Question 1

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 "centered" curvilinear model to this data.The results obtained by Microsoft Excel follow,where the dose (X)given has been "centered."
 
-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 TABLE 15-3
A chemist employed by a pharmaceutical...

Question 2

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 "centered" curvilinear model to this data.The results obtained by Microsoft Excel follow,where the dose (X)given has been "centered."
 
-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...

Question 3

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 4

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 "centered" curvilinear model to this data.The results obtained by Microsoft Excel follow,where the dose (X)given has been "centered."
 
-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 TABLE 15-3
A chemist employed by a pharmaceutical...

Question 5

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

Accepted Answer

Collinearity typically results in excessively high standard errors of the parameter estimates, making it difficult to determine the individual effect of collinear variables on the dependent variable.

Question 6

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 "centered" curvilinear model to this data.The results obtained by Microsoft Excel follow,where the dose (X)given has been "centered."
 
-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 7

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 indicates a strong relationship between the dependent variable and all the independent variables combined. However, if the t-values for the individual parameter estimates are insignificant, it suggests that none of the independent variables are significantly related to the dependent variable. This usually happens when there is high multicollinearity, i.e. the independent variables are highly correlated with each other, leading to unstable and unreliable estimates of the coefficients.

Question 8

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 "centered" curvilinear model to this data.The results obtained by Microsoft Excel follow,where the dose (X)given has been "centered."
 
-Referring to Table 15-3,the prediction of time to relief for a person receiving a dose of the drug 10 units above the mean dose (i.e.,the prediction of Y for X = 10)is ________.

Accepted Answer

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

Question 9

One of the consequences of collinearity in multiple regression is biased estimates on the slope coefficients.

Accepted Answer

Collinearity primarily causes high variances in the slope coefficients, making them unstable and unreliable, but it does not inherently bias the estimates.

Question 10

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 "centered" curvilinear model to this data.The results obtained by Microsoft Excel follow,where the dose (X)given has been "centered."
 
-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 answer of TABLE 15-3
A chemist employed by a pharmaceutical...

Question 11

The parameter estimates are biased when collinearity is present in a multiple regression equation.

Accepted Answer

The answer of The parameter estimates are biased when collinearity...

Question 12

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 situation described indicates that there is high correlation between the two independent variables, which is known as collinearity. When both variables are included in the same multiple regression model, they become redundant and do not add significant predictive power to the model, leading to non-significant parameter estimates and little increase in explained variance (R²).

Question 13

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 high correlation between independent variables, which causes instability in the estimation of the regression coefficients. As a result, the standard errors of the estimated coefficients can be inflated, making it difficult to identify the true effects of the independent variables on the dependent variable.

Question 14

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 "centered" curvilinear model to this data.The results obtained by Microsoft Excel follow,where the dose (X)given has been "centered."
 
-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

From the table, we can see that the t-value for the linear term is 2.055, which is greater than the critical value of 2.160 for a two-tailed test with 12 degrees of freedom at a significance level of 0.05. Therefore, we reject the null hypothesis that the linear term is not significant and conclude that it is significant.

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 "centered" curvilinear model to this data.The results obtained by Microsoft Excel follow,where the dose (X)given has been "centered."
 
-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

In Table 15-3, the p-value for the linear term is 0.038, which is greater than the level of significance of 0.01. Therefore, the chemist would fail to reject the null hypothesis that the linear model is sufficient and conclude that there is no significant difference between the linear model and the curvilinear model that includes a linear term.

Question 16

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 "centered" curvilinear model to this data.The results obtained by Microsoft Excel follow,where the dose (X)given has been "centered."
 
-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 answer of TABLE 15-3
A chemist employed by a pharmaceutical...

Question 17

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 "centered" curvilinear model to this data.The results obtained by Microsoft Excel follow,where the dose (X)given has been "centered."
 
-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 TABLE 15-3
A chemist employed by a pharmaceutical...

Question 18

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 "centered" curvilinear model to this data.The results obtained by Microsoft Excel follow,where the dose (X)given has been "centered."
 
-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

The p-value for the quadratic term in the model is less than 0.05, indicating that there is a significant curvilinear relationship between time and dose. Therefore, the chemist would decide that there is a significant curvilinear relationship.

Question 19

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

Dummy variables are used to encode categorical data into numeric form so that they can be included in regression models, not for converting one variable into a different form to fit curves. Mathematical manipulations for fitting curves often involve transforming the variables themselves, such as through polynomial regression or logarithmic transformation.

Question 20

Collinearity is present if the dependent variable is linearly related to one of the explanatory variables.

Accepted Answer

Collinearity refers to a situation where two or more explanatory variables in a multiple regression model are highly linearly related, not the relationship between an explanatory variable and the dependent variable.

Quiz 15: Multiple Regression Model Building

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

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

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.

One of the consequences of collinearity in multiple regression is biased estimates on the slope coefficients.

The parameter estimates are biased when collinearity is present in a multiple regression equation.

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

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.

Collinearity is present if the dependent variable is linearly related to one of the explanatory variables.