Exam 18: Model Building

In order to represent a nominal variable with m categories,we must create m− 1 indicator variables.

In general,on what basis are independent variables selected for entry into the equation during stepwise regression?

An indicator variable (also called a dummy variable)is a variable that can assume either one of two values (usually 0 and 1),where one value represents the existence of a certain condition,and the other value indicates that the condition does not hold.

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} Find the coefficient of determination of this simple linear model.What does this statistic tell you about the model?

The model y = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₂ + ε is referred to as a:

Silver Prices An economist is in the process of developing a model to predict the price of silver.She believes that the two most important variables are the price of a barrel of oil (x₁)and the interest rate (x₂).She proposes the first-order model with interaction: y = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₃ + ε.A random sample of 20 daily observations was taken.The computer output is shown below. THE REGRESSION EQUATION IS y = 115.6 + 22.3x₁ + 14.7x₂− 1.36x₁x₂ S = 20.9 R−Sq = 55.4% ANALYSIS OF VARIANCE ​ ​ -{Silver Prices Narrative} Interpret the coefficient b₂.

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} Determine if there is sufficient evidence at the 5% significance level to infer that the relationship between x and y is positive and significant.

An indicator variable is a variable that can assume:

Motorcycle Fatalities A traffic consultant has analyzed the factors that affect the number of motorcycle fatalities.She has come to the conclusion that two important variables are the number of motorcycle and the number of cars.She proposed the model (the second-order model with interaction),where y = number of annual fatalities per county,x₁ = number of motorcycles registered in the county (in 10,000),and x₂ = number of cars registered in the county (in 1000).The computer output (based on a random sample of 35 counties)is shown below: THE REGRESSION EQUATION IS S = 15.2 R−Sq = 47.2% ANALYSIS OF VARIANCE ​ ​ -{Motorcycle Fatalities Narrative} Test at the 1% significance level to determine if the interaction term should be retained in the model.

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 grade point average in first three years is linearly related to the fourth-year medical final grade?

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} Is there enough evidence at the 1% significant level to conclude that general practitioners earn more on average than psychiatrists?

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} Use the quadratic model to predict the value of y when x = 45.

____________________ means that the effect of x₁ on y is influenced by the value of x₂,and vice versa.

When a dummy variable is included in a multiple regression model,the interpretation of the estimated slope coefficient does not make any sense anymore.

Suppose that the sample regression equation of a model is .The term is referred to as:

Silver Prices An economist is in the process of developing a model to predict the price of silver.She believes that the two most important variables are the price of a barrel of oil (x₁)and the interest rate (x₂).She proposes the first-order model with interaction: y = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₃ + ε.A random sample of 20 daily observations was taken.The computer output is shown below. THE REGRESSION EQUATION IS y = 115.6 + 22.3x₁ + 14.7x₂− 1.36x₁x₂ S = 20.9 R−Sq = 55.4% ANALYSIS OF VARIANCE ​ ​ -{Silver Prices Narrative} Is there sufficient evidence at the 1% significance level to conclude that the interest rate and the price of silver are linearly related?

In building a regression model,it is best to use the ____________________ number of independent variables that produce a satisfactory model.

One of the requirements of regression analysis is that the dependent variable must be:

In the first-order model ,a unit increase in x₂,while holding x₁ constant at a value of 3,decreases the value of y on average by 3 units.

Hockey Teams An avid hockey fan was in the process of examining the factors that determine the success or failure of hockey teams.He noticed that teams with many rookies and teams with many veterans seem to do quite poorly.To further analyze his beliefs he took a random sample of 20 teams and proposed a second-order model with one independent variable,average years of professional experience.The selected model is y = β₀ + β₁x + β₂x² + ε,where y = winning team's percentage,and x = average years of professional experience.The computer output is shown below. THE REGRESSION EQUATION IS y = 32.6 + 5.96x− .48x² S = 16.1 R−Sq = 43.9% ANALYSIS OF VARIANCE ​ ​ -{Hockey Teams Narrative} Predict the winning percentage for a hockey team with an average of 6 years of professional experience.