Question 1

Which of the following is an example of a time-series data set?
A)amount of labor employed in each factory in the U.S.in 2010
B)amount of labor employed yearly in a specific factory from 1990 through 2010
C)average amount of labor employed at specific times of the day at a specific factory in 2010
D)All of the above are time-series data sets.

Accepted Answer

A time-series data set involves data collected over time, usually at regular intervals. Option B provides data on the amount of labor employed yearly in a specific factory from 1990 through 2010, making it a clear example of a time-series data set. Option A provides data for a specific year, while option C provides data for specific times of the day, but neither of these is collected over time.

Question 2

If an analyst believes that more than one explanatory variable explains the variation in the dependent variable,what model should be used?
A)a simple linear regression model
B)a multiple regression model
C)a nonlinear regression model
D)a log-linear model

Accepted Answer

A multiple regression model should be used when there is more than one explanatory variable that explains the variation in the dependent variable.

Question 3

If the p-value is 10%,then the
A)level of significance is 10%.
B)level of confidence is 90%.
C)probability of a Type I error is 90%.
D)both a and b
E)null hypothesis should not be rejected if the level of significance is 5%

Accepted Answer

The null hypothesis should not be rejected if the level of significance is 5% because the p-value (10%) is greater than the significance level (5%).

Question 4

a linear regression equation of the form Y = a + bX,the slope parameter b shows
A)$\Delta$X / $\Delta$Y.
B)$\Delta$Y / $\Delta$X.
C)$\Delta$Y /$\Delta$b.
D)$\Delta$X / $\Delta$b.
E)none of the above

Accepted Answer

The slope parameter b represents the amount of change in the dependent variable Y for a unit change in the independent variable X. So, b can be calculated as the ratio of the change in Y to the change in X. Therefore, b = (ΔY)/(ΔX). This implies that the correct option is B, as the slope parameter b can be calculated as the ratio of the change in Y to the change in X.

Question 5

The quadratic equation Y = a + bX +cX² can be estimated using linear regression by estimating A)Y = a + bX + ZX where Z = c² B)Y = a + ZX where Z = (b + c) C)Y = a + bZ where Z = X² D)Y = a + ZX where Z = (b + c)² E)none of the above will work

Accepted Answer

The answer of The quadratic equation Y = a +...

Question 6

a linear regression equation Y = a + bX,the fitted or predicted value of Y is
A)the value of Y obtained by substituting specific values of X into the sample regression equation.
B)the value of X associated with a particular value of Y.
C)the value of X that the regression equation predicts.
D)the values of the parameters predicted by the estimators.
E)the value of Y associated with a particular value of X in the sample.

Accepted Answer

The fitted or predicted value of Y is obtained by substituting specific values of X into the sample regression equation. This is what the regression equation is designed to do - predict Y values based on measured X values.

Question 7

sample regression line
A)shows the actual (or true)relation between the dependent and independent variables.
B)is used to estimate the population regression line.
C)connects the data points in a sample.
D)is estimated by the population regression line.
E)maximizes the sum of the squared differences between the data points in a sample and the sample regression line.

Accepted Answer

A sample regression line is used to estimate the population regression line. It is not meant to show the actual relation between the dependent and independent variables, as that would be represented by the population regression line. The sample regression line connects the data points in a sample, but it does not necessarily maximize the sum of squared differences between the data points and the sample regression line. Therefore, B is the best choice.

Question 8

method of least squares
A)can be used to estimate the explanatory variables in a linear regression equation.
B)can be used to estimate the slope parameters of a linear equation.
C)minimizes the distance between the population regression line and the sample regression line.
D)all of the above

Accepted Answer

The method of least squares is primarily used to estimate the parameters (including the slope) of a linear regression model by minimizing the sum of the squares of the differences between the observed values and the values predicted by the model. Choices A and C describe concepts not directly related to the primary function of the method of least squares.

Question 9

Suppose you are testing the statistical significance (at the 5% significance level)of a parameter estimate from the regression equation: Y = a + bR + cS + dW Which is estimated using a time-series sample containing monthly observations over a 30-month time period.The critical value of the appropriate test statistic is A)t_critical = 2.042. B)t_critical = 2.056. C)F_critical = 4.22. D)F_critical = 7.76.

