Explain in detail the approach of Weighted Least Square used by applied economists to address heteroskedasticity in empirical work.
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Explain in detail the approach of Weighted Least Square used by applied economists
to address heteroskedasticity in empirical work.
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- 3. A Ross MAP team is trying to estimate the revenues of major-league baseball teams during the regular season using a regression model. Currently, the independent variables include stadium capacity, the number of weekend games, the number of night games, and the number of Wins (out of 162 regular season games). One of your team members suggests that the model also should include the number of losses as it provides additional explanatory power. Assume that ties are not possible; so every game results in exactly one team winning and the other team losing. Which of the following statements is the most likely conclusion of the new regression model? (a) R2 will increase, adjusted R2 will decrease, and Serror will decrease. (b) R2 and adjusted R2 will increase, and serror will decrease. (c) R, adjusted R2, and Serror will increase. (d) We cannot trust the regression output as some variables are highly correlated, resulting in multicollinearity. Answer to Question 3:8a) A researcher aims to assess the associative impact of coffee consumption on death rates from heart diseases. For this objective the researcher collects data from 10 countries and intends to use methods of regression. The following table shows data on average per capita coffee consumption and heart disease rate in a random sample of 10 countries. a) State which of the given variables is the outcome variable. b) Provide a scatterplot for the objective of interest using R software, and state if a simple quadratic regression model would be suitable for this data. c) Perform the simple quadratic regression modeling using R software. Provide the fitted model equation and interpret the intercept (if any).True or False: In a model with an interaction variable, we can drop the interaction term if its pvalue>.05
- Determine the heteroscedasticity in a scatter plot?4. We would like to determine how a man's weight can be used to predict his systolic blood pressure. We measure the weights (in pounds) and the systolic blood pressures of a sample of 17 men. The data are plotted on a scatterplot and it can be seen that a linear relationship is a reasonable assumption. The least squares regression line is calculated to be ŷ = 125.561 + 0.145x. The ANOVA table (with some values missing) is shown below: |Source of Variation | df | Sum of Squares Mean Square F Regression Error Total 26.46 617.82 (a) We would like to test whether a linear relationship exists between a man's weight and his systolic blood pressure. We will conduct an analysis of variance to test Ho: B1 = 0 vs. Ha: B1 + 0 at the 5% level of significance. Enter all missing values in the ANOVA table. Calculate the value of the test statistic, find the P-value of the test and provide a properly worded conclusion. (b) What is the value of the correlation between weight and systolic blood pressure…The article "A Robust Optimization Approach for the Capacitated Vehicle Routing Problem with Demand Uncertainty" (I. Sungur, F. Ordonez, and M. Dessouky, IIE Transactions, 2008:509-523) discusses methods to reduce transportation costs while satisfying demands. In one study, the percent demand that is unmet (y) and the percent of vehicle capacity (x) needed to meet the expected demand were recorded for 27 different scenarios. The results are presented in the following table. х У 0.5 82 0.0 0.7 1.3 0.8 11 0.9 1.2 1.3 0.2 0.8 1.4 0.9 1.4 0.4 1.7 93 11 93 0.8 90 0.3 0.2 1.0 1.0 89 1.0 93 1.3 91 1.3 94 1.2 94 0.7 Compute the least-squares line for predicting unmet demand (y) from vehicle capacity (X). b. Compute 95% confidence intervals for B, and B,- Predict the unmet demand when the vehicle capacity is 93%. d. a. c. Find a 95% confidence interval for the mean unmet demand when the vehide capacity is 93%. Find a 95% prediction interval for the unmet demand for a scenario whose vehicle…
- 16. A scatterplot of the monthly salary (in thousands of pesos) versus years of education for seven full-time workers is displayed below. The least- squares regression line is drawn on the plot. Six of the data points are plotted with open circles and the seventh is plotted with a solid circle. The data point plotted with a solid circle to 20 Ne stynan eftdutatien A. has a large residual and is influential. B. has a small residual and is influential. C. has a large residual and is not infiluential. D. has a small residual and is not influential. 00 09 oad jo umroy sTrue or false: a) For any set of data, there is always one best model. b) When there is no physical theory to specify a model, there is usually no best model, but many that are about equally good. c) Model selection methods such as best subsets and stepwise regression, when properly used, are scientifically designed to find the best available model. d) Model selection methods such as best subsets and stepwise regression, when properly used, can suggest models that fit the data well.A random sample of 104 marketing vice presidents from large Fortune 500 corporations was questioned on future developments in the business environment. Of those sample members, 50 indicated some measurement of agreement with this statement: Firms will concentrate their efforts more on cash flow than on profits. What is the lowest level of significance at which the null hypothesis, which states that the true proportion of all such executives who would agree with this statement is one-half, can be rejected against a two-sided alternative?
- Suppose a new production method will be implemented if a hypothesis test supports theconclusion that the new method reduces the mean operating cost per hour.a. State the appropriate null and alternative hypotheses if the mean cost for the currentproduction method is $220 per hour.b. what is the type i error in this situation? what are the consequences of making this error?c. what is the type ii error in this situation? what are the consequences of making this error?A recent survey conducted by Gallup (an analytic and advice firm) estimated that 50% of students in Massachusetts prefer learning full-time in person, while the remaining 50% prefer a full-time remote or a hybrid arrangement. Suppose we assume that, among UCI students, the proportion of those who prefer learning full-time in person instruction is the same as that estimated by Gallup for Massachusetts. We interview a random sample of 70 USC students regarding their preferences over full-time in person versus remote/hybrid instruction. a. Under our assumption that the preferences of USC students are the same as those estimated by Gallup for Massachusetts, what is the exact distribution of the number of interviewed students who prefer full-time in person instruction over remote/hybrid arrangements? b. Under our assumption that the preferences of UCI students are the same as those estimated by Gallup for Massachusetts, what is the exact probability that the number of interviewed students…If there is a significant interaction in a factorial design, why do researchers typically ignore (or minimize the importance of) the main effects?
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