A key assumption for the identification of the ceteris paribus effect in a multiple linear regression model, Yt = XtB+ €t Homoskedasticity: Zero unconditional mean: Zero conditional mean: Simple random samplin: V (€₂) = 0² E(et |Xt) = 0 E(et| Xt) = 0 Cov(Et, Es) = 0
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- Consider the following regression model and corresponding output for a dataset with n = 104 observations: y=ß₁+ß2x2+ß³¸*¸+4 3 4x4+u Variable β Std. Error t P>|t| X2 -0.012 0.006 -2.289 0.022 X3 0.596 0.014 41.139 0.000 X4 0.52 1.06 Constant 8.860 1.766 5.017 0.000 What is the marginal effect of x4 on y? (approximate at least to 3 decimal places)A key assumption for the identification of the ceteris paribus effect in a multiple linear regression model, Yt = XtB + Et Homoskedasticity: Zero unconditional mean: Zero conditional mean: Simple random samplin: V (et) = 0² E(et |Xt) = 0 E(et | Xt) = 0 Cov(Et, Es) = 0Consider 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.
- True or False For a linear regression model including only an intercept, the OLS estimator of that intercept is equal to the sample mean of the independent variable.Consider the polynomial regression model Yį = ßo + B₁X; + ß₂X² + uį, which of the following is true? This is a second-degree polynomial regression model This is a simple regression model because there is only one explanatory variable OLS is problematic in estimating the parameters due to the multicollinearity problem All the parameters (B's) must have the same signGiven the following regression output, Predictor Coefficient SE Coefficient t p-value Constant 84.998 1.863 45.62 0.000 x1 2.391 1.200 1.99 0.051 x2 -0.409 0.172 -2.38 0.021 Analysis of Variance Source DF SS MS F p-value Regression 2 77.907 38.954 4.138 0.021 Residual Error 62 583.693 9.414 Total 64 661.600 answer the following questions: d-1. State the decision rule for 0.05 significance level: H0: β1 = β2 = 0; H1: Not all β's are 0. (Round your answer to 2 decimal places.) d-2. Compute the value of the F statistic. (Round your answer to 2 decimal places.) d-3. What is the conclusion? Use the 0.05 significance level.
- Given the following regression output, Predictor Coefficient SE Coefficient t p-value Constant 84.998 1.863 45.62 0.000 x1 2.391 1.200 1.99 0.051 x2 -0.409 0.172 -2.38 0.021 Analysis of Variance Source DF SS MS F p-value Regression 2 77.907 38.954 4.138 0.021 Residual Error 62 583.693 9.414 Total 64 661.600 answer the following questions: Write the regression equation. (Round your answers to 3 decimal places. Negative values should be indicated by a minus sign.) If x1 is 4 and x2 is 11, what is the expected or predicted value of the dependent variable? (Round your answer to 3 decimal places.) How large is the sample? How many independent variables are there?In the linear model ,E (X*u) = a)X*u b) 0 c) u d) none of tha aboveSuppose the Sherwin-Williams Company has developed the following multiple regression model, with paint sales Y (x 1,000 gallons) as the dependent variable and promotional expenditures A (x $1,000) and selling price P (dollars per gallon) as the independent variables. Y=α+βaA+βpP+εY=α+βaA+βpP+ε Now suppose that the estimate of the model produces following results: α=344.585α=344.585, ba=0.102ba=0.102, bp=−11.192bp=−11.192, sba=0.173sba=0.173, sbp=4.487sbp=4.487, R2=0.813R2=0.813, and F-statistic=11.361F-statistic=11.361. Note that the sample consists of 10 observations. 1.) According to the estimated model, holding all else constant, a $1,000 increase in promotional expenditures decrease or increase sales by approximately 102,813 or 11,192 gallons. Similarly, a $1 increase in the selling price decrease or increase sales by approximately 813,11,192 or 102 gallons. 2.)Which of the independent variables (if any) appears to be statistically significant (at the 0.05…
- Refrigerator prices are affected by characteristics such as whether or not the refrigerator is on sale, whether or not it is listed as a Sub- Zero brand, the number of doors (one door or two doors), and the placement of the freezer compartment (top, side, or bottom). The table below shows the regression output from a regression model using the natural log of price as the dependent variable. The model was developed by the Bureau of Labor Statistics. Variable Coefficient Standard Error t Statistic 5.4841 Intercept 0.13081 41.92 Sale price -0.0733 0.0234 -3.13 Sub-Zero brand 1.1196 0.1462 7.66 0.06956 0.005351 13.00 Total capacity (in cubic feet) Two-door, freezer on bottom Two-door, side freezer 0.04657 0.08085 0.58 Two-door, freezer on top 0.03596 -9.55 Base -0.3432 -0.7096 -0.8820 One door with freezer 0.1310 -5.42 -5.92 One door, no freezer 0.1491 (a) Write the regression model, being careful to exclude the base indicator variable. (Negative amounts should be indicated by a minus…Which one of the following statements is true for a linear regression model with non-spherical disturbances (i.e. E(uu') = Ω): The GLS estimator covariance matrix is unreasonable. The OLS estimator is not consistent. The standard formula for the OLS estimator covariance matrix is incorrect. The GLS estimator is not consistent. All of the above. None of the above.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.