Suppose you want to test whether X₂ and X3 can jointly explain Y in the following regression model: Y = Bo + B₁X₁ + B₂X₂ + ß3X3 + u You obtain data for 85 observations and conduct a joint test of significance at 1% level. Your restricted model is given by, OY = Bo + B3X3 + u OY = Bo + B₁X₁ + B3X3 + u OY = Bo + B₁ X₁ + u OY = Bo + u
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- The table below shows the parameters for four multiple linear regression bridge deterioration models. The full model has age as continuous independent variable, traffic (Average Daily Traffic (ADT)) and bridge design as categorical variables. The bridge design is expressed as codes “H’ or “HS” for a single-unit truck and a tractor pulling a semitrailer respectively. The numeric suffix represents the gross weight in tons for H truck or weight on the first two axle sets of the HS truck. For example, H_10 denotes a truck with a gross work of 10 tons. The table also contains the following model validation indicators: adjusted r-squared, Akaike’s Information Criteria (AIC), Mean Absolute Error (MAE) and Bayesian Information Criteria (BIC). Write the multiple regression equation for each of the four models and comment on the accuracy of prediction of bridge deterioration of each model.The table below shows the parameters for four multiple linear regression bridge deterioration models. The full model has age as continuous independent variable, traffic (Average Daily Traffic (ADT)) and bridge design as categorical variables. The bridge design is expressed as codes “H’ or “HS” for a single-unit truck and a tractor pulling a semitrailer respectively. The numeric suffix represents the gross weight in tons for H truck or weight on the first two axle sets of the HS truck. For example, H_10 denotes a truck with a gross work of 10 tons. The table also contains the following model validation indicators: adjusted r-squared, Akaike’s Information Criteria (AIC), Mean Absolute Error (MAE) and Bayesian Information Criteria (BIC). Which model is the best predictor model, give logical justification for your answer. Discuss how these models are utilized in Highway Asset management.The administration of a midwestern university commissioned a salary equity study to help establish benchmarks for faculty salaries. The administration utilized the following regression model for annual salary, y : ?(?) β0+β1x ,where ?=0 if lecturer, 1 if assistant professor, 2 if associate professor, and 3 if full professor. The administration wanted to use the model to compare the mean salaries of professors in the different ranks. a) Explain the flaw in the model. b)Propose an alternative model that will achieve the administration’s objective. c) If the global F-test for the model you proposed in 2 is conducted, what would be the value of the numerator degrees of freedom?
- We expect a car's highway gas mileage to be related to its city gas mileage (in miles per gallon, mpg). Data for all 12591259 vehicles in the government's 2019 Fuel Economy Guide give the regression line highway mpg=8.720+(0.914×city mpg)highway mpg=8.720+(0.914×city mpg) for predicting highway mileage from city mileage. (c) Find the predicted highway mileage, ?̂ ,�^, for a car that gets 1212 mpg in the city. Give your answer to three decimal places. ?̂ =�^= mpg Find the predicted highway mileage, ?̂ ,�^, for a car that gets 2222 mpg in the city. Give your answer to three decimal places. ?̂ =�^= mpgWe expect a car's highway gas mileage to be related to its city gas mileage (in miles per gallon, mpg). Data for all 12591259 vehicles in the government's 2019 Fuel Economy Guide give the regression line highway mpg=8.720+(0.914×city mpg)highway mpg=8.720+(0.914×city mpg) for predicting highway mileage from city mileage. (b) What is the intercept? Give your answer to three decimal places. intercept:Identify two different conditions under which the regression line should not be used to make predictions.
- A consumer advocacy group recorded several variables on 140 models of cars. The resulting information was used to produce two models for predicting miles per gallon in the city (mpg_city), one based on the engine displacement (in cubic inches) and a second one based the power of the engine (in horsepower). Model 1: mpg vs engine displacement The regression equation is mpg_city=33.8 - 0.0622*displacement S = 3.10179 R-squared = 66.9% Model 2: mpg vs horsepower The regression equation is mpg_city=32.4 - 0.0579*horsepower S = 3.30296 R-squared = 52.9% The variable horsepower is better because it has a higher residual standard error (S=3.30296) and a lower R-square (52.9%). The displacement variable is better because it has a higher R-square (66.9%). (C) The variable horsepower is better because it has a higher residual standard error (S=3.30296).A study was conducted on 64 female college athletes. The researcher collected data on a number of variables including percent body fat, total body weight, height, and age of athlete. The researcher wondered if % body fat (%BF), height (HGT), and/or age are significant predictors of total body weight. All conditions have been checked and are met and no transformations were needed. The technology output from the multiple regression analysis is given below. Interpret the coefficient of % body fatSuppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.72, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 72000 and the sum of squared errors (SSE) is 28000. From this information, what is MSE/MST? (a) .4000 (b) .3000 (c) .5000 (d) .2000 (e) NONE OF THE OTHERS
- The marketing manager wants to estimate the effect of the MBA program on Salary controlling for the other factors. Which regression model is the MOST appropriate? Oa. Salary = B_0+B_1 MBA + ε Ob. Salary = 3_0+ B_1 MBA + B_2 Work + e c. Salary = B_0+B_1 MBA+B_2 Work + B_3 Age +8 Od. Salary = B_0+ B_1 MBA + B_2 Work + B_3 Age +B_4 Gender + εWe expect a car’s highway gas mileage to be related to its city gas mileage (in mpg). Data for all 12091209 vehicles in the government’s 2016 Fuel Economy Guide give the regression line highway mpg=7.903+(0.993×city mpg)highway mpg=7.903+(0.993×city mpg) for predicting highway mileage from city mileage. (a) What is the slope of this line? (Enter your answer rounded to three decimal places.) (b) What is the intercept? (Enter your answer rounded to three decimal places.)We expect a car’s highway gas mileage to be related to its city gas mileage (in mpg). Data for all 12091209 vehicles in the government’s 2016 Fuel Economy Guide give the regression line highway mpg=7.903+(0.993×city mpg)highway mpg=7.903+(0.993×city mpg) for predicting highway mileage from city mileage. (a) What is the slope of this line? (Enter your answer rounded to three decimal places.) What does the numerical value of the slope tell you? On average, highway mileage decreases by 0.9930.993 mpg for each additional mpg in city mileage. On average, highway mileage increases by 0.9930.993 mpg for each additional mpg in city mileage. For every 7.9037.903 mpg in city gas mileage, highway gas mileage increases about 0.9930.993 mpg. Highway gas mileage increases with city gas mileage by 7.9037.903 mpg for each additional mpg in city mileage. On average, highway mileage increases by 7.9037.903 mpg for each additional mpg in city mileage. (b) What is the intercept?…
