Exam 18: Model Building

Senior Medical Students A professor of Anatomy wanted to develop a multiple regression model to predict the students' grades in her fourth-year medical course.She decides that the two most important factors are the student's grade point average in the first three years and the student's major.She proposes the model y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε,where y = Fourth-year medical course final score (out of 100),x₁ = G.P.A.in first three years (range from 0 to 12),x₂ = 1 if student's major is medicine and 0 if not,and x₃ = 1 if student's major is biology and 0 if not.The computer output is shown below. THE REGRESSION EQUATION IS y = 9.14 + 6.73x₁ + 10.42x₂ + 5.16x₃ S = 15.0 R−Sq = 44.2% ANALYSIS OF VARIANCE ​ ​ -{Senior Medical Students Narrative} Do these results allow us to conclude at the 1% significance level that on average biology majors outperform those whose majors are not medical or biology?

In regression analysis,indicator variables are also called dependent variables.

In the first-order model ,a unit increase in x₁,while holding x₂ constant at a value of 2,decreases the value of y on average by 8 units.

The model y = β₀ + β₁x + β₂x² + ε is referred to as a:

In general,to represent a nominal independent variable that has m possible categories,we must create:

Incomes of Physicians An economist is analyzing the incomes of physicians (general practitioners,surgeons,and psychiatrists).He realizes that an important factor is the number of years of experience.However,he wants to know if there are differences among the three professional groups.He takes a random sample of 125 physicians and estimates the multiple regression model y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε,where y = annual income (in $1,000),x₁ = years of experience,x₂ = 1 if physician and 0 if not,and x₃ = 1 if surgeons and 0 if not.The computer output is shown below. THE REGRESSION EQUATION IS y = 71.65 + 2.07x₁ + 10.16x₂− 7.44x₃ S = 42.6 R−Sq = 30.9% ANALYSIS OF VARIANCE ​ ​ -{Incomes of Physicians Narrative} Estimate the annual income for a surgeon with 15 years of experience.

We interpret the coefficients in a multiple regression model by holding all variables in the model constant.

At each step of the stepwise regression procedure,the p-values of all variables are computed and composed to the F-to-remove.If a variable's F-statistic falls below this standard,it is removed from the equation.

It is possible to include nominal variables in a regression model.This is accomplished through the use of ____________________ variables,also known as ____________________ variables.

Which of the following is not an advantage of multiple regression as compared with analysis of variance?

Computer Training Consider the following data for two variables,x and y.The independent variable x represents the amount of training time (in hours)for a salesperson starting in a new computer store to adjust fully,and the dependent variable y represents the weekly sales (in $1000s). Use statistical software to answer the following question(s). ​ ​ -{Computer Training Narrative} Develop a scatter diagram for the data.Does the scatter diagram suggest an estimated regression equation of the form ? Explain.

In the first-order regression model ,a unit increase in x₁ increases the value of y on average by 6 units.

If the probability of an event is .20,then the odds ratio in favor of the event occurring is expressed as

The graph of the model is shaped like a straight line going upwards.

An indicator variable can assume either one of only two values (usually 0 and 1),where _______________ represents the existence of a certain condition and _______________ indicates that the condition does not hold.

Suppose that we want to model the randomized block design of the analysis of variance with,say,one nominal variable with three categories and one nominal variable with four categories.We would create:

Incomes of Physicians An economist is analyzing the incomes of physicians (general practitioners,surgeons,and psychiatrists).He realizes that an important factor is the number of years of experience.However,he wants to know if there are differences among the three professional groups.He takes a random sample of 125 physicians and estimates the multiple regression model y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε,where y = annual income (in $1,000),x₁ = years of experience,x₂ = 1 if physician and 0 if not,and x₃ = 1 if surgeons and 0 if not.The computer output is shown below. THE REGRESSION EQUATION IS y = 71.65 + 2.07x₁ + 10.16x₂− 7.44x₃ S = 42.6 R−Sq = 30.9% ANALYSIS OF VARIANCE ​ ​ -{Incomes of Physicians Narrative} Estimate the annual income for a general practitioner with 15 years of experience.

Senior Medical Students A professor of Anatomy wanted to develop a multiple regression model to predict the students' grades in her fourth-year medical course.She decides that the two most important factors are the student's grade point average in the first three years and the student's major.She proposes the model y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε,where y = Fourth-year medical course final score (out of 100),x₁ = G.P.A.in first three years (range from 0 to 12),x₂ = 1 if student's major is medicine and 0 if not,and x₃ = 1 if student's major is biology and 0 if not.The computer output is shown below. THE REGRESSION EQUATION IS y = 9.14 + 6.73x₁ + 10.42x₂ + 5.16x₃ S = 15.0 R−Sq = 44.2% ANALYSIS OF VARIANCE ​ ​ -{Senior Medical Students Narrative} Do these results allow us to conclude at the 1% significance level that on average medical majors outperform those whose majors are not medical or biology?

Senior Medical Students A professor of Anatomy wanted to develop a multiple regression model to predict the students' grades in her fourth-year medical course.She decides that the two most important factors are the student's grade point average in the first three years and the student's major.She proposes the model y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε,where y = Fourth-year medical course final score (out of 100),x₁ = G.P.A.in first three years (range from 0 to 12),x₂ = 1 if student's major is medicine and 0 if not,and x₃ = 1 if student's major is biology and 0 if not.The computer output is shown below. THE REGRESSION EQUATION IS y = 9.14 + 6.73x₁ + 10.42x₂ + 5.16x₃ S = 15.0 R−Sq = 44.2% ANALYSIS OF VARIANCE ​ ​ -{Senior Medical Students Narrative} Interpret the coefficient b₂.

If two indicator variables are used in a logistic regression model,then the nominal variable they represent has only two categories.