ordinal scale,then the proper regression model to use is the

A) linear regression model with geometric transformation of the dependent variable
B) ordered probit model
C) ordered logit model
D) any of the above
E) either b or c

Question 47

Which list of common variables below would be examples of continuous data?

A) price, time, volume, length, sales
B) gender, coupon used, college degree, promotion (yes/no)
C) education level, age group, survey scale response (e.g., 1 to 7)
D) ethnic group, product category, SKU, payment method

Question 48

The test for autocorrelation is the

A) Durbin-Watson
B) Kolmogorov-Smirnov
C) Shapiro-Wilk
D) Anderson-Darling

Question 49

_______________ takes both binary and interval data and produces probabilities of an outcome,such as purchase probabilities and market share projections,as functions of the marketing mix.

A) The weighted least squares model
B) Logistic regression
C) The Breusch-Pagan model
D) The discrete choice model

Question 50

When using rank-ordered data,the regression model that will be used is the

A) multinomial logit regression model
B) discrete choice model
C) exploded logit regression model
D) ordered probit model

Question 51

Use the regression output below to answer the following questions.

Which variable(s)is/are (a)significant,strong predictor(s)of Weight in the regression above?

A) Age and Height
B) Gender only
C) Height only
D) Age, Height, Gender, MBA and Year
E) Height and Gender

Question 52

In multiple regression,the intercept is the value of Y when

A) all of the independent variables are 0
B) the dependent variables is 0
C) all of the significant independent variables are set to 1
D) all of the coefficients are set to 1

Question 53

Which list of common variables below would be examples of ordinal data?

A) price, time, volume, length, sales
B) gender, coupon used, college degree, promotion (yes/no)
C) education level, age group, survey scale response (e.g., 1 to 7)
D) ethnic group, product category, SKU, payment method

Question 54

If the dependent variable is count data,the regression model that will be used is the

A) multinomial logit regression model
B) discrete choice model
C) exploded logit regression model
D) Poisson regression model

Question 55

Use the regression output below to answer the following questions.

According to the regression output above,if Age is increased by one year,what will the impact be on Weight?

A) 0.660 lb. increase
B) 0.279 lb. increase
C) 2.363 lb. increase
D) cannot be determined

Question 56

In binary regression,probability data for predicting binary variables is transformed using

A) an exponential transformation
B) a geometric transformation
C) the logarithm of the odds
D) dummy variables

Question 57

If the dependent variable in a regression model is continuous interval data,the analysis should employ

A) multiple linear regression
B) binary regression
C) Poisson or count regression
D) multinomial regression
E) ordinal regression

Question 58

Use the regression output below to answer the following questions.

In using Poisson regression,the researcher also must know

A) both the observed count and the number of opportunities
B) the relative percentages of each outcome
C) the distribution of the population
D) both the variance and the population mean

Question 59

Use the regression output below to answer the following questions.

According to the regression output above,which of the following statements most accurately summarizes what can be said,for the entire population,about the weight of individuals with an MBA (MBA=1)versus the weight of individuals without an MBA (MBA=0)?

A) They weigh on average 3.122 pounds less than individuals who do not have an MBA.
B) They weigh on average 3.122 pounds more than individuals who do not have an MBA.
C) Their weights are roughly the same.
D) The variable is not a significant predictor, so, even though its coefficient estimate is -3.222, we cannot assume it has an impact on weight.

Question 60

Based on the binary regression output above,which of the independent variable(s)are significant predictors of Gender?

A) Age and Weight
B) Age and Height
C) Height and Weight
D) Age, Height and Weight
E) all of the variables are significant
F) none of the variables is significant

Question 61

Based on the output above,the LOGIT model correctly predicted the female gender

A) 87 percent of the time
B) 91.3 percent of the time
C) 89.5 percent of the time
D) cannot be determined

Question 62

Which independent variable is,taken by itself,the best predictor of Gender?

A) Age
B) Height
C) Weight
D) cannot be determined

Question 63

Use the regression output below to answer the following questions.

Given that Gender was coded female=0 and male=1,on the average,how much more do males weight than females,"correcting for" (i.e.,including the effects of)all the other variables in the regression?

Question 64

Describe the different types of analysis for the different data types of dependent variable.

