Question 1

Multiple regression is the process of using several independent variables to predict a number of dependent variables.

Accepted Answer

Multiple regression is the process of using several independent variables to predict a single dependent variable.

Question 2

SCENARIO 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units and total SAT scores of each.She takes a sample of students and generates the following Microsoft Excel output: 
-Referring to Scenario 14-7, the department head wants to test  .The p-value of the test is ________.

Accepted Answer

The answer of SCENARIO 14-7 The department head of the...

Question 3

From the coefficient of multiple determination, you cannot detect the strength of the relationship between Y and any individual independent variable.

Accepted Answer

The coefficient of multiple determination only tells you the overall proportion of variation in the dependent variable that is explained by all the independent variables together. It does not provide information on the strength of the relationship between Y and any individual independent variable.

Question 4

SCENARIO 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units and total SAT scores of each.She takes a sample of students and generates the following Microsoft Excel output: 
-Referring to Scenario 14-7, the value of the coefficient of multiple determination,  is ________.

Accepted Answer

The answer of SCENARIO 14-7 The department head of the...

Question 5

A multiple regression is called "multiple" because it has several data points.

Accepted Answer

A multiple regression is called "multiple" because it involves multiple independent variables being used to predict a dependent variable. It can still have a single data point, but it would require information on multiple independent variables for that one data point.

Question 6

SCENARIO 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units and total SAT scores of each.She takes a sample of students and generates the following Microsoft Excel output: 
-Referring to Scenario 14-7, the department head wants to test  The appropriate alternative hypothesis is ________.

Accepted Answer

The answer of SCENARIO 14-7 The department head of the...

Question 7

A multiple regression is called "multiple" because it has several explanatory variables.

Accepted Answer

A multiple regression involves having more than one explanatory variable, hence the term "multiple".

Question 8

A regression had the following results: SST = 82.55, SSE = 29.85.It can be said that 63.84% of the variation in the dependent variable is explained by the independent variables in the regression.

Accepted Answer

The coefficient of determination (R-squared) can be calculated as:
R-squared = 1 - (SSE/SST)
R-squared = 1 - (29.85/82.55)
R-squared = 0.6384
Therefore, 63.84% of the variation in the dependent variable is explained by the independent variables in the regression.

Question 9

SCENARIO 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units and total SAT scores of each.She takes a sample of students and generates the following Microsoft Excel output: 
-Referring to Scenario 14-7, the net regression coefficient of  is ________.

Accepted Answer

The answer of SCENARIO 14-7 The department head of the...

Question 10

A regression had the following results: SST = 102.55, SSE = 82.04.It can be said that 90.0% of the variation in the dependent variable is explained by the independent variables in the regression.

Accepted Answer

To determine the proportion of variation in the dependent variable explained by the independent variables, we use the coefficient of determination (R-squared), which is calculated as (SST - SSE) / SST. In this case, R-squared would be (102.55 - 82.04) / 102.55 = 0.20. This means that only 20% of the variation in the dependent variable is explained by the independent variables, not 90%. Therefore, the statement is false.

Question 11

SCENARIO 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units and total SAT scores of each.She takes a sample of students and generates the following Microsoft Excel output: 
-Referring to Scenario 14-7, the estimate of the unit change in the mean of Y per unit change in  holding  constant, is ________.

Accepted Answer

The answer of SCENARIO 14-7 The department head of the...

Question 12

A regression had the following results: SST = 102.55, SSE = 82.04.It can be said that 20.0% of the variation in the dependent variable is explained by the independent variables in the regression.

Accepted Answer

The answer of A regression had the following results: SST...

Question 13

SCENARIO 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units and total SAT scores of each.She takes a sample of students and generates the following Microsoft Excel output: 
-Referring to Scenario 14-7, the value of the adjusted coefficient of multiple determination,  is ________.

Accepted Answer

The answer of SCENARIO 14-7 The department head of the...

Question 14

You have just computed a regression model in which the value of coefficient of multiple determination is 0.57.To determine if this indicates that the independent variables explain a significant portion of the variation in the dependent variable, you would perform an F-test.

Accepted Answer

The coefficient of multiple determination (R-square) measures the proportion of the variation in the dependent variable that is explained by the independent variables in the regression model. An R-square of 0.57 indicates that the independent variables explain 57% of the variation in the dependent variable. To determine if this is a significant amount of variation explained, an F-test is used. Therefore, the statement in the question is true.

