In the regression model Y, =a, +aX, +a,D, +a,(X, *D,)+ X is a continuous variable and D is dummy variable. To test that the two regressions are identical, you must use the a. t-statistics separately for az=0, az=0, b. t-statistics separately for az=0 C. F-statistics for the joint hypothesis that ao=0, a;=0 d. F-statistics for the joint hypothesis that az=0, a=0
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- You have data on the training regime of 100m elite runners. For each runner you observe their best run of the year (in second) (pb), the number of hours they train each week (tr) and a dummy variable equal to 1 if thei are male (male). Using OLS you get the following regression: pb= 36.2 1.3male -0.92tr +0.009tr² -0.09male tr +0.001male * (tr²) How many hours should a male elite runner train each week to minimize the time of their best run of the year? (round to the closest decimal)Consider a linear causal model Ya+BX+yW+u, with cov(X, W) > 0. Suppose we do not observe the variable W and have to omit it from the regression, then O OLS is expected to be larger than 3 in large samples. BOLS is expected to be equal to 3 in large samples. OLS is expected to be smaller than 3 in large samples. Since we do not know whether X and u are correlated and the sign of y, there is not enough information to compare OLS and B.Consider the regression model Yi=bot Bi Xitui Suppose that you know Bo = 0. Derive the formula for the least squares estimator of B₁. The least squares objective function is O A. n O B. O C. O D. E (Yi-bo-b1Xi) i=1 n Σ (Yi-bo-biXi) i=1 2 n Σ (v₁²-bo-b₁x₁²) i=1 n E (Yi-bo-b+Xi) 3 i=1
- Consider the regression model Yi = b0 + b1X1i + b2X2i + ui. Use approach 2from Section 7.3 to transform the regression so that you can use a t-statistic to testa. b1 = b2.b. b1 + 2b2 = 0.c. b1 + b2 = 1. (Hint: You must redefine the dependent variable in theregression.)C. "If two series are cointegrated, it is not possible to make inferences regarding the cointegrating relationship using the Engle-Granger technique since the residuals from the cointegrating regression are likely to be autocorrelated." How does Johansen circumvent this problem to test hypotheses about the cointegrating relationship? D. Compare the Johansen maximal eigenvalue test with the test based on the trace statistic. State clearly the null and alternative hypotheses in each case.A. B. Consider data on births to women in the United States. Two variables of interest are the dependent variable, infant birth weight in ounces (bwght), and an explanatory variable, average number of cigarettes the mother smoked per day during pregnancy (cigs). The following simple regression was estimated using data on n = 1,388 births: bwght = 119.772 (0.572) n = 1,388, 0.514 cigs (0.091) R² = 0.0227, where standard errors are shown in parenthesis. What percent of the variation in birth weight is explained by cigs? What is the predicted birth weight when cigs = 0? What about when cigs = 20 (one pack per day)? Comment on the difference.
- Discuss the FIVE (5) importance of adding error term in the regression model.If in a regression, there are many variables, two of them show a square relationship (for example, A and A^2), A and A^2 show a strong positive correlation. Is there any problem with the model specificationConsider the regression model Y₁ = BX; +u; Where u; and X; satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ß = Show that ẞ is a linear function of Y₁, Y2,..., Yn. where Y and X are the sample means of Y; and X;, respectively. Show that ẞ is conditionally unbiased. 1. E (Y;|X1, X2,..., Xn) = 1 -B (X ₁ + X 2 + ... + Xn) Х answer these part correctly + ... + Y) +X₂+ ... + Xn) = B 2. E (B|×₁, ×2,..., Xn) = E | (X1, X2,..., Xn) BX; ☑ BX BY
- Consider the IV regression model Yi = β0 + β1Xi + β2Wi + ui, where Xi is correlated with ui and Zi is an instrument. Suppose that the first three assumptions in Key Concept (The IV Regression Assumptions) are satisfied. Which IV assumption is not satisfied whena) Zi is independent of (Yi, Xi, Wi)?b) Zi=Wi?c) Wi is1 for all i?d) Zi=Xi?Consider the following regression model where Suppose and are highly (but not perfectly) correlated. Then, a. b. C. d. e. OLS estimators are biased. OLS estimators are not consistent. OLS estimators will have large standard errors. One of,, or the constant should be dropped. cannot be interpreted as the population intercept.Past class data has shown that the regression line relating the final exam score and the midterm exam score for students who take statistics from the College of Information Technology and Engineering from Dr. Kalaw is: final exam = 50 + 0.5 × midterm One interpretation of the slope is a. students only receive half as much credit (.5) for a correct answer on the final exam compared to a correct answer on the midterm exam. b. a student who scored 0 on the midterm would be predicted to score 50 on the final exam. c. a student who scored 10 points higher than another student on the midterm would be predicted to score 5 points higher than the other student on the final exam. d. a student who scored 0 on the final exam would be predicted to score 50 on the midterm exam.