HBX Business Analytics Exam | Verified Exam Questions and Answers |
Latest Updated Study Material 2026
Question:
A/B test
Answer:
An experiment that compares the value of a specified
dependent variable (such as the likelihood that a web site visitor purchases an item) across two
different groups (usually a control group and a treatment group). The members of each group
must be randomly selected to ensure that the only difference between the groups is the
"manipulated" independent variable (for example, the size of the font on two otherwise-identical
web sites). An A/B test is a hypothesis test that tests whether the means of the dependent variable
are the same across the two groups. (An A/B test can also be used to test whether another
parameter, such a standard deviation, is the same across two groups.)
Question:
adjusted R-squared
Answer:
A measure of the explanatory power of a
regression analysis. Adjusted R-squared is equal to R-squared multiplied by an adjustment factor
that decreases slightly as each independent variable is added to a regression model. Unlike R-
squared, which can never decrease when a new independent variable is added to a regression
model, Adjusted R-squared drops when an independent variable is added that does not improve
the model's true explanatory power. Adjusted R2 should always be used when comparing the
explanatory power of regression models that have different numbers of independent variables.
Question:
alternative hypothesis
Answer:
An alternative hypothesis is the theory or
claim we are trying to substantiate, and is stated as the opposite of a null hypothesis. When our
data allow us to nullify the null hypothesis, we substantiate the alternative hypothesis.
Question:
asymmetric distribution
Answer:
A probability distribution that is not
,symmetric around the mean.
Question:
base case
Answer:
The category of a categorical variable for which a
dummy variable is NOT included in a regression model. A regression model with a categorical
variable that has n categories should have n-1 dummy variables. The coefficients of the dummy
variables included in the regression model are interpreted in relation to the base case. The analyst
can select any category to be excluded from the regression model; however, different base cases
lead to different interpretations of the dummy variables' coefficients. For example, suppose we
are trying to determine the average difference in height between men and women in a sample,
Question:
and suppose that on average men are 5 inches taller than women in the sample. If we use Female
as the base case then the coefficient for the dummy variable for Male would be +5. If we use
Male as the base case, the coefficient for the dummy variable for Female would be -5.
bias
Answer:
The tendency of a measurement process to over- or under-
estimate the value of a population parameter. Although a sample statistic will almost always
differ from the population parameter, for an unbiased sample, the difference will be random. In
contrast, for a biased sample, the statistic will differ in a systematic way (e.g., tend to be too
high). Some common reasons for bias include non-random sampling methods and non-neutral
question phrasing.
Question:
biased sample
Answer:
A sample that is not representative of the
population from which it is collected. Sampling practices that can introduce bias include poorly
phrased survey questions and non-random sampling.
Question:
bimodal distribution
Answer:
A multi-modal distribution with two
clearly discernable peaks. The two peaks may be of the same height (that is, have equal
, frequency), or one may be the true mode while the other has a very high (but not the highest)
frequency.
Question:
bin
Answer:
A range of values used to categorize data. In a histogram,
observations are divided into a set of non-overlapping bins, each corresponding to a range of
values. The bins are constructed to ensure that the set of bins contains all observations in the data
set. The height of the bar corresponding to a bin is equal to the number of observations in the
data set that fall within that bin's range. Typically, all bins in a given histogram are the same
width (i.e., the difference between the largest value and the smallest value is the same for each
bin). In an Excel histogram, each bin is labeled by the value of the upper boundary of the bin's
range. For example, in a histogram with three bins (each of width 1), labeled 1, 2, and 3, the bin
labeled 2 contains all observations greater than 1 and less than or equal to 2. See histogram.
Question:
binomial distribution
Answer:
A distribution of the possible successful
outcomes in a given number of trials, where there are only two possible outcomes for each trial,
and each trial has the same probability of success (e.g., flipping a coin). For example, the
binomial distribution for the number of "heads" that result from flipping a coin 50 times specifies
the probability for each possible outcome, from observing 0 "heads" to observing 50 "heads".
The binomial distribution is used to create confidence intervals for proportions.
Question:
Central Limit Theorem
Answer:
A theorem stating that if we take
sufficiently large randomly-selected samples from a population, the means of these samples will
be normally distributed regardless of the shape of the underlying population. (Technically, the
underlying population must have a finite variance.)
