Question 1

The range of values in which we can be confident that the true regression coefficient lies within a given degree of probability is called a:

Accepted Answer

A confidence interval is a statistical range of values that includes the true value of the population parameter with a given probability. In regression analysis, we use confidence intervals to estimate the range of values for a regression coefficient that is likely to include the true population parameter. A prediction interval, on the other hand, is a range of values that predicts the value of a future observation or outcome with a given degree of probability. Logistic regression is a type of regression analysis used for modeling binary outcomes.

Question 2

When using expert opinion,consumer surveys,test marketing,and price experiments to analyze consumer behavior,managers must consider whether the answers given in these formats represent actual market behavior.

Accepted Answer

While these methods can provide valuable insights into consumer behavior, the answers given may not always accurately reflect actual market behavior. Therefore, managers must use these tools in conjunction with other data and make informed decisions based on a comprehensive analysis.

Question 3

Scenario 1: The demand model relating the quantity of good XYZ sold (QXYZ)to the price of good (PXYZ)is reported below:
 
-Refer to Scenario 1.Is the slope coefficient statistically different from zero?

Accepted Answer

The answer of Scenario 1: The demand model relating the...

Question 4

An estimated regression coefficient is 10 with a standard error of 5.The null hypothesis is that the partial regression coefficient equals zero.What is the value of the t-statistic for testing the null hypothesis of the regression coefficient?

Accepted Answer

The t-statistic is calculated as the estimated coefficient divided by the standard error, which is 10 / 5 = 2.

Question 5

In a multiple regression problem involving two independent variables,if b₁ is computed to be +2.0,it means that:

Accepted Answer

A coefficient of +2.0 for variable X₁ in a multiple regression problem means that the estimated value of Y increases by an average of 2 units for each increase of 1 unit of X₁, holding X₂ constant. This assumes that X₂ has no effect on the relationship between X₁ and Y.

Question 6

The F-statistic is an alternative measure of goodness-of-fit of an estimated regression equation and defined as the:

Accepted Answer

The F-statistic measures the ratio of the variation explained by the regression equation to the variation not explained, which is the opposite of option A. Therefore, the correct option is B.

Question 7

Scenario 1: The demand model relating the quantity of good XYZ sold (QXYZ)to the price of good (PXYZ)is reported below:
 
-Refer to Scenario 1.What is the total sum of squares?

Accepted Answer

The total sum of squares (SST) is the sum of the squared differences between each observation and the overall mean. In this scenario, the correct value is 3860.8.

Question 8

The total sum of squares is 400 and the sum of squares errors is 100,what is the coefficient of determination?

Accepted Answer

The coefficient of determination, denoted by R^2, is calculated as 1 - (SSE/SST), where SSE is the sum of squares errors and SST is the total sum of squares. Therefore, R^2 = 1 - (100/400) = 0.75, which is choice B.

Question 9

Scenario 1: The demand model relating the quantity of good XYZ sold (QXYZ)to the price of good (PXYZ)is reported below:
 
-Refer to Scenario 1.What is the t-statistic for the slope coefficient?

Accepted Answer

The answer of Scenario 1: The demand model relating the...

Question 10

Scenario 1: The demand model relating the quantity of good XYZ sold (QXYZ)to the price of good (PXYZ)is reported below:
 
-Refer to Scenario 1.What is the coefficient of determination?

Accepted Answer

The coefficient of determination, often denoted as R^2, measures the proportion of the variance in the dependent variable that is predictable from the independent variable(s). A value of 0.037 suggests that 3.7% of the variance in the dependent variable can be explained by the model, indicating a very weak explanatory power.

Question 11

The coefficient of determination will range between what values?

Accepted Answer

The coefficient of determination, also known as R-squared, is a measure of how well the regression line fits the data. It ranges from 0 to 1, where 0 represents no linear relationship between the variables and 1 represents a perfect linear relationship. Therefore, the correct option is A. B is incorrect because the range -1 to 1 is for the correlation coefficient, not the coefficient of determination. C is incorrect because coefficient of determination can never be negative, let alone range between -3 and +3.

Question 12

The coefficient of determination is .90,the number of observations is 30,and a multiple regression model using 2 independent variables is estimated.What is the value of the adjusted coefficient of determination?

