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- In terms of the model parameters, state the null hypothesis that, after controlling for sales and roe, ros has no effect on CEO salary. State the alternative that better stock market performance increases a CEO’s salary.The line of best fit through a set of data is y=29.267+0.881xAccording to this equation, what is the predicted value of the dependent variable when the independent variable has value 60?y =An industrial concern has experimented with several different mixtures of the fourcomponents—magnesium, sodium nitrate, strontium nitrate, and a binder—that comprise arocket propellant. The company has found that two mixtures, in particular, give higher flare illumination values than the others. Mixture 1 consists of a blend composed of the proportions.40, .10, .42, and .08, respectively, for the four components of the mixture; mixture 2 consists ofa blend using the proportions .60, .25, .10, and .05. Twenty different blends (10 of each mixture)are prepared and tested to obtain the flare-illumination values. These data appear here (in unitsof 1,000 candles).Mixture 1 185 192 201 215 170 190 175 172 198 202Mixture 2 221 210 215 202 204 196 225 230 214 217a. Plot the sample data. Which test(s) could be used to compare the meanillumination values for the two mixtures?b. Give the level of significance of the test and interpret your findings
- What type of experiement is typically used to estimate the parameters of the model? y = b0 +b1x1+b2x2+b12x1x2+b3x21+b4x22 1- traditional experimentation, process variables x1 and x2 take on just 2 different values. 2- structured experiement where variables x1 and x2 take on at least 3 different values 3- expereiment where all combinations of the process variables x 1 and x2 are considered but when x1 and x2 have only two different valuesAt the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that z − u = 3(x − y) + 12 x + y = 44 + z + u and x − y + z − u = 36. How large was the audience of each of the four companies at the end of that year? Microsoft million Time Warner million Yahoo million Google millionAt the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that z − u = 3(x − y) + 22 x + y = 50 + z + u and x − y + z − u = 58. How large was the audience of each of the four companies at the end of that year? Microsoft Time Warner Yahoo Google
- At the end of a certain year, the four companies with the largest number of home Internet users in the United States were Microsoft, Time Warner, Yahoo, and Google, with a combined audience of 284 million users. Taking x to be the Microsoft audience in millions, y the Time Warner audience in millions, z the Yahoo audience in millions, and u the Google audience in millions, it was observed that z − u = 3(x − y) + 10 x + y = 50 + z + u and x − y + z − u = 46. How large was the audience of each of the four companies at the end of that year?The demand for a commodity is given by Q = β0 + β1P + u, whereQ denotes quantity, P denotes price, and u denotes factors other thanprice that determine demand. Supply for the commodity is given byQ = ϒ0 + ϒ1P + v, where v denotes factors other than price that determinesupply. Suppose that u and v both have a mean of zero, have variancesσ2u and σ2v, and are mutually uncorrelated.a. Solve the two simultaneous equations to show how Q and P dependon u and v.b. Derive the means of P and Q.c. Derive the variance of P, the variance of Q, and the covariancebetween Q and P.d. A random sample of observations of (Qi, Pi) is collected, and Qi isregressed on Pi. (That is, Qi is the regressand, and Pi is the regressor.)Suppose that the sample is very large. i. Use your answers to (b) and (c) to derive values of the regressioncoefficients. ii. A researcher uses the slope of this regression as an estimate of theslope of the demand function (β1). Is the estimated slope too largeor too small?The owner of the ABC Restaurant would like to determine the fixed and variable components of the restaurant's utility expenses. The owner believes that the variable component of the utilities cost is driven by the number of meals served. Meals Utilities served CostJanuary 3,600 P1,560February 2,000 P1,060March 2,900 P1,350April 3,500 P1,500May 3,900 P1,580June 2,100 P1,250July 1,900 P1,100August 1,000 P 850September 1,250 P 990October 1,400 P 880November 2,600 P1,180 Required:Compute the expected utilities cost if 5,200 meals are served, using: 1) THE HIGH-LOW METHOD ANALYSIS 2) USING THE LEASE-SQUARES REGRESSION METHOD.
- The owner of the ABC Restaurant would like to determine the fixed and variable components of the restaurant's utility expenses. The owner believes that the variable component of the utilities cost is driven by the number of meals served. Meals Utilities served CostJanuary 3,600 P1,560February 2,000 P1,060March 2,900 P1,350April 3,500 P1,500May 3,900 P1,580June 2,100 P1,250July 1,900 P1,100August 1,000 P 850September 1,250 P 990October 1,400 P 880November 2,600 P1,180 Compute the expected utilities cost if 5,200 meals are served, using:The Lease - Squares Regression MethodSuppose that in a research it was discovered that those who majored in math, engineering, or computer science scored higher on tests measuring "problem-solving" ability at the end of 4 years of college than did those students who did not major in these fields. A. What is (are) the independent variable(s)?Imagine a predator–prey interaction in which a certain number of the prey population cannot be eaten because of a refuge in their environment that the predator cannot enter. a. Why might interaction terms like −s(P − w)Q and v(P − w)Q be reasonable in the modeling equations? Explain what those interaction terms mean? b. What is the meaning of w? (What does the variable stand for?) c. In a biologically realistic model, can P < w? Why or why not?