statistical inference for bivariate regression
the assignment consist of a multiple choice question
Multiple Choice
Q1)
| a. | It is true – we can’t use OLS | |
| b. | We can still use OLS – “Life=B1+B2Inc+u” model is appropriate for this data | |
| c. | We can still use OLS – “Log(Life)=B1+B2Inc+u” model is appropriate for this data | |
| d. | We can still use OLS – “Life=B1+B2Log(Inc)+u” model is appropriate for this data |
Q2)
Suppose that a researcher, using wage data on randomly selected male and female workers, obtains the estimated regression model “Wagei =12.52+2.12 Malei +ei ” , where Wage is measured in dollars per hour and Male is a dummy variable that is equal to 1 if the person is male and 0 if the person is female. Another researcher uses the same data, but regresses Wage on Female, a dummy variable that is equal to 1 if the person is female and 0 if the person is male. What are the regression estimates obtained from this regression?
| a. Wagei =10.40 -2.12 Femalei +ei | ||
| b. Wagei =12.52 -2.12 Femalei +ei | ||
| c. Wagei =14.64 -2.12 Femalei +ei | ||
| d. We don’t have enough information to answer this question |
Q3)
When a regressor is added to a regression model
| a. Adjusted R2 always increases when R2 increases | ||
| b. Adjusted R2 always decreases when R2 increases | ||
| c. Adjusted R2 may or may not increase if R2 increases | ||
| d. All of the above |
Q4)
Calculate the missing number ???A??? in the regression output. (Round to 4 decimal places )
Q5)
Calculate the missing number ???B??? in the regression output. (Round to 2 decimal places)
Q6)
Calculate the missing number ???C??? in the regression output. (Round to 4 decimal places)
Q7)
Calculate the missing number ???D??? in the regression output. (Round to 4 decimal places)
Q8)
a.
b.
c.
d.
None of the above
Q9)
Which of the following is true about OLS estimation in a model with only an intercept,
| a. The total sum of squares (TSS) is equal to the residual sum of squares (RSS). | ||
| b. The total sum of squares (TSS) is equal to the explained sum of squares (ExpSS). | ||
| c. The explained sum of squares (ExpSS) is equal to the residual sum of squares (RSS). | ||
| d. OLS cannot be applied in this case |
Q10)
When testing the significance of a subset of regressors, the RSS of the unrestricted model will always be
| a. Greater than or equal to the RSS of the restricted model | ||
| b. Less than or equal to the RSS of the restricted model | ||
| c.Equal to the RSS of the restricted model | ||
| d.It could be greater than, less than or equal to the RSS of the restricted model. |
Q11)
You have to worry about perfect multicollinearity in the multiple regression model because
| a. many economic variables are perfectly correlated. | ||
| b. the OLS estimator is no longer BLUE. | ||
| c. the OLS estimator cannot be computed in this situation. | ||
| d. in real life, economic variables change together all the time. |
Q12)
Consider the following multiple regression models (a) to (d) below. DFemme = 1 if the individual is a female, and is zero otherwise; DMale is a binary variable which takes on the value one if the individual is male, and is zero otherwise;DMarried is a binary variable which is unity for married individuals and is zero otherwise, and DSingle is (1-DMarried). Regressing weekly earnings (Earn) on a set of explanatory variables, you will experience perfect multicollinearity in the following cases unless
a.
c
Q13)
The formula for the standard error of the regression coefficient, when moving from one explanatory variable to two explanatory variables,
| a. stays the same | ||
| b. changes, unless the second explanatory variable is a dummy variable | ||
| c. changes | ||
| d. changes, unless you test for a null hypothesis that the addition regression coefficient is zero |
Q14)
When testing joint hypothesis, you should
| a. use t-statistics for each hypothesis and reject the null hypothesis is all of the restrictions fail | ||
| b. use the F-statistic and reject all the hypothesis if the statistic exceeds the critical value | ||
| c. use t-statistics for each hypothesis and reject the null hypothesis once the statistic exceeds the critical value for a single hypothesis | ||
| d. use the F-statistics and reject at least one of the hypothesis if the statistic exceeds the critical value |
Q15)
If you wanted to test, using a 5% significance level (degrees of freedom is 238), whether or not a specific slope coefficient is equal to “-1”, then you should
| a. subtract 1 from the estimated coefficient, divide the difference by the standard error, and check if the resulting ratio is larger than 1.96. | ||
| b. add and subtract 1.96 from the slope and check if that interval includes 1. | ||
| c. add 1 from the estimated coefficient, divide the difference by the standard error, and check if the resulting ratio is larger than 1.96. | ||
| d. check if the adjusted R2 is close to 1. |
Q16)
A 95% confidence set for a coefficient is a set that contains
| a. the sample values of this coefficient in 95% of randomly drawn samples | ||
| b. Integer value only | ||
| c. The same value as the 95% confidence intervals constructed for the coefficients | ||
| d. the population value of this coefficient in 95% of randomly drawn samples |
Q17)
Suppose that we run a regression with the log of pounds of rice purchased from a store as the dependent variable and log of the price of a pound of rice as the independent variable. A slope coe cient of 0.3 would be interpreted as:
| a. A one dollar increase in the price of a pound of rice is associated with a 0.3 pound increase in the amount of rice purchased. | ||
| b. A one percent increase in the price of a pound of rice is associated with a 30 percent increase in the amount of rice purchased. | ||
| c. A one percent increase in the price of a pound of rice is associated with a 0.3 percent increase in the amount of rice purchased. | ||
| d. A one dollar increase in the price of a pound of rice is associated with a 30 percent increase in the amount of rice purchased. |
Q18)
Which of the following would make you more likely to reject the hypothesis that an individual slope coefficient is equal to zero?
| a. A larger standard error for that slope coefficient . | ||
| b. A smaller t statistic for that slope coe fficient. | ||
| c. A smaller F statistic for the regression. | ||
| d. A larger value for the ratio of the coefficient to its standard error. |
Q19)
All other things being equal, which of the following decreases the standard error of OLS estimators in the multivariate regression?
| a. A larger variance of the error term u. | ||
| b. A higher correlation between the independent variables. | ||
| c. A smaller intercept | ||
| d. A bigger sample size. |
Q20)
- dividing the error by the explanatory variable results in a zero (on average).
- the sample regression function residuals are unrelated to the explanatory variable.
- the sample mean of the Xs is much larger than the sample mean of the errors.
- the conditional distribution of the error given the explanatory variable has a zero mean
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