Question 65

Use the regression output below to answer the following questions.
Lingar Reperaidion Anthyis: Dep Var $( X ) =$ Weight
$X = \{ A$ Ee, Gender, Heifht, MBA, $Y$ ear $\}$
$\begin{array}{||c|c|c|c|c|c|}\hline \text { Coefficients } & \boldsymbol{b} & \begin{array}{c}\text { Std. } \\\text { Error }\end{array} & \begin{array}{c}\text { Std. } \\\text { Beta }\end{array} & \begin{array}{c}\boldsymbol{t} \text {-test } \\\text { Statistic }\end{array} & \begin{array}{c}\boldsymbol{p} \text {-value } \\\text { Two Tailed }\end{array} \\\hline \text { Intercept } & -210.603 & 20.560 & & -10.243 & 0.0000 \\\hline \text { Age } & 0.660 & 0.279 & 0.101 & 2.363 & 0.0186 \\\hline \text { Gender } & 17.449 & 2.450 & 0.267 & 7.122 & 0.0000 \\\hline \text { Height } & 4.999 & 0.294 & 0.613 & 16.982 & 0.0000 \\\hline \text { MBA } & -3.122 & 3.063 & -0.043 & -1.019 & 0.3087 \\\hline \text { Year } & -0.111 & 0.507 & -0.006 & -0.218 & 0.8274 \\\hline\end{array}$
$\begin{array}{|c|c|c|c|c|}\hline \boldsymbol{r} & \boldsymbol{r}^{2} & \text { Adj. } \boldsymbol{r}^{2} & \mathrm{SE}(\mathrm{Reg}) & \boldsymbol{h} \\\hline 0.834 & 0.696 & 0.693 & 17.879 & 448 \\\hline \hline\end{array}$
$\begin{array}{|c|c|c|c|c|c|}\hline \begin{array}{c}\text { Source of } \\\text { Variation }\end{array} & \begin{array}{c}\text { Sum of } \\\text { Squares }\end{array} & \boldsymbol{d f} & \begin{array}{c}\text { Mean } \\\text { Squares }\end{array} & \begin{array}{c}\text { F-test } \\\text { Statistic }\end{array} & \begin{array}{c}\boldsymbol{p} \text {-value } \\\text { One Tailed }\end{array} \\\hline \text { Regression } & 323592.24 & 5 & 64718.4 & 202.471 & 0.0000 \\\hline \text { Error } & 141282.23 & 442 & 319.643 & & \\\hline \text { Total } & 464874.47 & 447 & & & \\\hline\end{array}$



-Write the regression equation for the regression output above.

Question 66

The regression output above indicates that a 1 inch increase in Height increases the chance a respondent is male by

A) 39.1 percent
B) 8.2 percent
C) 22.669 percent
D) 47.8 percent

Question 67

Describe what regression is and what it is used for.

Question 68

Use the regression output below to answer the following questions.

For each additional inch of Height,how much additional Weight would be added?

Question 69

Explain the problems of non-normality,heteroscedasticity,and autocorrelation and how researchers can detect each.

Question 70

Describe how transformations can be used to apply linear regression to nonlinear relationships.

Question 71

Discuss its limitations of regression.

Question 72

What does the Constant signify in this regression?

A) the probability of Gender=1 when no other variables are changed
B) the average age of males in the sample
C) the average age of females in the sample
D) It does not signify anything useful here.

Question 73

Use the regression output below to answer the following questions.
Lingar Reperaidion Anthyis: Dep Var $( X ) =$ Weight
$X = \{ A$ Ee, Gender, Heifht, MBA, $Y$ ear $\}$
$\begin{array}{||c|c|c|c|c|c|}\hline \text { Coefficients } & \boldsymbol{b} & \begin{array}{c}\text { Std. } \\\text { Error }\end{array} & \begin{array}{c}\text { Std. } \\\text { Beta }\end{array} & \begin{array}{c}\boldsymbol{t} \text {-test } \\\text { Statistic }\end{array} & \begin{array}{c}\boldsymbol{p} \text {-value } \\\text { Two Tailed }\end{array} \\\hline \text { Intercept } & -210.603 & 20.560 & & -10.243 & 0.0000 \\\hline \text { Age } & 0.660 & 0.279 & 0.101 & 2.363 & 0.0186 \\\hline \text { Gender } & 17.449 & 2.450 & 0.267 & 7.122 & 0.0000 \\\hline \text { Height } & 4.999 & 0.294 & 0.613 & 16.982 & 0.0000 \\\hline \text { MBA } & -3.122 & 3.063 & -0.043 & -1.019 & 0.3087 \\\hline \text { Year } & -0.111 & 0.507 & -0.006 & -0.218 & 0.8274 \\\hline\end{array}$
$\begin{array}{|c|c|c|c|c|}\hline \boldsymbol{r} & \boldsymbol{r}^{2} & \text { Adj. } \boldsymbol{r}^{2} & \mathrm{SE}(\mathrm{Reg}) & \boldsymbol{h} \\\hline 0.834 & 0.696 & 0.693 & 17.879 & 448 \\\hline \hline\end{array}$
$\begin{array}{|c|c|c|c|c|c|}\hline \begin{array}{c}\text { Source of } \\\text { Variation }\end{array} & \begin{array}{c}\text { Sum of } \\\text { Squares }\end{array} & \boldsymbol{d f} & \begin{array}{c}\text { Mean } \\\text { Squares }\end{array} & \begin{array}{c}\text { F-test } \\\text { Statistic }\end{array} & \begin{array}{c}\boldsymbol{p} \text {-value } \\\text { One Tailed }\end{array} \\\hline \text { Regression } & 323592.24 & 5 & 64718.4 & 202.471 & 0.0000 \\\hline \text { Error } & 141282.23 & 442 & 319.643 & & \\\hline \text { Total } & 464874.47 & 447 & & & \\\hline\end{array}$



-Based on the regression printout,what would be the predicted (mean)weight of a female,20 years old,68 inches tall,without an MBA,and in Year 1.

Question 74

The regression output above indicates that an additional year in age increases the chance a respondent is male by

A) 11 percent
B) 17.1 percent
C) 0.61 percent
D) 15.8 percent