Accepted Answer

The adjusted coefficient of determination formula is:
Adjusted R-squared = 1 - [(1 - R-squared) * (n - 1) / (n - k - 1)]
where R-squared is the coefficient of determination, n is the number of observations, and k is the number of independent variables.

Substituting the given values, we get:
Adjusted R-squared = 1 - [(1 - 0.90) * (30 - 1) / (30 - 2 - 1)]
Adjusted R-squared = 1 - (0.10 * 29 / 27)
Adjusted R-squared = 1 - 0.1074
Adjusted R-squared = 0.8926

Therefore, the answer is A) .8926 as it is the correct value of the adjusted coefficient of determination.

Question 13

An estimated regression coefficient is 10 with a standard error of 5.The null hypothesis is that the partial regression coefficient equals one.What is the value of the t-statistic for testing the null hypothesis of the regression coefficient?

Accepted Answer

The t-statistic can be calculated as (estimated coefficient - hypothesized value of the coefficient) / standard error of the estimated coefficient. 
In this case, the estimated coefficient is 10 and the hypothesized value is 1, so the numerator of the t-statistic is 9. 
Dividing 9 by 5 (the standard error) gives a t-statistic of 1.8.

Question 14

Reliance on expert opinion to predict consumer behavior has the advantage of being a relatively low cost approach to gathering information.In many situations,however,it is subject to several sources of bias that can undermine its reliability.

Accepted Answer

Expert opinion may be biased by the expert's own experiences, opinions, and assumptions, as well as by the specific context in which the opinion is given. Therefore, while reliance on expert opinion can provide some information about consumer behavior, it should be supplemented by other sources of data to ensure accuracy and reduce bias.

Question 15

When using expert opinion,consumer surveys,test marketing,and price experiments to analyze consumer behavior,managers must consider how to isolate the effect of different variables that influence demand.

Accepted Answer

Managers must consider how to isolate the effect of different variables that influence demand when using expert opinion, consumer surveys, test marketing, and price experiments to analyze consumer behavior. This is because there are multiple factors that can influence demand, and it is important to identify which variables are impacting consumer behavior the most.

Question 16

Conjoint analysis employs an approach to consumer behavior that is similar to the economic indifference curve model.

Accepted Answer

Conjoint analysis, like the economic indifference curve model, seeks to understand consumer preferences and trade-offs through the use of hypothetical scenarios and attribute-based analysis. Therefore, the statement is true.

Question 17

A constant-elasticity demand function can be obtained by:

Accepted Answer

A constant-elasticity demand function can be obtained by taking the logarithm of both the dependent and independent variables. This is because the elasticity of demand is equal to the coefficient on the independent variable in the logarithmic form of the demand function. Thus, taking the logarithm of both variables creates a linear relationship with a constant elasticity.

Question 18

The estimated regression equation is Y = 10 + 2.5X,if X =0 than the predicted value of Y is equal to:

Accepted Answer

The estimated regression equation Y = 10 + 2.5X predicts Y = 10 when X = 0, because substituting X = 0 gives Y = 10 + 2.5(0) = 10.

Question 19

Given the demand function in log-linear form: Q = 120 - 1.5P + 12ADV where Q = quantity,P = price,and ADV = advertising expenditures,what is the price elasticity?

Accepted Answer

To calculate the price elasticity, we need to take the derivative of the demand function with respect to price (P) and multiply it by P/Q. Taking the derivative of the demand function, we get:

dQ/dP = -1.5

Multiplying by P/Q, we get:

(P/Q)dQ/dP = (-1.5)(P/Q)

Using the midpoint formula, we can rewrite this as:

(P2 - P1) / [(P1 + P2)/2] / (Q2 - Q1) / [(Q1 + Q2)/2] = (-1.5)(P/Q)

Since we do not have specific values for P and Q, we cannot solve for the price elasticity exactly. However, we can determine that the price elasticity is negative (since the derivative is negative) and greater than 1 (since the absolute value of the derivative is greater than 1. This means that demand is elastic with respect to price. The correct answer is therefore B.

Question 20

When using expert opinion,consumer surveys,test marketing,and price experiments to analyze consumer behavior,managers must consider whether the participating groups are representative of the larger population.

Accepted Answer

Managers need to make sure that the groups participating in these analyses are representative of the larger population to ensure accurate and reliable results. Otherwise, the conclusions drawn from the analysis may be biased or incomplete.

Quiz 4: Techniques for Understanding Consumer Demand and Behavior