Question 1

Dependent Variable: WHY Method: Least Squares Sample(adjusted): 19652006 Included observations: 30 atter adjusting endpoints $\begin{array}{lllll} \hline \text { Variable } & \text { Coefficient } & \text { Std. Error } & \text { t-Statistic } & \text { Prob. } \ \hline \hline \text { C } & -19.60486 & 123.5064 & -0.158736 & 0.8747 \ \text { EX1 } & 20.04112 & 12.56987 & 1.594377 & 0.1189 \ \text { EX2 } & 0.517140 & 0.007738 & 66.83540 & 0.0000 \ \hline \text { R-squared } & 0.991948 &\text { Mean dependent var } && 2775.633 \ \text { Adjusted R-squared } & 0.991536 & \text { S.D. dependent var } && 1915.813 \ \text { S.E. of regression } & 176.2591 & \text { Akaike info criterion }&& 13.25054 \ \text { Sum squared resid } & 1211624 . & \text { Schwarz criterion } && 13.37466 \ \text { Log likelihood } & -275.2613 & \text { F-statistic }&& 2402.403 \ \text { Durbin-Watson stat } & 0.289425 &\text { Prob(F-statistic) } && 0.000000 \end{array}$ Use the Eviews output above to help with A) through I) below. A) Interpret the coefficient on EX1. B) Interpret R² for this regression. C) Replace the "?"'s with the appropriate values. An 80% confidence interval around the coefficient on EX1 is: 20.04112 +/- (?)(?) D) Perform a positive sign test on the coefficient attached to EX2. Show the 5-step procedure. E) IF you performed a test of significance on the constant term at the 87 percent critical level, would you reject the null hypothesis or not? Explain. F) Perform a test to determine if the coefficient attached to EX2 is greater than 7.47. Show the 5-step procedure. G) Based on the information in the table above (and ignoring Ramsey's Reset test which we will perform in a moment) do you think the regression above is under or over specified? Explain. H)1.Perform Ramsey's Reset Test on the regression above using the Eviews printout below. Show the 5-step procedure. 2. What is the difference between "FITTED^2" and "FITTED^3" in the Eviews printout above? Do the two terms appear in the restricted or unrestricted regression?

Accepted Answer

A) If EX1 increases 1 unit, then WHY is expected to increase 20.04 units holding EX2 constant. B) 99% of the variation in WHY is explained by EX1 and EX2. C) 12.57 and 1.314 D) 1) Ho: $B _ { 2 }$ = 0 Ha: $B _ { 2 }$ > 0 (minus 2 for messing up step 1) 2) 5% 3) If t-ratio > t^c, then reject Ho 4) 66.84 > 1.703 (d.f. = n- k = 30 - 3 =27) 5) Reject Ho $\rightarrow$ $\beta _ { 1 }$ is not significantly positive E) Not reject because the P-value > .87 F) 1. Ho: $\beta _ { 2 } = 7.47 \quad$ Ha: $\beta _ { 2 } > 7.47$ $2.5 \%$ 3. If t-ratio $> t$, then reject $\mathrm { Ho }$ 4. $( 20.04 - 7.47 ) / 12.57 = 1 < 1.703$ (d.f. $= \mathbf { n } - \mathbf { k } = 30 - 3 = 27$ ) 5. Do not reject Ho; $\beta _ { 2 }$ is not statistically greater than 7.47 . G) All we have to go on is significance and EX1 is insignificant at the 5% critical level. So the equation may be over specified. H) 1)

Question 2

A) Criticize stepwise regression
B) What criteria are important for determining if a particular explanatory variable belongs in a regression. (4pts.)

Accepted Answer

A) It ignores theory.
Perhaps the pool stinks.
Includes or excludes variables based on biased statistics.
Ignores Ramsey's reset test, Akaike, Schwarz, Hannan-Quinn
B) Theory, significance, measures of goodness-of-fit, altered estimators, Ramsey's reset test.

Question 3

If a regression is underspecified, then the estimators will not average out to equal the
true values of the structural parameters in repeated sampling.

Accepted Answer

An underspecified regression model omits relevant variables, leading to biased and inconsistent estimators that do not converge to the true parameter values with repeated sampling.

Question 4

If a regression is over specified then the estimators should change markedly once the extraneous variables are removed.

Accepted Answer

Over-specification in regression, which involves including unnecessary variables, does not typically change the estimators of the relevant variables markedly when the extraneous variables are removed, assuming there is no multicollinearity. The main issue with over-specification is reduced efficiency and unnecessarily complex models, rather than a significant change in the estimates of the coefficients for relevant variables.

Question 5

The constant term is biased in a regression missing an important explanatory variable.

Accepted Answer

When an important explanatory variable is omitted from a regression model, the estimates of the coefficients, including the constant term, can be biased because the omitted variable's effect on the dependent variable may be incorrectly attributed to the included variables.

Question 6

A 95% confidence interval for a given coefficient can never be larger than a 90% confidence interval.

Accepted Answer

A 95% confidence interval is wider than a 90% confidence interval because it requires capturing more of the data to be 95% confident, thus it includes a larger range of values.

Question 7

The standard error of the regression (SER) is monotonically decreasing with respect to the number of explanatory variables.

Accepted Answer

The standard error of the regression (SER) does not necessarily decrease monotonically with the addition of explanatory variables. While adding relevant variables can improve the model and potentially reduce the SER, adding irrelevant or poorly chosen variables can actually increase the SER or leave it unchanged.

Question 8

Raising the critical level of a test from 5% to 10% decreases the probability that the test will result in a TYPE II error.

Accepted Answer

Raising the critical level (alpha) increases the likelihood of rejecting the null hypothesis, thus reducing the probability of a Type II error, which is failing to reject a false null hypothesis.

Question 9

The Schwarz Criterion is monotonically decreasing with respect to the number of explanatory variables.

Accepted Answer

The Schwarz Criterion, also known as the Bayesian Information Criterion (BIC), increases with the number of explanatory variables due to the penalty term for the number of parameters in the model, discouraging overfitting by adding complexity.

Question 10

If the prob-value is less than .05, then the hypothesis test will reject Ho at the 5% critical level.

Accepted Answer

If the p-value is less than the significance level (in this case, .05), it indicates that the observed data are highly unlikely under the null hypothesis, leading to the rejection of the null hypothesis (H0) at the 5% critical level.

Question 11

You can conduct a positive sign test on a negative coefficient, but the results will be the same every time: Do not reject Ho.

Accepted Answer

A positive sign test is a one-tailed test that tests whether the median of a population is greater than a specified value. If the coefficient is negative, then the median is less than the specified value, and the test will always reject the null hypothesis.

Question 12

If a test of significance results in "Do not reject Ho", then there is absolutely no chance that a TYPE II error has been committed

Accepted Answer

Choosing not to reject the null hypothesis (Ho) when it is actually false is the definition of a Type II error, so there is indeed a chance that a Type II error has been committed.

Quiz 2: Simple Regression Analysis

A) Criticize stepwise regression B) What criteria are important for determining if a particular explanatory variable belongs in a regression. (4pts.)

If a regression is underspecified, then the estimators will not average out to equal the true values of the structural parameters in repeated sampling.