Which decomposition relates total variation of Y into explained and unexplained parts in regression?
Explanation
ANOVA decomposition in regression: total sum of squares equals explained plus unexplained variation (chapter ANOVA table).
Other questions
Which sampling method guarantees that every member of a population has an equal chance of selection?
You want the standard error of a sample mean to be at most 0.5 units. If the population standard deviation is estimated to be 4.0, what minimum sample size n do you need (use the population formula)?
Which statement best describes the central limit theorem as used for sample means?
An analyst has a sample of n = 25 independent observations from a population with unknown variance. The sample mean is 10 and the sample standard deviation is 5. What is the estimated standard error of the sample mean?
Which sampling method is most appropriate when you need to ensure representation across known subgroups (for example, bond duration buckets) and to improve precision?
An analyst has a sample of 50 returns and computes a 95 percent confidence interval for the mean. Which significance level alpha corresponds to this interval?
Which statement about bootstrap resampling is true?
You compute a t-statistic of 2.5 with df = 20 for a two-sided test. Which statement is correct at alpha = 0.05?
An analyst wants to test whether two independent samples have equal means and assumes equal variances. What test should she use?
What is the formula for an expected cell frequency Eij in a contingency table under the null hypothesis of independence?
Which of the following is a valid reason to use a nonparametric test instead of a parametric t-test?
When performing a bootstrap with B resamples to estimate the standard error of a statistic theta_hat, which expression gives the bootstrap standard error estimate?
You test H0: sigma^2 = 0.04 for a normally distributed variable using a sample of n = 16 and obtain sample variance s^2 = 0.02. Which test statistic should you use?
Which of the following best describes a Type I error in hypothesis testing?
An analyst uses a two-sample t-test with pooled variance and obtains a p-value of 0.03. At alpha = 0.05 what should she conclude?
Which test is appropriate to examine whether the variance of returns changed after a policy event using two independent samples (before and after) of normally distributed returns?
A researcher has a single sample of size n = 12 of monthly returns and wishes to estimate the standard error of the sample median but no analytic formula is available. Which method is most appropriate?
Which of the following is the correct test statistic to test whether a sample Pearson correlation r differs from zero for n observations?
Which approach is best if you have ranked (ordinal) performance scores for fund managers and you want to test whether two groups have different central tendency?
You observe two time periods with very different volatilities in a regression residual plot, indicating heteroskedasticity. Which statement is true?
In a simple linear regression Y = b0 + b1 X + e, what is the meaning of b1?
In simple linear regression, how is the coefficient of determination R^2 related to the sample correlation r between X and Y?
You estimated a simple regression with n = 30 observations and obtained SSR = 45 and SSE = 155. What is R^2?
In regression output, the F-statistic tests which null hypothesis for a simple linear regression?
Which regression assumption is violated if residuals plotted against time display a clear seasonal pattern?
You run a simple regression Y on X and obtain slope b1_hat = 0.8, se(b1_hat) = 0.2, n = 25. What is the t-statistic to test H0: b1 = 0?
Which transformation yields a model where the slope approximates an elasticity (percent change in Y per percent change in X)?
If residuals of a regression are not normally distributed but the sample size is very large, what does the chapter recommend regarding inference?
Which of the following is an advantage of cluster sampling relative to simple random sampling?
An analyst computes sample correlation r = 0.3 with n = 12. Using t = r sqrt((n - 2)/(1 - r^2)), what is the approximate t-statistic (round to two decimals)?
Which of the following correctly describes the jackknife resampling method?
If a regression's residuals have a mean not equal to zero, what does the chapter say about that result?
Which of these is a correct expression for the standard error of the forecast for a new Xf in SLR (prediction standard error)?
Which functional transformation would you try if plotting Y versus X shows curvature suggesting exponential growth of Y?
Which of the following is TRUE about the relationship between the t-test for slope and the F-test of overall fit in a simple linear regression?
Which of the following best describes the purpose of a paired (dependent) samples t-test?
A contingency table has 4 rows and 3 columns. What are the degrees of freedom for the chi-square test of independence?
Which statement about the bootstrap and jackknife methods is consistent with the chapter?
You conduct a chi-square test of independence on a 3x3 contingency table and obtain chi-square statistic = 12.5. The critical value at alpha = 0.05 with df = 4 is 9.49. What is your decision?
When is the pooled variance estimator used in two-sample t-tests?
You construct a 95 percent prediction interval for an SLR forecast and find it wide. According to the chapter, which factor would contribute MOST to the interval width?
Which of the following is an example of non-probability sampling?
When comparing means for two dependent samples, which distribution does the test statistic follow under normality assumptions?
An analyst performs stratified sampling with k strata and samples proportional to stratum sizes. Which effect does stratification typically have compared with simple random sampling of the same overall sample size?
Which of the following best describes the p-value reported by software for a regression coefficient?
Which of the following is NOT an advantage of bootstrap resampling mentioned in the chapter?
If you want to test whether two categorical classifications are independent using a sample of 1,000 observations in a 2x3 table, which test and degrees of freedom are appropriate?
Which diagnostic plot is most helpful to detect heteroskedasticity in a regression model?
Which of these is a correct interpretation of an R^2 value of 0.80 in a simple linear regression of ROA on CAPEX, as illustrated in the chapter example?