Exam 18: Model Building

Regression analysis allows the statistics practitioner to use mathematical models to realistically describe relationships between the dependent variable and independent variables.

For the following regression equation ,which combination of x₁ and x₂,respectively,results in the largest average value of y?

In stepwise regression,the independent variable with the largest F-statistic,or equally the smallest p-value,is chosen as the first entering variable.

In the first-order model ,a unit increase in x₂,while holding x₁ constant at 1,changes the value of y on average by −5 units.

In multiple regression,which procedure permits variables to enter and leave the model at different stages of its development?

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} What does the coefficient of tell you about the model?

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

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} Predict the final grade (out of 100)in the fourth-year medical course for a biology major student who has a 10.95 G.P.A.in their first three years (range from 0 to 12).

When we plot x versus y,the graph of the model y = β₀ + β₁x + β₂x² + ε is shaped like a:

In stepwise regression procedure,the independent variable with the largest F-statistic,or equally with the smallest p-value,is chosen as the first entering variable.The standard,also called the F-to-enter,is usually set at F equals:

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 term should be retained in the model.

The model y = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₂ + ε is referred to as a second-order model with two predictor variables with interaction.

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 b₁.

In explaining the amount of money spent on children's shoes each month,which of the following independent variables is best represented with an indicator variable?

Dummy variables are variables that can take on only two values (namely,0 or 1)and that are used to indicate the absence or presence of a particular nominal characteristic.

The model y = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₂ + ε is a(n)____________________-order polynomial model with ____________________ predictor variables and ____________________.

For the following regression equation ,a unit increase in x₁ increases the value of y on average by:

In explaining students' test scores,which of the following independent variables would not best be represented with indicator variables?

The two largest values in a correlation matrix are the .89 correlation between y and x₃,and the .83 correlation between y and x₇.During a stepwise regression analysis x₃ is the first independent variable brought into the equation.Will x₇ necessarily be next? If not,why not?

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 an estimated regression equation of the form .