Week 12-13 Review Reading

True or false: R2 can decrease as we add more predictor variables to the linear regression model

False

Select all that apply: Often it is more in-formative to provide a range of values—an interval—rather than a single point estimate for the unknown population parameter. What two terms are used for this range of values called?

- Interval estimate - Confidence interval

Select all that apply Which of the following is true regarding the graph depicting the normal probability density function f(x)?

- Is symmetric around the mean - Is often referred to as the bell curve - Is often referred to as the normal curve

Select all that apply: Scores on a management aptitude examination are normally distributed with a mean of 72 and a standard deviation of 8.We want to find the lowest score that will place a manager in the top 10% (90th percentile) of the distribution. Which of the following is true to solve this problem?

- The 90th percentile is a numerical value x such that P(X < x) = 0.90 - z = 1.28 - a score of 82.24 or higher will place a manager in the top 10% of the distribution

Select all that apply: What is used to evaluate how well the sample regression equation fits the data?

- The coefficient of determination, R² - The standard error of the estimate

What is used to evaluate how well the sample regression equation fits the data?

- The coefficient of determination, R² - The standard error of the estimate

Select all that apply: In order to avoid the possibility of R2 creating a false impression, virtually all software packages include adjusted R2. Unlike R2, adjusted R2 explicitly accounts for what?

- The number of predictor variables k - The sample size n

Select all that apply: Which of the following are the two defining properties of probability?

- The probability of any event A is a value between 0 and 1; that is, 0 ≤ P(A) ≤ 1. - The sum of the probabilities of any list of mutually exclusive and exhaustive events equals 1.

In order to select the preferred model, we examine several goodness-of-fit measures: Select all goodness-of-fit measures examined!

- The standard error of the estimate - The coefficient of determination - The adjusted coefficient of determination

For the 99% confidence interval, what is α/2?

.005

The z value associated with a probability of .5040 is '_____'

.01

An economist predicts a 70% chance that country A will perform poorly and a 35% chance that country B will perform poorly. There is also a 20% chance that both countries will perform poorly. What is the probability that country A performs poorly given that country B performs poorly?

.20/.35 =.57

Johnny feels that he has a 85% chance of getting an A in Marketing and a 45% chance of getting an A in Managerial Economics. He also believes he has a 35% chance of getting an A in both classes.What is the probability that he gets an A in at least one of these courses?

.95

MC: Suppose we want to find the value tα,dftα,df with α = 0.10 and df = 10; that is, t0.10,10t0.10,10. Using Table 5.2, The value X suggests that P(T10T10 ≥ x) = 0.10; what is X?

1.372

'_____' theorem uses the total probability rule to update the probability of an event that has been affected by a new piece of evidence

Bayes'

The degrees of freedom determine the extent of the broadness of the tails of the distribution; If there are fewer degrees of freedom, the tail of the distribution is more:

Broad

Are the following examples; the return on a mutual fund, time to completion of a task, or the volume of beer sold as 16 ounces, examples of continuous or discrete random variables?

Continuous

A simple probability distribution for a continuous random variable is called the:

Continuous uniform distribution

If the value of the response variable is uniquely determined by the values of the predictor variables, we say that the relationship between the variables is: (Choose the correct response)

Deterministic

A '_____' random variable assumes a countable number of distinct values such as x1, x2, x3, and so on

Discrete

What type of variable assumes a countable number of distinct values such as x1, x2, x3, and so on?

Discrete

If the linear regression model includes an intercept, the number of dummy variables representing a categorical variable should be one less than the number of categories of the variable. This solution helps avoid which problem?

Dummy variable trap

What do we refer to events which include all outcomes in the sample space?

Exhaustive

True or false: A discrete random variable is characterized by uncountable values, whereas a continuous random variable assumes a countable number of distinct values.

False

In the case of a dummy variable categorizing a person's gender, we can define 1 for male and 0 for female. In this case, what would the reference category be?

Female

What are some measures that summarize how well the sample regression equation fits the data?

Goodness-of-fit

Two events are '_____' if the occurrence of one event does not affect the probability of the occurrence of the other event.

Independent

A simple linear regression model and is represented as y = β0 + β1x1 + ɛ,; What do β0and β1 (the Greek letters read as betas) represent? (They must be shown in the correct order!)

Intercept, slope

When comparing models with the same response variable, we prefer the model with a smaller se. A smaller se implies that there is '_____' dispersion of the observed values from the predicted values.

Less

A manager believes that 20% of consumers will respond positively to the firm's social media campaign. Also, 24% of those who respond positively will become loyal customers. Find the probability that the next recipient of their social media campaign will react positively and will become a loyal customer?

P(R ∩ L) =P(L∣R)P(R) = 0.24 × 0.20 =.048

Scores on a management aptitude exam are normally distributed with a mean of 72 and a standard deviation of 8. If we are trying to find the probability that a randomly selected manager will score above 75, what is the corresponding Z value?

P(Z >.375) P(Z>75−72875−728=P(Z >.375)

There is only one population, but many possible samples of a given size can be drawn from the population. Which of the following is a constant, even though its value may be unknown?

Population Parameter

On the basis of new information, we update the prior probability to arrive at a conditional probability called a '_____' probability.

Posterior

The original probability is an unconditional probability called a '_____' probability, in the sense that it reflects only what we know now before the arrival of any new information.

Prior

Instead of se2,we generally report the standard deviation of the residual, denoted se, more commonly referred to as

The standard error of the estimate

What is the probability theory rule that is a tool for breaking the computation of a probability into distinct cases?

Total probability rule

We use analysis of variance (ANOVA) in the context of the linear regression model to derive R2.We denote the total variation in y as Σ(yi−y ̄)2, which is the numerator in the formula for the variance of y. What is this total variation called?

Total sum of squares

We cannot describe the possible values of a '_____' random variable X with a list x1, x2,... because the value (x1 + x2)/2, not in the list, might also be possible

continuous

A standard normal table, also referred to as the z-table, provides what information that is under the z curve?

probabilities

Match each probability concept with its definition: probability: experiment: sample space:

probability --> a numerical value that measures the likelihood that an event occurs. experiment --> a process that leads to one of several possible outcomes. sample space --> contains all possible outcomes of the experiment.

Which of the following defines a probability that is based on an individual's personal judgment or experience?

subjective probability