Question:
coefficient of variation (CV)
Answer:
A measure of a data set's
variability relative to its mean. The coefficient of variation (CV) is particularly helpful when
Latest Updated Study Material 2026
Question:
A/B test
Answer:
An experiment that compares the value of a specified
dependent variable (such as the likelihood that a web site visitor purchases an item) across two
different groups (usually a control group and a treatment group). The members of each group
must be randomly selected to ensure that the only difference between the groups is the
"manipulated" independent variable (for example, the size of the font on two otherwise-identical
web sites). An A/B test is a hypothesis test that tests whether the means of the dependent variable
are the same across the two groups. (An A/B test can also be used to test whether another
parameter, such a standard deviation, is the same across two groups.)
Question:
adjusted R-squared
Answer:
A measure of the explanatory power of a
regression analysis. Adjusted R-squared is equal to R-squared multiplied by an adjustment factor
that decreases slightly as each independent variable is added to a regression model. Unlike R-
squared, which can never decrease when a new independent variable is added to a regression
model, Adjusted R-squared drops when an independent variable is added that does not improve
the model's true explanatory power. Adjusted R2 should always be used when comparing the
explanatory power of regression models that have different numbers of independent variables.
Question:
alternative hypothesis
Answer:
An alternative hypothesis is the theory or
claim we are trying to substantiate, and is stated as the opposite of a null hypothesis. When our
data allow us to nullify the null hypothesis, we substantiate the alternative hypothesis.
Question:
asymmetric distribution
Answer:
A probability distribution that is not
,symmetric around the mean.
Question:
base case
Answer:
The category of a categorical variable for which a
dummy variable is NOT included in a regression model. A regression model with a categorical
variable that has n categories should have n-1 dummy variables. The coefficients of the dummy
variables included in the regression model are interpreted in relation to the base case. The analyst
can select any category to be excluded from the regression model; however, different base cases
lead to different interpretations of the dummy variables' coefficients. For example, suppose we
are trying to determine the average difference in height between men and women in a sample,
Question:
and suppose that on average men are 5 inches taller than women in the sample. If we use Female
as the base case then the coefficient for the dummy variable for Male would be +5. If we use
Male as the base case, the coefficient for the dummy variable for Female would be -5.
bias
Answer:
The tendency of a measurement process to over- or under-
estimate the value of a population parameter. Although a sample statistic will almost always
differ from the population parameter, for an unbiased sample, the difference will be random. In
contrast, for a biased sample, the statistic will differ in a systematic way (e.g., tend to be too
high). Some common reasons for bias include non-random sampling methods and non-neutral
question phrasing.
Question:
biased sample
Answer:
A sample that is not representative of the
population from which it is collected. Sampling practices that can introduce bias include poorly
phrased survey questions and non-random sampling.
Question:
bimodal distribution
Answer:
A multi-modal distribution with two
clearly discernable peaks. The two peaks may be of the same height (that is, have equal
, frequency), or one may be the true mode while the other has a very high (but not the highest)
frequency.
Question:
bin
Answer:
A range of values used to categorize data. In a histogram,
observations are divided into a set of non-overlapping bins, each corresponding to a range of
values. The bins are constructed to ensure that the set of bins contains all observations in the data
set. The height of the bar corresponding to a bin is equal to the number of observations in the
data set that fall within that bin's range. Typically, all bins in a given histogram are the same
width (i.e., the difference between the largest value and the smallest value is the same for each
bin). In an Excel histogram, each bin is labeled by the value of the upper boundary of the bin's
range. For example, in a histogram with three bins (each of width 1), labeled 1, 2, and 3, the bin
labeled 2 contains all observations greater than 1 and less than or equal to 2. See histogram.
Question:
binomial distribution
Answer:
A distribution of the possible successful
outcomes in a given number of trials, where there are only two possible outcomes for each trial,
and each trial has the same probability of success (e.g., flipping a coin). For example, the
binomial distribution for the number of "heads" that result from flipping a coin 50 times specifies
the probability for each possible outcome, from observing 0 "heads" to observing 50 "heads".
The binomial distribution is used to create confidence intervals for proportions.
Question:
Central Limit Theorem
Answer:
A theorem stating that if we take
sufficiently large randomly-selected samples from a population, the means of these samples will
be normally distributed regardless of the shape of the underlying population. (Technically, the
underlying population must have a finite variance.)
Question:
coefficient of variation (CV)
Answer:
A measure of a data set's
variability relative to its mean. The coefficient of variation (CV) is particularly helpful when
