Exam
1.
In a regression model with one independent variable X, the intercept or constant (b_{0}) represents the
A) predicted value of the dependent variable Y when the X = 0.
B) estimated average per unit change in the dependent variable for every unit change in X.
C) predicted or fitted value of dependent variable.
D) Average variation around the sample regression line.
2.
In a regression model with one independent variable X, the slope coefficient (b_{1}) represents the
A) predicted value of the dependent variable Y when the X = 0.
B) estimated average per unit change in the dependent variable for every unit change in X.
C) predicted or fitted value of dependent variable.
D) average variation around the sample regression line.
3.
If one examines the relationship between two variables, the correlation (r) and the slope coefficient (b_{1}) in a simple regression model
A) may have opposite signs.
B) must have the same signs.
C) must have opposite signs.
D) are equal.
4.
If one examines the relationship between two variables, the correlation (r) and the slope coefficient (b_{1}) in a multiple regression model
A) may have opposite signs.
B) must have the same signs.
C) must have opposite signs.
D) are equal.
5.
Suppose you were given data on number of radio ads and sales for a local department store. You had observations for 20 months. The correlation between ads and sales is 0.40. Does this indicate a positive and significant relationship between ads and sales at the 0.005 level of significance?
A) Yes
B) No
C) Not enough information to determine significance
6.
R^{2} detects the strength of the relationship between the dependent variable and any individual independent variable.
A) True
B) False
7.
When an explanatory variable is dropped from a multiple regression model, R^{2} can increase.
A) True
B) False
8.
If one tests to see if the value of R-squared is statistically different from zero, one should use a
A) t-statistic.
B) F-statistic.
C) z-statistic.
D) correlation coefficient (r).
9.
In a multiple regression model, the adjusted R^{2}
A) can be negative.
B) must be positive.
C) has to be larger than R^{2}.
D) can be larger than 1.
10.
In a multiple regression model, the intercept or constant (b_{0})
A) forces the regression line to go through the origin (point where dependent variable is zero when the independent variable is zero).
B) is typically unimportant in interpreting the model so can be omitted from model with little effect on results.
C) measures the portion of variation in the dependent variable that is explained by the variation in all the independent variables.
D) provides flexibility so the least squares method can estimate the best line fit for data in the relevant range of firm operations.
11.
Which of the following is NOT a part of regression specification?
A) Selecting the dependent variable.
B) Identifying important independent variables.
C) Explaining expected signs for the coefficients of each independent variable.
D) Forecasting the expected value of R^{2} for your model.
Situation 7.1.1:
A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank’s charges (Y) — measured in dollars per month — for services rendered to local companies. One independent variable used to predict service charge to a company is the company’s annual sales revenue (X) — measured in millions of dollars. Data for 21 companies who use the bank’s services were used to fit this model:
(Y) = b_{0} + b_{1}X
The results of the simple linear regression are provided below.
Model | Variable | Coefficient | t-statistic (absolute value) |
B_{0} | Constant | -270 | 1.25 |
B_{1} | X | 200 | 1.75 |
R^{2} = 0.63 |
12.
Referring to Situation 7.1.1, interpret the estimate of b_{0}.
A) All companies will be charged at least $270 by the bank.
B) There is no practical interpretation since bank charges of less than $0 is a nonsensical value.
C) About 95% of the observed service charges fall within $270 of the least squares line.
D) For every $1 million increase in sales revenue, we expect a service charge to decrease $2,700.
13.
Referring to Situation 7.1.1, interpret b_{1} using the appropriate t-test (Hint: first determine whether this should be a one-tail or two-tail test).
A) There is insufficient information to determine the statistical significance of sales revenue.
B) There is sufficient evidence (at the a = 0.05) to conclude that sales revenue (X) is a significant predictor of service charge (Y).
C) There is insufficient evidence (at the a = 0.10) to conclude that sales revenue (X) is a significant predictor of service charge (Y).
D) For every $1 million increase in sales revenue, we expect the service charge to decrease by $70.
14.
Referring to Situation 7.1.1, what is the percentage of the total variation in bank charges explained by variations in company sales revenue?
A) 175%
B) 125%
C) 95%
D) 63%
15.
Referring to Situation 7.1.1, what is the fitted value of bank charges when company sales revenue is $10m?
A) $1260
B) $1730
C) $2000
D) $6300
Situation 7.1.2:
An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The economist used observations from 15 industrialized countries to estimate the relationship. The Microsoft Excel output of this regression is partially reproduced below.
Variable | Coefficient | Standard Error |
Constant | -0.086 | 0.567 |
GDP | 0.765 | 0.057 |
Price | -0.0006 | 0.0028 |
R^{2} = 0.96; Adjusted R^{2} = 0.93 | ||
F = 18.63 |
16.
Referring to Situation 7.1.2, one economy in the sample had an aggregate consumption level of $3 billion, a GDP of $3.5 billion, and an aggregate price level of 125. What is the residual for this data point?
A) $2.52 billion
B) $0.48 billion
C) – $1.33 billion
D) – $2.52 billion
17.
Which of the independent variables (price, GDP) in Situation 7.1.2 is statistically significant and, therefore, important to explaining variations in consumption (Hint: you are provided standard errors not t-statistics in the table)?
A) GDP only
B) Price only
C) Both GDP and Price
D) Neither GDP or Price
18.
Referring to Situation 7.1.2, interpret the test to determine whether the model (all independent variables taken together) have statistically significant explanatory power.
A) Since the R_{2} indicates that variation in all independent variables explain 96% of the variation in the dependent variables, the model can be interpreted as having significant explanatory power.
B) Using a = 0.05 and F = 3.59, the null hypothesis is rejected and the model can be interpreted as having significant explanatory power.
C) Using a = 0.05 and F_{2,12} = 3.89, the null hypothesis is rejected and the model can be interpreted as having significant explanatory power.
D) Using a = 0.05 and t_{12} = 1.7823, the null hypothesis is rejected and the model can be interpreted as having significant explanatory power.
19.
The economist in Situation 7.1.2 decided to add a new variable, the percentage of GDP devoted to agriculture, to the model. The new results included an R^{2} = 0.98 and Adjusted R^{2} = 0.92. How do you interpret these changes?
A) Since R^{2} increased by more than adjusted R^{2} decreased, the new variable was an important addition to the model.
B) The change in adjusted R^{2} implies that the benefit of the information added by the new variables is less than the cost in lost degrees of freedom caused by adding the new variable so the new variable is not an important addition to the model.
C) One cannot evaluate the importance of the new variable to the model without knowing either the standard error or t-statistic for the variable’s coefficient.
20.
There are several reasons why choices between alternative regression models should NOT be based on which model has the highest R^{2}. Which of the following is NOT one of those reasons?
A) Models using time series data will have higher R^{2} than models using cross-sectional data.
B) Some variables are inherently more unstable and thus harder to predict.
C) R^{2} indicates relationships not causality.
D) R^{2} captures the individual effects of variables but not the effects of all variables.