Unformatted text preview: ret β0 (the y intercept) and β1 (the β coefficient for the X variable). Does the parabola
open upward or downward? Why? 11466 Chapter 01  An Introduction to Business Statistics 81. A multiple linear regression analysis involving 45 observations resulted in the following
least squares prediction equation:
.
The SSE for the above model is 49.
Addition of two other independent variables to the model, resulted in the following multiple
linear regression equation:
.
The latter model's SSE is 40. Determine the degrees of freedom regression, degrees of
freedom error, and degrees of freedom total for the model with two independent variables. 82. A multiple linear regression analysis involving 45 observations resulted in the following
least squares prediction equation:
.
The SSE for the above model is 49.
Addition of two other independent variables to the model, resulted in the following multiple
linear regression equation:
.
The latter model's SSE is 40. Determine the degrees of freedom regression, degrees of
freedom error, and degrees of freedom total for the latter model (the model with four
independent variables). 11467 Chapter 01  An Introduction to Business Statistics 83. A multiple linear regression analysis involving 45 observations resulted in the following
least squares prediction equation:
.
The SSE for the above model is 49.
Addition of two other independent variables to the model, resulted in the following multiple
linear regression equation:
.
The latter model's SSE is 40. The analyst performing the study wants to determine if at least
one of the two new independent variables makes a significant contribution to the multiple
regression model. State the appropriate null and alternative hypotheses. 84. A multiple linear regression analysis involving 45 observations resulted in the following
least squares prediction equation:
.
The SSE for the above model is 49.
Addition of two other independent variables to the model, resulted in the following multiple
linear regression equation:
.
The latter model's SSE is 40. At
= .05 test to determine if at least one of the two new
independent variables make a significant contribution to the multiple regression model. 11468
Chapter 01  An Introduction to Business Statistics 85. A county has four major hospitals: 1) Regional Memorial; 2) General; 3) Charity; and 4)
City. A multiple regression model is used to compare the time spent in the hospital after a
heart bypass surgery among the four hospitals. The response variable is the amount of time
spent in the hospital (in days), the quantitative independent variables include the age of the
patient, cholesterol level of the patient, and blood pressure of the patient. Define the dummy
variables so that all other hospitals are compared to the City hospital (base). 86. A county has four major hospitals: 1) Regional Memorial; 2) General; 3) Charity; and 4)
City. A multiple regression model is used to compare the time spent in the hospital after a
heart bypass surgery among the four hospitals. The response (dependent) variable is the
amount of time spent in the hospital (in days). The variables used to predict the time spent in
the hospital include the patient's age, cholesterol level (in mlg.), blood pressure, as well as
variables indicating the hospital in which the surgery was performed. Determine the total
number of independent variables in the multiple regression model. Indicate how many of
these are quantitative variables and how many are indicator (dummy) variables. 87. If the multiple coefficient of determination that relates x1 to all the other independent
variables, R2(x1) = .25, calculate the variance inflation factor for x1. Should the analyst be
concerned about multicollinearity? Why? 11469 Chapter 01  An Introduction to Business Statistics 88. If the multiple coefficient of determination that relates x2 to all the other independent
variables, R2(x2) = .94, calculate the variance inflation factor for x2. Should the analyst be
concerned about multicollinearity? Why? 89. If the multiple coefficient of determination that relates x3 to all the other independent
variables, R2(x3) = .8, calculate the variance inflation factor for x3. Should the analyst be
concerned about multicollinearity? Why? 90. Calculate the studentized (standardized) residual where the residual is equal to 11.951 and
s is 14.8 and the leverage value (h) is equal to 0.0975. 11470 Chapter 01  An Introduction to Business Statistics 91. In a multiple regression model with 4 independent variables and 25 observations, an
observation's actual y value is 128.2, and the predicted value of the dependent variable based
on the multiple regression equation is equal to 114.7. The computer output also shows that
MSE is equal to 144 and the leverage value is 0.19. Calculate the studentized residual for this
observation. 92. In a multiple regression model with 4 independent variables and 25 observations, an
observation's actual y value is 128.2, and the predicted value of the dependent variable based
on the multiple regression equation is equal to 114.7. The comput...
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