Exam 17: Model Building

Suppose that the sample regression equation of a second-order model is given by: $\hat{ Y }$ = 2.50 + 0.15x + 0.45x² What is the predicted value of y when x = 2?

In the general polynomial model, $\mathrm { y } _ { \mathrm { i } } = \beta _ { 0 } + \beta _ { 1 } \mathrm { x } _ { \mathrm { i } } + \beta _ { 2 } \mathrm { x } _ { \mathrm { i } } ^ { 2 } + \beta _ { 3 } \mathrm { x } _ { \mathrm { i } } ^ { 3 } + \ldots \ldots + \beta _ { \mathrm { p } } \mathrm { x } _ { \mathrm { i } } ^ { \mathrm { p } } + \epsilon _ { 1 }$ the order of the polynomial is:

A researcher suspects that the dependent variable y is linearly related to both x₁ and x₂ but believes there is a little or no interaction between the two predictor variables.Which model would likely be most suitable for this situation?

Stepwise regression is especially useful when there are:

The estimated regression equation for a sample of 500 college professors is given by: $\hat { Y }$ = 275 - 3x - 2D,where y is retirement age,x is pre-retirement annual income (in $1000s),and D is a dummy variable that takes the value of 0 for female professors and 1 for male professors.Assume that there is a relationship between y,x and D.What is the average age of retirement for male professors with pre-retirement income of $68,500? ____________________ years

A scatter diagram for a set of data shows that as x increases,y initially increases,then it decreases,and then it increases again.What does the scatter diagram indicate?

Suppose that the sample regression equation of a second-order model is given by: $\hat { Y }$ = 2.50 + 0.15x + 0.45x².What does the value 2.50 represent?

Consider the first-order regression model $\hat{ y }$ = 15 + 6x₁ + 5x₂ + 4x₁x₂. A unit increase in x1 increases the value of y on average by:

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

Data transformation may include converting x to its square root or inverse.

The exponential model $\hat { Y }$ = b₀b₁^x can be converted to a linear model by taking the logarithms of both sides of the equation (either natural or common logarithms can be used as long as we are consistent).

If two or more independent variables are highly correlated with each other,multicollinearity is present,and the partial regression coefficients will be unreliable.

As the temperature increases,an experimental lubricant initially decreases in viscosity (resistance in flow),then increases,then decreases again.Of the first,second,and third polynomial models discussed in this section,which would tend to be most applicable for such data? What would be the signs of the partial regression coefficient(s)in the model?

The regression model $\hat{ Y }$ = 180 + 6x₁ - 2x₂ has been fitted to a set of data.If x₂ = 20,what will be the effect on $\hat{ Y }$ if x₁ increases by 1 unit? $\hat{ Y }$ will ____________________ by ____________________

The model $\mathrm { y } _ { \mathrm { i } } = \beta _ { 0 } + \beta _ { 1 } \mathrm { x } _ { i } + \beta _ { 2 } \mathrm { x } _ { i } ^ { 2 } + \beta _ { 3 } \mathrm { x } _ { i } ^ { 3 } + \ldots \ldots + \beta _ { y } \mathrm { x } _ { \mathrm { i } } ^ { \mathrm { p } } + \epsilon _ { 1 }$ is referred to as a:

The second-order polynomial model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$ allows the plotted line to reverse the direction in which it is curving.

How do we identify multicollinearity?

The model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$ is not suitable when

In general,to represent a qualitative predictor variable that has n possible categories we must create:

In general,we should attempt to use the simplest possible model that satisfies the goal for which the model is being developed.