Accepted Answer

Since we are testing the significance of a single parameter estimate, we will use a t-test. With a sample size of 30 and a significance level of 5%, the critical value for a two-tailed test is t-critical = 2.042. Therefore, the answer is choice B as it is the closest option to the critical value of 2.042.

Question 10

To test whether the overall regression equation is statistically significant one uses A)the t-statistic. B)the R²-statistic. C)the F-statistic. D)the standard error statistic.

Accepted Answer

The F-statistic is used to test the overall significance of the regression equation. It compares the variance explained by the regression to the residual variance, and a significant F-statistic indicates that at least one of the independent variables has a significant relationship with the dependent variable.

Question 11

The critical value of t is the value that a t-statistic must exceed in order to
A)reject the hypothesis that the true value of a parameter equals zero.
B)accept the hypothesis that the estimated value of parameter equals the true value.
C)reject the hypothesis that the estimated value of the parameter equals the true value.
D)reject the hypothesis that the estimated value of the parameter exceeds the true value.

Accepted Answer

The critical value of t is used in hypothesis testing to determine whether to reject the null hypothesis, which states that the true value of a parameter equals zero. If the calculated t-statistic exceeds the critical value of t, then the null hypothesis can be rejected and it can be concluded that the true value of the parameter is not zero. Therefore, choice A is the correct answer.

Question 12

In the regression model $Y = a + b X + c Z$ ,a test of the hypothesis that parameter c equals zero is A)an F-test. B)an R²-test. C)a zero-statistic. D)a t-test. E)a Z-test.

Accepted Answer

A t-test is appropriate for testing the hypothesis that a single regression coefficient (in this case, c) equals zero. An F-test would be appropriate for testing multiple coefficients simultaneously, but that is not the case here. The other options (R²-test, zero-statistic, Z-test) are not tests commonly used in regression analysis.

Question 13

Tests for statistical significance must be performed
A)because the TRUE values of the intercept and slope parameters are random variables.
B)because the ESTIMATED values of the intercept and slope parameters are not,in general,equal to the true values of the intercept and slope parameters.
C)because the computed t-ratios are random variables and may be too large to provide evidence that b is not equal to zero.
D)in order to determine whether or not the parameter estimates are far enough away from zero to conclude that the true parameter values are not equal to zero.
E)both b and d

Accepted Answer

Both options B and D are reasons for performing hypothesis testing for statistical significance, therefore answer E is correct.

Question 14

Suppose you are testing the statistical significance (at the 1% significance level)of a parameter estimate from the regression model: M = a + bR + cI Which is estimated using a cross-section data set on 22 firms.The critical value of the appropriate test statistic is A)t_critical = 2.861. B)t_critical = -2.845. C)t_critical = 2.845. D)F_critical = 5.93. E)F_critical = 19.44.

Accepted Answer

The critical value for a t-test at the 1% significance level with a small sample size (such as 22 firms) would typically be looked up in a t-distribution table. Given the options, A) t_critical = 2.861 is the correct choice because it is a value from the t-distribution, which is used for testing the statistical significance of a parameter estimate in regression models. The other options either present values that are not typical for a t-distribution at this significance level and degrees of freedom (B and C), or refer to an F-distribution critical value (D and E), which is not appropriate for testing a single parameter estimate in regression analysis.

Question 15

a regression equation,the ______ captures the effects of factors that might influence the dependent variable but aren't used as explanatory variables.
A)intercept
B)slope parameter
C)R-square
D)random error term

Accepted Answer

The random error term captures the effects of all factors that influence the dependent variable but are not included in the explanatory variables explicitly. It is also known as the residual and represents the variation in the dependent variable that cannot be explained by the chosen explanatory variables.

Question 16

parameter estimate is said to be statistically significant if there is sufficient evidence that the
A)sample regression equals the population regression.
B)parameter estimated from the sample equals the true value of the parameter.
C)value of the t-ratio equals the critical value.
D)true value of the parameter does not equal zero.

