FIN 360 TEST 3

In a multiple regression, an R-squared of 0.35 is most consistent with:

35 percent of the variation in the dependent variable is explained by the independent variables

A simple regression with 45 observations has how many degrees of freedom?

43

A simple regression with 46 observations has how many degrees of freedom?

44

If the coefficient of determination is 56%, which of the following statements is true? Indicate all true statements.

56 percent of the variation in the dependent variable is explained by the indpendent variable or variables.

The model: 𝐸(𝑅𝑝)=𝑅𝑓+𝛽𝑝,1𝑅𝑀𝑅𝐹+𝛽𝑝,2𝑆𝑀𝐵+𝛽𝑝,3𝐻𝑀𝐿+𝛽𝑝,4𝑊𝑀𝐿E(Rp)=Rf+βp,1RMRF+βp,2SMB+βp,3HML+βp,4WML is best described as the:

Carhart model

Which of the following can be used to examine the fit of a multiple regression equation?

Coefficient of determination, F-statistic

Which of the following is a desirable quality of a time series' residuals? (indicate all that apply)

Covariance stationarity, Homoskedastic residuals

Which of the following is used to test whether there is serial correlation of the residuals of a time-series model?

Durbin-Watson test

A coefficient of determination has a range from -1 to +1.

False

A correlation between variables X and Y of 0.25 indicates that 25% of the relationship between the two variables is explained.

False

If a slope coefficient is different from zero at the 5% level of significance, it is also different from zero at the 1% level of significance.

False

If the coefficient of determination for a simple regression of Y regressed on X is positive, the correlation coefficient between Y and X must be positive.

False

If you have a regression with four independent variables, the F-statistic to test: H0: 𝑏1=𝑏2=𝑏3=𝑏4=0b1=b2=b3=b4=0 Ha: 𝑎𝑡𝑙𝑒𝑎𝑠𝑡𝑜𝑛𝑒𝑏𝑖≠0atleastonebi≠0 is the sum of the t-statistics for the four independent variables.

False

The coefficient of determination for a simple regression is the square root of the correlation between the dependent and independent variables.

False

The covariance is the ratio of the covariation to the product of the two variables' standard deviations.

False

Which of the following is a desirable quality of a time series' residuals? (indicate all that apply)

Homoskedastic residuals, Covariance stationarity

Which of the following statements is correct regarding the following estimated regression (indicate all that apply): Y = 0.01 + .785 X

If X has a value of -1, Y has a value of -0.775., If X has a value of zero, the value of Y is 0.01., A one unit change in X will produce a 0.785 unit change in Y., The elasticity of Y with respect to X is 0.785.

Anna Goldberg is analyzing the relation between a company's weighted average cost of capital and its dividend payout ratio. She collects data on 600 companies for fiscal year 2016, and regresses the dividend payout against the weighted average cost of capital: DPOi = 0.90 - 2.5 WACCi Which of the following are correct interpretations of her results? Indicate all that apply.

If a company has a WACC of 0.10, we expect its dividend payout ratio to be 0.65, A change in a company's WACC from 0.06 to 0.07 would result in a reduction in its dividend payout ratio of -0.025, The lower the company's WACC, the greater the company's dividend payout ratio

Which of the following is a correct statement? Indicate all that apply.

If the p-value of a test statistic is less than the level of significance, we reject the null hypothesis., 1 -𝑅2R2 is the variation in the dependent variable that is not explained by the independent variable., The coefficient of determination is the ratio of the sum of squares regression (RSS or SSR) to the total sum of squares of the dependent variable (SST)., The t-statistic for the test of the correlation of X & Y is the same value as the t-statistic for the test of the slope in the regression of Y on X.

Which of the following independent variables is a significant explanatory variable based on the following regression results and a 1% level of significance: CoefficientCalculated t-statistic forH0: bk=0p-valueDividend yield2.1000.0382Net profit margin1.2650.2088Number of employees2.3550.0205Industry concentration3.1000.0025Sales growth-2.7890.0063 Indicate all that apply.

Industry concentration, Sales growth

Which of the following is a model with a qualitative dependent variable?

Logit model, Probit model

Which of the following are problems that may arise in multiple regression? Indicate all that apply.

