Exam 17: Model Building

Consider the model described by the equation $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 }$ .The slope of the relationship between $E ( y )$ and $x _ { 1 }$

What is stepwise regression?

The model $\hat { Y }$ = b₀ + b₁x₁ + b₂x₂ + b₃x₁x₂ is referred to as the:

Economist An economist is in the process of developing a model to predict the price of gold.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 $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 } + \epsilon$ A random sample of 20 daily observations was taken.The computer output is shown below. The regression equation is: $y = 115.6 + 22.3 x _ { 1 } + 14.7 x _ { 2 } - 1.36 x _ { 1 } x _ { 2 }$ Predictor Coef SE Coef T Constant 115.6 78.1 1.480 22.3 7.1 3.141 14.7 6.3 2.333 -1.36 0.52 -2.615 $\mathrm { S } = 20.9 \quad \mathrm { R } - \mathrm { Sq } = 55.4 \%$ ANAL YSIS OF VARIANCE Source of Variation DF SS MS F Regression 3 8661 2887.0 6.626 Error 16 6971 435.7 Total 19 15632 -Interpret the coefficient b₁. b₁ = ____________________ Interpretation:

In stepwise regression procedure,if two independent variables are highly correlated,then:

The ____________________ method involves forward selection or reverse elimination of one predictor variable at a time.

For underlying relationships that are not linear,____________________ transformation methods can be employed in constructing exponential and multiplicative models.

The two largest values in a correlation matrix are the 0.89 correlation between y and x₃ and the 0.83 correlation between y and x₇.During a stepwise regression analysis $\mathrm { X } _ { 3 }$ is the first independent variable brought into the equation.Will x₇ necessarily be next? If not,why not?

The model $\hat { Y }$ = b₀ + b₁x₁ + b₂x₂ is used whenever the statistician believes that:

As x increases,y decreases,and at an increasing rate.If a second-order polynomial model were fitted to the scatterplot of the data,what would be the signs of the partial regression coefficients in the model?

If the goal for the regression analysis is simply to predict the value of the dependent variable based on a set of predictor variables,we need not worry about ____________________,which means that some of the predictor variables might be highly correlated with each other.

Consider the model described by the equation $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 } + \beta _ { 3 } x ^ { 3 }$ .Which term provides a nonlinear component to the model allowing the line to curve?

What is a correlation matrix,and what role does it play in multiple regression?

Economist An economist is in the process of developing a model to predict the price of gold.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 $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 } + \epsilon$ A random sample of 20 daily observations was taken.The computer output is shown below. The regression equation is: $y = 115.6 + 22.3 x _ { 1 } + 14.7 x _ { 2 } - 1.36 x _ { 1 } x _ { 2 }$ Predictor Coef SE Coef T Constant 115.6 78.1 1.480 22.3 7.1 3.141 14.7 6.3 2.333 -1.36 0.52 -2.615 $\mathrm { S } = 20.9 \quad \mathrm { R } - \mathrm { Sq } = 55.4 \%$ ANAL YSIS OF VARIANCE Source of Variation DF SS MS F Regression 3 8661 2887.0 6.626 Error 16 6971 435.7 Total 19 15632 -Is there sufficient evidence at the 1% significance level to conclude that the interest rate and the price of gold are linearly related? Test statistic = ____________________ = ____________________ Critical Value = ____________________ Conclusion: _____________________ Interpretation: _____________________________________________________

In a first-order model with two predictors x₁ and x₂,an interaction term may be used when:

The ____________________ indicates the proportion of variation in the dependent variable that is "explained" by the set of predictor variables.

In forward selection stepwise regression with ten predictor variables,which of the following statements is correct?

The regression model $\hat{ Y }$ = 180 + 6x₁ - 2x₂ has been fitted to a set of data.Comment on whether interaction appears to exist between x₁ and x₂. Interaction: _________________________________ Comments:

Economist An economist is in the process of developing a model to predict the price of gold.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 $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 } + \epsilon$ A random sample of 20 daily observations was taken.The computer output is shown below. The regression equation is: $y = 115.6 + 22.3 x _ { 1 } + 14.7 x _ { 2 } - 1.36 x _ { 1 } x _ { 2 }$ Predictor Coef SE Coef T Constant 115.6 78.1 1.480 22.3 7.1 3.141 14.7 6.3 2.333 -1.36 0.52 -2.615 $\mathrm { S } = 20.9 \quad \mathrm { R } - \mathrm { Sq } = 55.4 \%$ ANAL YSIS OF VARIANCE Source of Variation DF SS MS F Regression 3 8661 2887.0 6.626 Error 16 6971 435.7 Total 19 15632 -Is there sufficient evidence at the 1% significance level to conclude that the price of a barrel of oil and the price of gold are linearly related? Test statistic = ____________________ = ____________________ Critical Value = ____________________ Conclusion: ____________________ Interpretation: _______________________________________________________

As x increases,y increases,but at a decreasing rate.If a second-order polynomial model were fitted to the scatter plot of the data,what would be the signs of the partial regression coefficients in the model?