Question 28 of 50

In a simple linear regression of Y on X using OLS, which expression gives the estimated slope coefficient b_hat1?

Which equality holds in a correctly estimated simple linear regression with an intercept?

If the sample correlation between X and Y in SLR is r = 0.8 and SD(X)=2 and SD(Y)=5, what is the estimated slope b_hat1 (approx)?

Which statement best describes R-squared in simple linear regression?

You estimate SLR with n = 30 and find SSE = 180. What is the standard error of the estimate se?

Which assumption is violated if residuals plotted versus X show a clear U-shaped pattern?

In testing H0: b1 = 0 versus Ha: b1 ≠ 0 in SLR with n observations, what is the degrees of freedom for the t-statistic?

If sample size n increases while sample correlation r remains fixed, what happens to the t-statistic for testing r = 0?

Which of the following changes would reduce the standard error of the slope estimate SE(b_hat1) in SLR?

In SLR, the F-statistic for testing whether the model explains variance equals:

Which diagnostic plot would best help detect heteroskedasticity in a regression model?

When residuals in a time-series regression show seasonally higher positive values every fourth quarter, which assumption is violated?

You estimate Y on X and obtain b_hat1 = 1.25, SE(b_hat1) = 0.3124, and df = 4. For a two-sided 5% test of H0: b1 = 0, the critical t is ±2.776. Which conclusion is correct?

Which change will widen a 95% prediction interval for Yhat at a specific Xf?

What is the proper interpretation of the intercept b_hat0 in SLR?

If you regress monthly returns on an indicator variable EARN that equals 1 for months with earnings announcements and 0 otherwise, what does the slope coefficient represent?

Which functional form lets you interpret the slope b1 directly as the elasticity of Y with respect to X?

You fit SLR and find one observation has unusually large X and large residual; this point is best described as:

Which remedy is appropriate if residuals show increasing spread as X increases (heteroskedasticity)?

In SLR, you observe R^2 = 0.80 and se = 3.46. Which statement is most accurate?

You estimate ln(Y) = b0 + b1 X. A one-unit increase in X leads to what approximate change in Y?

Which is true regarding p-values reported for regression coefficients?

You have SLR with estimated b_hat1=0.98 and SE(b_hat1)=0.052. Test H0: b1 = 1.0 at 5% level (two-sided). Which result is correct? (t = (0.98-1)/0.052 = -0.385).

Which statement about the ANOVA decomposition SST = SSR + SSE is correct?

You forecast Y at Xf=6 given b_hat0=4.875, b_hat1=1.25. What is Yhat?

Which of the following increases the power of the t-test for a slope coefficient in SLR?

If residuals are not normally distributed in a small sample regression, which consequence is most direct?

Which statement about prediction intervals vs. confidence intervals for mean response is true?

When comparing two nested models (Model A with only intercept, Model B with intercept and one X), which test evaluates whether X adds explanatory power?

If you estimate ln Y = 0.6 + 0.2951 FATO and SE of estimate se = 0.2631, what is interpretation of coefficient 0.2951?

An analyst finds slope p-value = 0.044 in a regression with n=6. What is correct inference at 5% level?

Which phrase best describes heteroskedasticity?

You estimate SLR for CPI forecasts: intercept 0.0001 (SE 0.0002), slope 0.9830 (SE 0.0155), n=60. Test H0: slope = 1.0 at 5% two-sided. t = (0.9830 - 1)/0.0155 ≈ -1.097. What conclusion?

Which data situation favors use of Spearman rank correlation over Pearson correlation?

You have SLR and want a prediction interval for Y at Xf. Which of these reduces width of that interval?

Which functional form would you try if scatter of Y vs X shows curvature with increasing slope (convex)?

In SLR, what does the standardized residual equal?

Which test statistic equals the t-statistic squared in simple linear regression?

When should you prefer a lin-log model (Y = b0 + b1 ln X) over lin-lin?

Which of these is a direct consequence of autocorrelated residuals in a time-series regression?

Which statistic would you compute to examine whether residuals follow a normal distribution in a small-sample regression?

You fit SLR and obtain residuals with markedly fatter tails than normal in a small sample. Best action?

Which of these is a valid form for a log-lin regression where percent-change interpretation applies?

In a time-series SLR of revenue on time, residuals show upward jump each fourth quarter. A suitable regression modification is:

Which of the following best describes the standard error of the forecast sf used in prediction intervals?

Which of these indicates a good reason to use weighted least squares (WLS)?

You test H0: b0 ≤ 3 vs Ha: b0 > 3 and calculate t_intercept = 0.79 with critical one-sided t=2.132. Which decision?

Which of these best justifies transforming variables before regression (e.g., log transform)?

Which of the following is the most important first step before trusting regression outputs?