Multicollinearity, Autocorrelation, Heteroskedasticity

Log-linear trend model

Natural log of variable regressed against a variable indicating time

Consider the following regression estimation results, estimated using 1,000 cross-section sample firms: VariableCoefficientStandard errorIntercept15.26.23Number of employees-9.131.89Operating leverage-4.752.5Beta-0.50.63Proportion of independent directors-3.231.76Tax rate-0.30.18Segment diversification0.150.06 The dependent variable is the ratio of the market value of equity to the book value of equity.Which of these explanatory variables is different from zero at the 5 percent level? Indicate all that have coefficients different from zero at the 5 level of significance.

Number of employees, Segment diversification

For a regression of Y on X, which of the following is in terms of the measurement scale for Y? (e.g., if Y is in dollars, which of the following would also be in dollars?) Indicate all that apply.

Predicted value of Y, Change from a one unit change in X, Intercept, Standard error of the estimate, Residual

You ask Mr. John Dood, your research assistant, to analyze the relationship between the return on TAB common stock and the return on the market using the Standard and Poor's 500 Stock Index as a proxy for the market. The data include monthly returns for both TAB and the S&P 500 over a recent five-year period and returns are in decimal form (that is, a 1% return is 0.01). The results of the regression: RTAB,t = 0.0059 + 1.04 RS&P,t + et (0.70) (3.12) where RTAB,t = return on TAB common stock in month t,RS&P,t = return on S&P 500 Stock Index in month t, andet = residual error in month t. The numbers in parentheses are the t-statistics corresponding to the estimated parameter. The coefficient of determination for the regression is 0.1437. Which of the following are correct statements regarding these results? Indicate all that apply.

Reject the null hypothesis H0: b1=0 at the 5% level of significance, There is significant correlation between RTAB and RS&P at the 5% level of significance, There is a significant slope coefficient on RS&P at the 5% level of significance

Based on the following results from SAS for a cross-sectional sample of companies for fiscal year 2015, with the dividend payout ratio as the dependent variable, which of the explanatory variables has a slope different from zero at a 5 percent level of significance? Indicate all that apply. Analysis of VarianceSourceDFSum ofSquaresMeanSquareF ValuePr > FModel3224097469.5173351.66<.0001Error20529643144.59902 Corrected Total20852051 Root MSE12.02493R-Square0.4305Dependent Mean2.22477Adj R-Sq0.4222Coeff Var540.50232 Parameter EstimatesVariableLabelDFParameterEstimateStandardErrort ValuePr > |t|InterceptIntercept1-3.470012.81905-1.230.2198rturnReceivables turnover1-0.350670.22239-1.580.1164roaReturn on assets1-179.4551449.45220-3.630.0004investRate of investment1184.91329

Return on asssets, Rate of investment

Consider the following regression estimation results, estimated using 1,000 cross-section sample firms: CoefficientStandard errorIntercept18.254.85Size-9.431.60Leverage-4.502.68Beta-1.500.54Political risk-2.101.76Transparency-0.140.10Geographic diversification0.010.03 The dependent variable is the ratio of the market value of equity to the book value of equity.Which of these explanatory variables is different from zero at the 5 percent level? Indicate all that have coefficients different from zero at the 5 level of significance.

Size, Beta

Which of the following statements is correct? Indicate all that apply.

The Spearman correlation coefficient is the correlation of the ranks of two variables., The R-squared of the regression of Y on X is the square of the bivariate correlation of Y and X., If two variables Y and X have a statistically significant Pearson correlation, the regression of Y on X will have a statistically significant slope.

Which of the following is an assumption of least squares, simple regression? Indicate all that apply.

The mean of the residuals is zero, Residuals are homoskedastic, The residual for one observation is uncorrelated with residuals of another observation, The relationship between the dependent and independent variable is linear

The following results are available on a portfolio: FactorFundBenchmarkDifferenceFactor returnAbsolute contributionA0.501.00-0.51.00%-0.50%B0.701.20-0.52.00%-1.00%C1.600.401.27.00%8.40%Return from tilts6.90%Security selection-2.90%Active return4.00% Which of the following describes these results correctly? Indicate all that apply.

The portfolio manager is good at choosing factor tilts., The best tilt choice that the portfolio manager made was the tilt on factor C.

Which of the following are assumptions of simple linear regression? Indicate all that apply.

The residual terms are homoskedastic., The independent variable is not random., There is a linear relation between the dependent variable and the independent variable., The residual term is not correlated across sample observations.

Which of the following statements is a correct statement regarding simple regression? Indicate all that apply.

The square of the t-statistic on the slope coefficient is equal to the F-statistic used to test goodness of fit.

