FIN360 OLD EXAM QUESTIONS (EXAM 3)

Suppose you estimate a model such that 𝑦𝑡 = −1.5 + 4.0 𝑥𝑡. The predicted value of 𝑦𝑡 if 𝑥𝑡 has a value of zero is closest to:

-1.5

Which of the following statements are correct? I. A Type I error occurs when the null hypothesis is rejected when it is true. II. A Type II error occurs when the null is rejected when in fact it is true. III. The significance level is the probability of a Type I error. IV. The significance level is the probability of a Type II error.

1 & 3

Which of the following statements are true? I. If the critical values are 2.0 and the calculated test statistic is 2.5, we reject the null hypothesis. II. A two-tailed test using a z-distributed test statistic with a significance level of 5% has critical values of 1.96. III. If the calculated z is -2 and the critical z is -1.96, you should reject the null hypothesis.

1, 2, 3

Which of the following statements about hypothesis testing are true? I. The null hypothesis is a statement about the value of a population parameter. II. A Type II error is failing to reject a false hypothesis. III. A Type I error is rejecting the null when it is actually true. IV. If the alternative hypothesis is Ha: , you are performing a two-tailed test.

1, 2, 3, 4

Which is true, I. A Type II error is failing to reject a false hypothesis. II. A Type I error is rejecting the null when it is actually true. III. The null hypothesis is a statement about the value of a population parameter. IV. If the alternative hypothesis is Ha: 0, you are performing a two-tailed test.

1,2,3,4

Suppose you estimate a model such that 𝑦𝑡 = −1.5 + 4.0 𝑥𝑡. 𝑦𝑡 If 𝑥𝑡 changes by one unit, the expected change in 𝑦𝑡 is closest to:

4.0

Micado estimated a coefficient of determination of 0.45. This indicates that:

45 percent pf the variation in the rate of return is explained by the variation in oil prices.

Suppose you estimate a model such that 𝑦𝑡 = 2.3 − 3.5 𝑥𝑡 . The predicted value of 𝑦𝑡 if 𝑥𝑡 has a value of −2 is closest to:

9.3

Which of the following statements about hypothesis testing is TRUE?

A type I error is the probability of rejecting a true null hypothesis.

The appropriate test statistic for a test of whether the variance is equal to a specific value is the:

Chi Squared dist

Testing a single variance equal to a specific value requires the use of the:

Chi Squared test statistic

The appropriate test statistic for a test of equality of two variances is the:

F dist

The relation between the t-statistic for a test of the significance of the slope coefficient in a simple regression and the F-statistic is that the

F-statistic is the t-statistic squared.

Micado estimated the regression and observed an intercept of 0.03 and a slope of 0.9. If the standard error of the slope is 0.6, Micado should, using a five percent level of significance:

Fail to reject the null hypothesis

A correlation of 0.36 indicates that there is a 36 percent correlation between the two variables.

False

Autocorrelation is not a potential problem in a simple regression.

False

If two variables have a strong non-linear relationship, this will be detected in the pairwise correlation coefficient.

False

In the test of a slope coefficient, we fail to reject the null hypothesis if the corresponding p-value is less than the level of significance.

False

Tests of statistical significance of correlations using the Spearman and Pearson correlation will produce the identical reject/fail to reject decisions.

False

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

False

The slope of the regression of Y regressed on X represents the value of Y if X takes on a value of zero.

False

When regressing Y on X, if the t-statistic for the test of the slope coefficient different from zero is 3.4, the F-statistic for the simple regression of Y regressed on X is also 3.4.

False

Michael Micado, a portfolio manager, was interested in whether oil prices affect the rate of return of the Duplex Corporation. He gathered thirty years of data on the rate of return and oil prices, and regressed the rate of return on oil prices. -----To address his question whether oil prices affect the rate of return of Duplex, the hypotheses are best represented as:

H0: b1 =0 versus HA: b1 ≠ 0

Jo Su believes that there should be a relation between return and systematic risk. She intends to collect data on returns and systematic risk to test this theory. If the null hypothesis is H0: =0, what is the appropriate alternative hypothesis?

Ha: p does not equal 0

Ms. Stats examined a cross-sectional model's estimated 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

Which of the following statements is not correct?

Heteroskedasticity only occurs in cross-sectional regressions.

The Spearman correlation coefficient is best described as a:

Nonparametric statistic

If you estimate a Pearson correlation of 0.30 on a sample of 31 observations on Y and X, the correlation is:

Not statistically significant from zero at the 5 percent level.

