Question 1

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.

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. 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 decision to determine if there is a significant curvilinear relationship using an F test at a 0.01 significance level depends on the calculated F statistic and the critical F value from the F distribution table. Without these specific values, we cannot conclude whether the relationship is significant.

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 "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 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 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 5

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 6

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

When two independent variables are highly correlated, they are said to be collinear. In such cases, the multiple regression model may not improve the prediction accuracy significantly as compared to the simple regression models. Additionally, the parameter estimates for the collinear independent variables become unstable and may not be significantly different from 0. This description of the models indicates the presence of collinearity.

Question 7

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

A t-test is used to compare means, not models. To compare models, an F-test or other model comparison techniques would be more appropriate.

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, 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

Looking at the table, the p-value for the quadratic term (X^2) 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 if using a level of significance of 0.05.

Question 9

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 that the model explains a significant amount of variation in the dependent variable. However, if the t-values on all parameter estimates are insignificant, it suggests that none of the independent variables are individually making a significant contribution to the model. This could occur if there is high correlation between independent variables, which can lead to inflated R² values and difficulty in interpreting parameter estimates.

Question 10

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...

Question 11

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 increase the variance of the estimated regression coefficients, leading to inflated standard errors and decreasing the power of the regression analysis.

Question 12

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

The p-value for the linear model vs. the curvilinear model with a linear term is 0.038, which is greater than the 0.01 level of significance. Therefore, the chemist would fail to reject the null hypothesis that the linear model is sufficient and conclude that the linear model is appropriate for this data.

Question 13

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 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, 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 15

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 16

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 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 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

The t-value for the linear term is 2.23 and the p-value is 0.044, which is less than the level of significance of 0.05. Therefore, the chemist would conclude that the linear term is significant.

Question 19

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 20

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.

Quiz 15: Multiple Regression Model Building

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

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.

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.

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

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

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

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

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