An assumption of regression models is that the regression errors are not correlated across observations.

True

For a times series that is a random walk, the best predictor of next period's value is the current value.

True

If the slope coefficient in a simple regression is different from zero at the 5 percent level, the correlation coefficient between the independent and dependent variables is different from zero at the 5 percent level as well.

True

In a time trend model, the slope is the change in the dependent variable for the passage of one unit of time.

True

In the arbitrage pricing model, the return you should expect on a well-diversified portfolio is linearly related to the factor sensitives of that portfolio.

True

The coefficient of determination is the ratio of the variation of the dependent variable explained by the independent variables to the total variation of the dependent variable.

True

The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable.

True

Given the following regression results, which of the following variables has a slope coefficient different from zero at a 5 percent level of significance? (indicate all that are statistically significant) Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 3.2462 0.1843 17.6170 0.0000 2.8798 3.6127 Variable 1 0.0016 0.0064 0.2497 0.8035 -0.0111 0.0143 Variable 2 0.0871 0.0352 2.4727 0.0154 0.0171 0.1571 Variable 3 0.0057 0.0037 1.5289 0.1300 -0.0017 0.0130

Variable 2

Linear trend

Variable regressed against a variable indicating time

AR1

Variable regressed on the lagged value of itself

Arbitrage pricing theory relates expected returns to:

a number of factors.

A portfolio that has a factor sensitivity of 1.0 to factor j, yet has a factor sensitivity of 0.0 to all other factors, is best described as:

a pure factor portfolio.

A time series for which the best predictor of next period's value is this period's value is best described as:

a random walk.

If the coefficient on a lagged value of a time series is equal to 1.0, the series is best described as having:

a unit root.

(Σ{𝑃𝑜𝑟𝑓𝑜𝑙𝑖𝑜𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦𝑘−𝐵𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦𝑘}𝑥𝐹𝑎𝑐𝑡𝑜𝑟𝑟𝑒𝑡𝑢𝑟𝑛𝑘)+𝑆𝑒𝑐𝑢𝑟𝑖𝑡𝑦𝑠𝑒𝑙𝑒𝑐𝑡𝑖𝑜𝑛(Σ{Porfoliosensitivityk−Benchmarksensitivityk}xFactorreturnk)+Securityselection is best described as the:

active return.

𝑠(𝑅𝑝−𝑅𝐵)s(Rp−RB)is: Indicate all that apply.

active risk., tracking error., tracking risk.

We can break down the active risk squared of a portfolio into: Indicate all that apply.

active specific risk., active factor risk., security selection risk.

If a series' values are correlated with its own past values, we describe this series as:

autocorrelated.

The Durbin-Watson test is used to test whether there is:

autocorrelation.

Two series are said to be ___________________ if the series do not diverge from each other without bound in the long-term.

cointegrated

If regression errors' variance is correlated with independent variables in the regression, we refer to this as:

conditional heteroskedasticity

Growth that is exponential is growth that is consistent with:

continuous compounding.

We must assume that a time series is ___________________ in order to make appropriate statistical inference from the estimated values.

covariance stationary.

In regression models, the variable that is being predicted is best described as the:

dependent variable

Consider the regression of AAPL stock returns on the returns on the market (VWRETD) and an indicator variable for the financial crisis (crisis period = 1, otherwise 0). Analysis of VarianceSourceDFSum ofSquaresMeanSquareF ValuePr > FModel20.430670.21533662.38<.0001Error27230.885220.00032509 Corrected Total27251.31588 Root MSE0.01803R-Square0.3273Dependent Mean0.00146Adj R-Sq0.3268Coeff Var1230.75280 Parameter EstimatesVariableLabelDFParameterEstimateStandardErrort ValuePr > |t|InterceptIntercept10.001160.000345783.360.0008VWRETDValue-Weighted Return-incl. dividends10.943480.0298931.57<.0001CRISIS Crisis indicator (1 if crisis, 0 otherwise)10.371050.107443.450.0006 Given these results, and using a 1% level of significance, we should conclude that the market index returns [ Select ] the returns on AAPL stock, and the returns during the market crisis are [ Select ] from those of the non-crisis period.

explain, different

The model 𝑦𝑡=𝑒𝑏0+𝑏1𝑡yt=eb0+b1t is an example of:

exponential growth.

