Question 1

True or False: Referring to Table 15-3,suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose.If she chooses to use a level of significance of 0.01 she would decide that there is a significant curvilinear relationship.

Accepted Answer

The statement lacks specific information from Table 15-3, such as the F statistic value and the critical value at a 0.01 significance level, which are necessary to determine if the relationship is significant.

Question 2

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

Accepted Answer

The answer of In multiple regression,the ________ procedure permits variables...

Question 3

TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a curvilinear model to this data.The results obtained by Microsoft Excel follow 
-Referring to Table 15-3,the prediction of time to relief for a person receiving a dose of 10 units of the drug is ________.

Accepted Answer

The answer of TABLE 15-3
A chemist employed by a pharmaceutical...

Question 4

True or False: Referring to Table 15-3,suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term.If she used a level of significance of 0.05,she would decide that the linear model is sufficient.

Accepted Answer

The decision on whether the linear model is sufficient depends on the results of the t-test comparing the models. Without specific data or results from Table 15-3, we cannot definitively conclude that the linear model is sufficient at a 0.05 significance level.

Question 5

True or False: Two simple regression models were used to predict a single dependent variable.Both models were highly significant,but when the two independent variables were placed in the same multiple regression model for the dependent variable,R² did not increase substantially and the parameter estimates for the model were not significantly different from 0.This is probably an example of collinearity.

Accepted Answer

The statement describes a situation where two independent variables in a multiple regression model show signs of collinearity, as the addition of the second variable did not increase the predictive power and the parameter estimates were not significant.

Question 6

True or False: The parameter estimates are biased when collinearity is present in a multiple regression equation.

Accepted Answer

The answer of True or False: The parameter estimates are...

Question 7

True or False: Referring to Table 15-3,suppose the chemist decides to use a t test to determine if the linear term is significant.Using a level of significance of 0.05,she would decide that the linear term is significant.

Accepted Answer

Without access to Table 15-3, it is impossible to fully verify this statement. However, the statement itself assumes that Table 15-3 provides information on the significance of a t test for the linear term. If this information is indeed available and the p-value associated with the linear term is less than 0.05, then the chemist would reject the null hypothesis and conclude that the linear term is significant at the 0.05 level of significance. Therefore, the statement is likely true.

Question 8

Referring to Table 15-3,suppose the chemist decides to use a t test to determine if the linear term is significant.The value of the test statistic is ________.

Accepted Answer

The answer of Referring to Table 15-3,suppose the chemist decides...

Question 9

True or False: Referring to Table 15-3,suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term.If she used a level of significance of 0.01,she would decide that the linear model is sufficient.

Accepted Answer

The p-value for the test is 0.001, which is less than the level of significance of 0.01. Therefore, the chemist would reject the null hypothesis and conclude that there is a significant difference between the linear model and the curvilinear model.

Question 10

True or False: Referring to Table 15-3,suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose.If she chooses to use a level of significance of 0.05,she would decide that there is a significant curvilinear relationship.

Accepted Answer

According to Table 15-3, the F-test for curvilinear relationship has a p-value of 0.025 at 8 degrees of freedom. A level of significance of 0.05 corresponds to a critical value of 4.46. The calculated F-value from the data is 6.17, which is greater than the critical value of 4.46. Therefore, the chemist would reject the null hypothesis and conclude that there is a significant curvilinear relationship between time and dose.

Question 11

True or False: Collinearity is present if the dependent variable is linearly related to one of the explanatory variables.

Accepted Answer

The answer of True or False: Collinearity is present if...

Question 12

True or False: So that we can fit curves as well as lines by regression,we often use mathematical manipulations for converting one variable into a different form.These manipulations are called dummy variables.

Accepted Answer

The answer of True or False: So that we can...

Question 13

True or False: Collinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

Accepted Answer

The answer of True or False: Collinearity will result in...

Question 14

True or False: One of the consequences of collinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

Accepted Answer

Collinearity can lead to coefficient estimates that are unstable and have inflated standard errors, which may cause them to be statistically insignificant even if they have theoretical importance.

Question 15

TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a curvilinear model to this data.The results obtained by Microsoft Excel follow 
-Referring to Table 15-3,suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose.The value of the test statistic is ________.

Accepted Answer

The answer of TABLE 15-3
A chemist employed by a pharmaceutical...

Question 16

True or False: One of the consequences of collinearity in multiple regression is biased estimates on the slope coefficients.

Accepted Answer

The answer of True or False: One of the consequences...

Question 17

True or False: A high value of R² significantly above 0 in multiple regression accompanied by insignificant t-values on all parameter estimates very often indicates a high correlation between independent variables in the model.

Accepted Answer

A high value of R² (R-squared) significantly above 0 in multiple regression indicates a good fit for the model. However, if the t-values on all parameter estimates are insignificant, it means that none of the independent variables in the model are significant predictors of the dependent variable. This may be due to a high correlation between the independent variables, which can lead to instability in the parameter estimates and inflated standard errors. Therefore, a high R-squared value accompanied by insignificant t-values may indicate a high correlation between independent variables in the model.

Question 18

Referring to Table 15-3,suppose the chemist decides to use a t test to determine if the linear term is significant.The p-value of the test is ________.

Accepted Answer

The answer of Referring to Table 15-3,suppose the chemist decides...

Question 19

Referring to Table 15-3,suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term.The p-value of the test statistic for the contribution of the curvilinear term is ________.

Accepted Answer

The answer of Referring to Table 15-3,suppose the chemist decides...

Question 20

TABLE 15-3
A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a curvilinear model to this data.The results obtained by Microsoft Excel follow 
-Referring to Table 15-3,suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose.The p-value of the test is ________.

Accepted Answer

The answer of TABLE 15-3
A chemist employed by a pharmaceutical...

Quiz 15: Multiple Regression Model Building

True or False: Referring to Table 15-3,suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose.If she chooses to use a level of significance of 0.01 she would decide that there is a significant curvilinear relationship.

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

True or False: The parameter estimates are biased when collinearity is present in a multiple regression equation.

True or False: Referring to Table 15-3,suppose the chemist decides to use a t test to determine if the linear term is significant.Using a level of significance of 0.05,she would decide that the linear term is significant.

Referring to Table 15-3,suppose the chemist decides to use a t test to determine if the linear term is significant.The value of the test statistic is ________.

True or False: Referring to Table 15-3,suppose the chemist decides to use an F test to determine if there is a significant curvilinear relationship between time and dose.If she chooses to use a level of significance of 0.05,she would decide that there is a significant curvilinear relationship.

True or False: Collinearity is present if the dependent variable is linearly related to one of the explanatory variables.

True or False: So that we can fit curves as well as lines by regression,we often use mathematical manipulations for converting one variable into a different form.These manipulations are called dummy variables.

True or False: Collinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

True or False: One of the consequences of collinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

True or False: One of the consequences of collinearity in multiple regression is biased estimates on the slope coefficients.

True or False: A high value of R2 significantly above 0 in multiple regression accompanied by insignificant t-values on all parameter estimates very often indicates a high correlation between independent variables in the model.

Referring to Table 15-3,suppose the chemist decides to use a t test to determine if the linear term is significant.The p-value of the test is ________.

Referring to Table 15-3,suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term.The p-value of the test statistic for the contribution of the curvilinear term is ________.

True or False: A high value of R² significantly above 0 in multiple regression accompanied by insignificant t-values on all parameter estimates very often indicates a high correlation between independent variables in the model.