Which of the following statements is not correct?

Outliers in a sample do not generally affect the tests of hypotheses.

The coefficient of determination is also known as the:

R^2

If a sample of 50 observations has a mean of $60 and a sample standard deviation of $10, in a test whether the mean is different from $55, using a 5 percent level of significance, we:

Reject the null

Which of the following involves independent samples?

Test of difference of means

Which of the following statements is not correct?

The R^2 is the ratio of the unexplained variation divided by the explained variation of the dependent variable.

Which of the following statements is incorrect regarding multiple regression?

The degrees of freedom for a test of a slope coefficient are n-2, where n is the number of observations.

Joe Backer wants to test whether the estimated beta in a market model is equal to one. He collected a sample of sixty monthly returns on a stock and estimated the regression of the stock's returns against those of the market. The estimated beta is 1.1 and the standard error of the coefficient is equal to 0.2. What should Joe Backer conclude regarding the beta if he uses a 5 percent level of significance?

The null hypothesis that beta is equal to one cannot be rejected.

Which of the following statements is correct regarding regression analysis?

The regression equation is estimated with error; that is, not all observations lie along the regression line.

Which of the following is not an assumption of linear regression?

The residuals are mean reverting; that is, they tend towards zero.

Which of the following best describes the standard error of the estimate in a regression?

The standard error of the estimate is the standard deviation of the residual

The parametric correlation between two variables is the ratio of the covariance between the two variables to the product of the standard errors of the two variables.

True

Autoregressive residuals are most likely to occur in:

Time Series regression

An ARIMA model is most appropriate to apply in the case of:

Time series data

For a simple regression, the coefficient of determination in the regression of Y on X is equal to the square of the correlation of Y and X.

True

If the correlation between X and Y is statistically significantly different from zero at the 5 percent level, the slope of Y regressed on X will also be significantly different from zero at the 5 percent level.

True

If the correlation between two variables X and Y is statistically significantly different from zero, the slope of the regression of X regressed on Y will be statistically different from zero at the same level of significance.

True

If the correlation of variables Y and X is positive, this indicates that the slope coefficient in the regression of Y regressed on X is positive.

True

Multicollinearity is not a potential problem in a simple regression.

True

The advantage of the nonparametric statistics is that they typically require fewer assumptions than parametric statistics.

True

Serial correlation in a regression's residuals results in what type of problem?

Variances that are too large.

Which is correct?

We can test whether the residuals of a trend model are serially correlated using the Durbin Watson test statistic.

The coefficient of determination is the proportion of variation of

Y explained by the variation in X.

Modeling the trend in a time-series of a variable that grows at a constant rate is best done with

a log-linear transformation of the time-series

A Durbin-Watson test statistic is used to detect:

autocorrelation of residuals

The model 𝑥𝑡 = 𝑏0 + 𝑏1𝑥𝑡−1 + 𝑏2𝑥𝑡−4 + 𝜀𝑡 is best described as:

autoregressive model

When testing a single variance against an hypothesized value, which distribution are the test statistic and confidence interval based on?

chi square

Another name for the explanatory variable in a regression equation is the:

independent variable

The percentage at which the null hypothesis can be rejected is the

level of significance

All other things remaining constant, a confidence interval for a population mean, , based on a sample of n = 100 will be __________ a confidence interval for , , based on a sample of n = 25.

narrower than

When making a statistical inference about the mean, d, of a population of paired differences, which distribution are the test statistic and confidence interval based on

t

When testing the difference between the means of two normally distributed populations using independent samples with unknown variances but assumed equal variances, which distribution are the test statistic and confidence interval based on?

t

In the time series model: yt=b0 + b1 t + t, t=1,2,...,T,

the change in the dependent variable per time period is b1.

For a two-tailed test of hypothesis involving a z-distributed test statistic and a 5% level of significance, a calculated z-statistic of 1.5 indicates that:

the null hypothesis cannot be rejected.

If the p-value corresponding to a t-distributed test statistic for the test of the mean is 0.04 and the level of significance is 1%,

the null hypothesis cannot be rejected.

The sum of the residuals of a regression is equal to:

zero

Ken Wallace is interested in testing whether the average P/E of firms in the retail industry is 25. Using a t- distributed test statistic and a 5% level of significance, the critical values for a sample of 30 firms is/are:

−2.045 and + 2.045.

A random walk is described as 𝑥𝑡 = 𝑏0 + 𝑏1𝑥𝑡−1, where

𝑏0=0 and 𝑏1=1