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##### Math104 - Fall ?14

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Question;Math 104 - Fall ?14;Applied Regression Analysis;Lab Assignment #8: Model Building;Due: November 17, 2014;Name;ID#;Department of Mathematics;GOLDEN GATE UNIVERSITY;[1] A research analyst for an oil company;wants to develop a model to predict miles per gallon based on highway;speed. An experiment is designed in;which a test car is driven at speeds ranging from 10 miles per hour to 75 miles;per hour. The results are in the data set;(SPEED.xls).;a);Set;up a scatter diagram for speed and miles per gallon.;b);Apply;simple regression analysis, and then interpret the meaning of the slope b1 in this problem.;c);Interpret;the meaning of the regression coefficientb0 in this problem.;d);Determine;the coefficient of determination,r2, and interpret its meaning.;e);How;useful do you think this regression model is for predicting mileage?;[2] Refer to the data set given in [1]. Now assume a quadratic relationship between;speed and mileage;a);State;the quadratic regression equation.;b);Predict;the average mileage obtained when the car is driven at 55 miles per hour.;c);Determine;the coefficient of multiple determination,r2.;d);Determine;the adjustedr2.;e);Determine;the adequacy of the fit of the model.;f);At;the 0.05 level of significance, determine whether the quadratic model is a;better fit than the linear regression model.;[3] An auto manufacturing company wanted to;investigate how the price of one of its car models depreciates with age. The research department at the company took a;sample of eight cars of this model and collected the following information on;the ages (in years) and prices (in hundreds of dollars) of these cars. The data are in USEDCAR.xls.;Age (x);8;3;6;9;2;5;6;3;Price (y);16;74;40;19;124;36;33;89;a);Set;up a scatter diagram for age and price.;b);At;the 0.05 level of significance, determine whether there is a significant linear;relationship between age and price.;c);State;the linear regression equation.;d);Predict;the average price obtained when the age of the car is 7 years old.;e);Determine;the coefficient of determination,r2, and interpret its meaning.;f);How;useful do you think this regression model is for predicting price?;[4] Refer to the data set given in [3]. Now assume a quadratic relationship between age;and price;a);State;the quadratic regression equation.;b);Predict;the average price obtained when the age of the car is 7 years old.;c);Determine;the coefficient of multiple determination,r2.;d);Determine;the adjustedr2.;e);Determine;the adequacy of the fit of the model.;f);At;the 0.05 level of significance, determine whether the quadratic model is a;better fit than the linear regression model.;[5];Refer to the data set given in [3].;Perform a natural or common logarithmic transformation of the dependent;variable (price).;a);State;the regression equation.;b);Predict;the average price obtained when the age of the car is 7 years old.;c);Determine;the coefficient of multiple determination,r2.;d);Determine;the adjustedr2.;e);Determine;the adequacy of the fit of the model.;f);Compare;your results in [3], [4], and [5]. Which;model is best? Why?

Paper#60392 | Written in 18-Jul-2015

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