Question 1

A common misinterpretation of the principle of Occam's Razor is that a simple regression model (rather than a multiple regression model)is always best.

Accepted Answer

Occam's Razor suggests that among competing hypotheses that predict equally well, the one with the fewest assumptions should be selected. However, this principle is often misinterpreted to mean that simpler models are always better, which is not necessarily true, especially in cases where multiple variables genuinely affect the outcome.

Question 2

A parsimonious model is one with many weak predictors but a few strong ones.

Accepted Answer

A parsimonious model is actually one with few predictors, whether they are strong or weak. The goal of a parsimonious model is to have the simplest possible model that still accurately explains the data.

Question 3

In a regression,the model with the best fit is preferred over all other models.

Accepted Answer

A model with the best fit might overfit the data, capturing noise rather than the underlying trend, which can lead to poor predictive performance on new, unseen data. It's important to balance fit with the model's complexity to ensure generalizability.

Question 4

If R² and R²_adj differ greatly,we should probably add a few predictors to improve the fit.

Accepted Answer

The two models mentioned are identical in terms of predictors used (RS, U, P, S, B) and their configurations, with the difference being the addition of "adj" in the second model, which likely refers to an adjustment or interaction term rather than a new predictor. Adding more predictors is not suggested by a difference between these models, but rather exploring interaction effects or model specifications.

Question 5

In regression the dependent variable is referred to as the response variable.

Accepted Answer

In regression, the dependent variable is also known as the response variable because it's the variable being predicted or explained by the independent variable(s).

Question 6

The effect of a binary predictor is to shift the regression intercept.

Accepted Answer

When a binary predictor is added to the regression model, it creates two groups within the dataset. The intercept of the regression line for one group is different from the intercept of the other group. Therefore, the binary predictor can shift the regression intercept.

Question 7

For a certain firm,the regression equation Bonus = 2,000 + 257 Experience + 0.046 Salary describes employee bonuses with a standard error of 125.John has 10 years' experience,earns $50,000,and earned a bonus of $7,000.John is an outlier.

Accepted Answer

To determine if John is an outlier, we calculate his predicted bonus using the regression equation: Bonus = 2,000 + 257(10) + 0.046(50,000) = 2,000 + 2,570 + 2,300 = 6,870. John's actual bonus is $7,000, which is close to the predicted value, and the difference is not significantly larger than the standard error of 125, suggesting he is not an outlier.

Question 8

If a regression model's F test statistic is F_calc = 43.82,we could say that the explained variance is approximately 44 percent.

Accepted Answer

The F test statistic measures whether the overall regression model is significant. It does not directly provide information on the explained variance. The F test result can only be interpreted as significant or not significant, depending on the chosen significance level and the degrees of freedom for the model. Therefore, we cannot say that the explained variance is approximately 44 percent based solely on the F test statistic.

Question 9

The F statistic in a multiple regression is significant if at least one of the predictors has a significant t statistic at a given α.

Accepted Answer

The F statistic tests whether any of the predictors in a multiple regression model are jointly significant in explaining the variance in the dependent variable. If the F statistic is significant, it means that at least one of the predictors has a significant effect on the dependent variable. This conclusion can be confirmed by looking at the t statistics for each individual predictor, which will indicate which predictors are significant at a given alpha level.

Question 10

R²_adj can exceed R² if there are several weak predictors.

Accepted Answer

RS1U1P12S1S1P0S1U1B1adjS1U1U1B0 is designed to adjust for the number of predictors in a model, penalizing for adding weak predictors, thus it cannot exceed RS1U1P12S1S1P0 when weak predictors are added; instead, it should decrease or stay the same to reflect the penalty for model complexity.

Question 11

There is one residual for each predictor in the regression model.

Accepted Answer

There is one residual for each observation in the regression model, not for each predictor. Residuals are the differences between the observed values and the values predicted by the model.

Question 12

In a multiple regression with 3 predictors in a sample of 25 U.S.cities,we would use F_3,21 in a test of overall significance.

Accepted Answer

F_3,21 (or F-test) is commonly used in testing the overall significance of multiple regression models. Therefore, it is true that we would use this test in a multiple regression with 3 predictors in a sample of 25 U.S. cities.

Question 13

A binary (categorical)predictor should not be used along with nonbinary predictors.

Accepted Answer

It is not necessarily true that a binary predictor cannot be used along with nonbinary predictors. It depends on the specific modeling approach and research question. For example, in logistic regression modeling, it is common to include binary and continuous predictors in the same model.

Question 14

Confidence intervals for Y may be unreliable when the residuals are not normally distributed.

Accepted Answer

Confidence intervals are calculated based on the assumption that the residuals follow a normal distribution. If this assumption is violated, the calculated confidence interval may not be reliable.

Question 15

The random error term in a regression model reflects all factors omitted from the model.

Accepted Answer

The random error term in a regression model includes all factors that cannot be explained by the model, including factors that are omitted from the model.

Question 16

Evans' Rule says that if n = 50 you need at least 5 predictors to have a good model.

Accepted Answer

Evans' Rule states that as a general guideline, the number of predictors should be greater than 5 times the number of observations (n) for a good model. However, this is not a hard and fast rule and the optimal number of predictors can vary depending on the dataset and the purpose of the model. Therefore, it is not accurate to say that if n = 50, you need at least 5 predictors for a good model.

Question 17

A negative estimated coefficient in a regression usually indicates a weak predictor.

Accepted Answer

A negative estimated coefficient in a regression does not necessarily indicate a weak predictor. It simply means that as the predictor variable increases, the response variable tends to decrease. The strength of the predictor is determined by the magnitude and statistical significance of the coefficient, not just its sign.

Question 18

If the probability plot of residuals resembles a straight line,the residuals show a fairly good fit to the normal distribution.

Accepted Answer

When the probability plot of residuals resembles a straight line, it indicates that the residuals follow a normal distribution. Therefore, the residuals show a fairly good fit to the normal distribution.

Question 19

The model Y = β₀ + β₁X + β₂X² cannot be estimated by Excel because of the nonlinear term.

Accepted Answer

Excel can estimate models with nonlinear terms using tools like Solver or the Analysis ToolPak, which support nonlinear regression analysis.

Question 20

A predictor whose pairwise correlation with Y is near zero can still have a significant t-value in a multiple regression when other predictors are included.

Accepted Answer

This can happen when the predictor is correlated with other predictors in the model, leading to a partial correlation with Y that is significant even if the pairwise correlation is small. This is known as the "suppression effect" and can distort the interpretation of regression coefficients.

Quiz 13: Multiple Regression