In the APT model, 𝐸(𝑅𝑝)=𝑅𝑓+𝜆1𝛽𝑝,1+𝜆2𝛽𝑝,2...+𝜆𝐾𝛽𝑝,𝐾E(Rp)=Rf+λ1βp,1+λ2βp,2...+λKβp,K 𝜆2λ2 is best described as the:

factor risk premium for the second factor..

The expected reward for bearing the risk of a portfolio with a sensitivity of 1 for the specific factor and a zero sensitivity to all other factors is best described as a:

factor risk premium.

The BARRA models are examples of:

fundamental factor models.

Suppose you estimate a regression of a variable regressed on itself lagged (that is, an AR1 model). If the slope is not different from 1.0 you will conclude that the series: Choose all that apply.

has a unit root., is a random walk.

Susie Stats, an analyst with the FF Investments Company, regressed stocks returns on the ratio of book-to-market (B/M) and market capitalization (SIZE) using a sample of 250 companies. Ms. Stats examined the model's residuals and observed that the model seems to fit some industries better than others. The potential problem that this points out is referred to as:

heteroskedasticity

If the variance of regression errors differs across observations, this is described as:

heteroskedasticty

The coefficient of determination

is maximized by ordinary least squares, will generally increase if additional independent variables are added to the regression analysis, has a value between zero and one

If a times series tends to fall when its values are above its mean and increase when its values are below its mean, we refer to this as a series that is:

mean reverting.

In a multiple regression, the correlation among independent variables is best described as:

multicollinearity.

If the F test statistic for a regression is greater than the critical value from the F distribution, it implies that

one or more of the independent variables in the regression model have a significant effect on the dependent variable.

We compare forecasting models by choosing the model with the smallest:

root mean square error.

In the macroeconomic model: 𝑅𝑖=𝑎𝑖+𝑏𝑖1𝐹𝐺𝑁𝑃+𝑏𝑖2𝐹𝐶𝑆+𝑒𝑖Ri=ai+bi1FGNP+bi2FCS+ei where GNP is gross national product and CS is consumer spending, 𝑏𝑖1bi1 is the:

sensitivity of the return on stock i to surprises in GNP.

If the t ratio for the slope of a simple linear regression equation is -2.48 and the critical values of the t distribution at the 1% and 5% levels, respectively, are 3.499 and 2.365, then the slope is

significantly different from zero at the 5% level but not at the 1% level.

The capital asset pricing model is best described as a:

single-factor model.

A correlation that is simply by chance, not due to an underlying economic relationship, is best described as _____________ correlation.

spurious

The coefficient of determination is the ratio of the __________________ to the sum-of-squares total.

sum-of-squares regression

Which of the following is most appropriate in testing the role of an individual independent variable in a multiple regression?

t-statistic

The expected reward for bearing the risk of a portfolio with a sensitivity of 1 to the jth factor and sensitivity of 0 to all other factors is referred to as:

the factor risk premium.

The ratio of the active return to the tracking risk is best described as: Indicate all that apply.

the information ratio.

Autocorrelation may be the result of:

the omission of an important explanatory variable., the presence of a trend in the independent variable., nonlinearities in teh relationship between the dependent and independent variables.

If the return to stock selection is negative, this means that: Indicate all that apply.

the portfolio manager is not good at picking securities.

Multicollinearity refers to a situation in which

there is a high degree of correlation between the independent variables included in a multiple regression model.

𝜎(𝑅𝑃−𝑅𝐵)σ(RP−RB)is best described as the:

tracking error,

A macroeconomic models purport that returns are driven by:

unanticipated economic factors.

In a market that is semi-strong efficient, the average active return on portfolios (excluding any management fee) is most likely:

zero.

To test the hypotheses 𝐻0:𝑏1=0𝑣𝑠.𝐻𝐴:𝑏1≠0H0:b1=0vs.HA:b1≠0 we could use which of the following test statistics? Indicate all that apply.

𝐹=𝑀𝑒𝑎𝑛𝑠𝑞𝑢𝑎𝑟𝑒𝑟𝑒𝑔𝑟𝑒𝑠𝑠𝑖𝑜𝑛/𝑀𝑒𝑎𝑛𝑠𝑞𝑢𝑎𝑟𝑒𝑒𝑟𝑟𝑜𝑟, 𝑡=𝑏̂ 1−𝑏1/𝑠𝑏1

A test of correlation, testing whether correlation is different from zero, requires the test statistic:

𝑡=𝑟√𝑛−2 divided by √1-𝑟2