Question 27 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?

Which of the following is an effect of an outlier caused by data entry error far from the bulk of observations?

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?