Question 15

If you have considered all relevant explanatory factors, the residuals from a multiple regression model should be random.

Accepted Answer

Yes, if all relevant explanatory factors have been included in the model, the residuals should be random with no pattern or correlation to any of the variables. This indicates that the model is a good fit for the data and that no other significant factors need to be included. If the residuals show a pattern, it suggests that there are other explanatory variables that have not been included in the model or that the functional form of the model is incorrect. If all relevant explanatory factors have been considered and included in the model, the residuals should not show any systematic patterns or trends. This randomness of residuals indicates that the model has accounted for all the variability in the dependent variable that can be explained by the independent variables.

Question 16

SCENARIO 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units and total SAT scores of each.She takes a sample of students and generates the following Microsoft Excel output: 
-Referring to Scenario 14-7, the department head wants to test  .The value of the F-test statistic is ________.

Accepted Answer

The answer of SCENARIO 14-7 The department head of the...

Question 17

Consider a regression in which  = - 1.5 and the standard error of this coefficient equals 0.3.To determine whether x₂ is a significant explanatory variable, you would compute an observed t-value of - 5.0.

Accepted Answer

To determine the significance of x₂, we need to calculate its corresponding t-value and compare it to a critical t-value. The observed t-value of -5.0 indicates that x₂ is significant at a high level of confidence, as its value is much larger than the critical t-value for the given standard error of the coefficient. Therefore, the answer is A. The observed t-value of -5.0 means that the coefficient for x₂ is more than 5 standard errors away from zero, which indicates that it is highly likely to be a statistically significant explanatory variable. This conclusion is further supported by the fact that the coefficient for 11ebc114_12b1_c9f1_8acb_efcf59ae11a8_TB8562_11 is also statistically significant (given its low p-value), suggesting that the overall regression model has some predictive power.

Question 18

SCENARIO 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units and total SAT scores of each.She takes a sample of students and generates the following Microsoft Excel output: 
-Referring to Scenario 14-7, the predicted GPA for a student carrying 15 course units and who has a total SAT of 1,100 is ________.

Accepted Answer

The answer of SCENARIO 14-7 The department head of the...

Question 19

A regression had the following results: SST = 82.55, SSE = 29.85.It can be said that 73.4% of the variation in the dependent variable is explained by the independent variables in the regression.

Accepted Answer

The coefficient of determination, $R^2$, which represents the percentage of the variation in the dependent variable explained by the independent variables, is calculated as $R^2 = 1 - \frac{SSE}{SST}$. Using the given SST = 82.55 and SSE = 29.85, $R^2 = 1 - \frac{29.85}{82.55} = 1 - 0.3616 = 0.6384$, or 63.84%, not 73.4%.

Question 20

SCENARIO 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units and total SAT scores of each.She takes a sample of students and generates the following Microsoft Excel output: 
-Referring to Scenario 14-7, the department head wants to test  .The critical value of the F test for a level of significance of 0.05 is ________.

Accepted Answer

The answer of SCENARIO 14-7 The department head of the...

Quiz 14: Introduction to Multiple Regression

Multiple regression is the process of using several independent variables to predict a number of dependent variables.

From the coefficient of multiple determination, you cannot detect the strength of the relationship between Y and any individual independent variable.

A multiple regression is called "multiple" because it has several data points.

A multiple regression is called "multiple" because it has several explanatory variables.

A regression had the following results: SST = 82.55, SSE = 29.85.It can be said that 63.84% of the variation in the dependent variable is explained by the independent variables in the regression.

A regression had the following results: SST = 102.55, SSE = 82.04.It can be said that 90.0% of the variation in the dependent variable is explained by the independent variables in the regression.

A regression had the following results: SST = 102.55, SSE = 82.04.It can be said that 20.0% of the variation in the dependent variable is explained by the independent variables in the regression.

You have just computed a regression model in which the value of coefficient of multiple determination is 0.57.To determine if this indicates that the independent variables explain a significant portion of the variation in the dependent variable, you would perform an F-test.

If you have considered all relevant explanatory factors, the residuals from a multiple regression model should be random.

Consider a regression in which = - 1.5 and the standard error of this coefficient equals 0.3.To determine whether x₂ is a significant explanatory variable, you would compute an observed t-value of - 5.0.

A regression had the following results: SST = 82.55, SSE = 29.85.It can be said that 73.4% of the variation in the dependent variable is explained by the independent variables in the regression.