Accepted Answer

A parameter estimate is said to be statistically significant if the true value of the parameter does not equal zero. This is because a null hypothesis test is conducted to determine whether the parameter is significantly different from zero. If the test yields a p-value that is lower than the significance level (usually 0.05), then there is sufficient evidence to reject the null hypothesis and conclude that the parameter is statistically significant. Therefore, option D is correct. The other options do not fully capture the concept of statistical significance.

Question 17

An estimator is unbiased if it produces
A)a parameter from the sample that equals the true parameter.
B)estimates of a parameter that are close to the true parameter.
C)estimates of a parameter that are statistically significant.
D)estimates of a parameter that are on average equal to the true parameter.
E)both b and c

Accepted Answer

An estimator is unbiased if its estimates of a parameter are on average equal to the true parameter. This means that if the estimator is used repeatedly to estimate the parameter, the average estimate will converge to the true parameter value. Being statistically significant (choice C) is not a requirement for unbiasedness, and choice A is not possible since a parameter is a fixed value and cannot be estimated from a sample. Choice B is a desirable property for any estimator but does not necessarily imply unbiasedness, and choice E is incorrect as well.

Question 18

In a multiple regression model,the coefficients on the independent variables measure
A)the percent of the variation in the dependent variable explained by a change in that independent variable,all other influences held constant.
B)the change in the dependent variable from a one-unit change in that independent variable,all other influences held constant.
C)the change in that independent variable from a one-unit change in the dependent variable,all other influences held constant.
D)the change in the dependent variable explained by the random error,all other influences held constant.

Accepted Answer

The coefficients in a multiple regression model represent the change in the dependent variable (y) for a one-unit change in the independent variable (x), holding all other independent variables constant. Therefore, choice B is the correct option. Choice A is incorrect because the coefficients do not represent the percent of variation explained by a change in the independent variable. Choice C is incorrect because it refers to the concept of inverse regression, where the roles of the dependent and independent variables are reversed. Choice D is incorrect because the coefficients do not explain the random error variance, but rather the systematic variance in the dependent variable due to changes in the independent variables.

Question 19

the equation Y = a + bX,the objective of regression analysis is to
A)estimate the parameters a and B
B)estimate the variables Y and X.
C)fit a straight line through the data scatter in such a way that the sum of the squared errors is minimized.
D)both a and c

Accepted Answer

The objective of regression analysis is to estimate the parameters a and b (choice A) and fit a straight line through the data scatter in such a way that the sum of the squared errors is minimized (choice C). Therefore, both options A and C are correct, and the answer is D.

Question 20

a linear regression equation of the form Y = a + bX,the intercept parameter a shows
A)the value of X when Y is zero.
B)the value of Y when X is zero.
C)the amount that Y changes when X changes by one unit.
D)the amount that X changes when Y changes by one unit.

Accepted Answer

The intercept parameter, "a", is the point where the regression line crosses the Y-axis. Therefore, when X is zero, the value of Y can be found by adding "a" to the product of 0 and "b". Hence, the best choice is B which says that the value of Y when X is zero.

Quiz 4: Basic Estimation Techniques

Which of the following is an example of a time-series data set?

If an analyst believes that more than one explanatory variable explains the variation in the dependent variable,what model should be used?

If the p-value is 10%,then the

a linear regression equation of the form Y = a + bX,the slope parameter b shows

The quadratic equation Y = a + bX +cX² can be estimated using linear regression by estimating

a linear regression equation Y = a + bX,the fitted or predicted value of Y is

sample regression line

method of least squares

To test whether the overall regression equation is statistically significant one uses

The critical value of t is the value that a t-statistic must exceed in order to

In the regression model $Y = a + b X + c Z$ ,a test of the hypothesis that parameter c equals zero is

Tests for statistical significance must be performed

Suppose you are testing the statistical significance (at the 1% significance level) of a parameter estimate from the regression model: M = a + bR + cI Which is estimated using a cross-section data set on 22 firms.The critical value of the appropriate test statistic is

a regression equation,the ______ captures the effects of factors that might influence the dependent variable but aren't used as explanatory variables.

parameter estimate is said to be statistically significant if there is sufficient evidence that the

An estimator is unbiased if it produces

In a multiple regression model,the coefficients on the independent variables measure

the equation Y = a + bX,the objective of regression analysis is to

a linear regression equation of the form Y = a + bX,the intercept parameter a shows