# UCD Multiple Regression Population Variance T Test & F Test of Size on Cost Exam Practice

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Economics

University College Dublin

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The cost of attending your college has once again gone up. One of the administrators at UCI does not make the situation better by telling you that you pay more because the reputation of UCI is better than that of others. To investigate this hypothesis, you collect data randomly for 125 national universities from the 2000-2001 U.S. News and World Report annual rankings. You estimate the following regression Cost = a+b1 Reputation-b2Size+u. Here is the estimated regression: Cost=7,311+3,880 Reputation-0.21 Size (1,985) (600) (0.07) R?=0.62, n=125 where Cost is Tuition, Fees, Room and Board in dollars, Reputation is the index used in U.S. News and World Report, which ranges from 1 ("marginal") to 5 ("distinguished"), Size is the number of undergraduate students. The number in parentheses are standard errors. (5 points) What is the 95% confidence interval for the coefficient of Reputation? Please use the critical value 1.96. Is the estimated coefficient of Reputation significant at the 5% level based on the confidence interval? Justify your answer based on the calculated confidence interval. B I S Ix E : X х, x? Insert Formula Consider the multiple regression Y= a +B1X1 + B2X2 + u. When omitting X2 from the regression, then there will be omitted variable bias for By + A. if X1 and X2 are correlated and B1 90. B. if X1 and X2 are correlated and B2 = 0. O C. if X1 and X2 are correlated and B2+0. D. if X2 and Y are correlated and B2+0. Multicollinearity A. violates one of the Least Squares assumptions in a multiple regression model. B. implies that it will be difficult to estimate precisely one or more of the partial effects (the standard error for OLS estimators will be large, but the OLS estimators can still be unbiased). C. means that you cannot compute the OLS estimator for the regression coefficients. D. will lead to biased estimates of the regression coefficients. Suppose you are interested in estimating how class size affects learning and performance, you estimate TestScore=a+By ClassSize+B2 SAT+B3 HSperc+u. Suppose that accidentally you include in your regression student ID number, which is irrelevant. Which of the following is true? A. Adjusted R? wiill increase. B. R2 will increase. OC. R? will decrease. D. R2 will be greater than 1. The population relationship between household food expenditure, household income and household size is given by log(FoodExpenditure)=a+By log(HH_Income)+B2HH_Size+u. Suppose you are interested in estimating this population relationship. In which of the following cases OLS estimators of B1 and B2 will be biased, assuming what's described is the only problem? A. The variance of u is large. B. log(HH_Income) and HH_Size are correlated, but they are not perfectly correlated. C. The variance of u is correlated with HH_Size. OD. The mean of u depends on HH_Size.
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