Question 1

One of the requirements for conducting inference on the least-squares regression model is that the
A) mean of the response variable changes at a constant rate while the standard deviation remains constant.
B) mean of the explanatory variable changes at a constant rate while the standard deviation remains constant.
C) mean of the explanatory variable remains constant while the standard deviation changes at a constant rate.
D) mean of the response variable remains constant while the standard deviation changes at a constant rate.

Accepted Answer

The requirement for conducting inference on the least-squares regression model is that the mean of the response variable changes at a constant rate (as a linear function of the explanatory variable) while the standard deviation of the errors (residuals) remains constant across all levels of the explanatory variable. This is a description of homoscedasticity and linearity in the context of regression analysis.

Question 2

The least-squares regression model for one explanatory variable is given by the equation
A) y = mx + b
B) y -  = m(x -  )
C)  =  +   + 
D)  =   +

Accepted Answer

C

Question 3

Find the standard error of estimate,  , for the data below, given that  = 2x + 1. 
A) 0
B) 2
C) 1
D) 3

Accepted Answer

A

Question 4

Find the standard error of estimate,  , for the data below, given that  = -2.5x. 
A) 0.532
B) 0.349
C) 0.675
D) 0.866

Accepted Answer

The answer of Find the standard error of estimate, ...

Question 5

Find the standard error of estimate,  , for the data below, given that  
A) 0.976
B) -0.990
C) 0.980
D) 0.990

Accepted Answer

The answer of Find the standard error of estimate, ...

Question 6

Find the standard error of estimate,  , for the data below, given that  
A) 0.981
B) 0.011
C) 0.613
D) 0.312

Accepted Answer

The answer of Find the standard error of estimate, ...

Question 7

Find the standard error of estimate,  , for the data below, given that  
A) 3.203
B) 8.214
C) 5.918
D) 6.306

Accepted Answer

The answer of Find the standard error of estimate, ...

Question 8

The data below are the final exam scores of 10 randomly selected engineering students and the number of hours they slept the night before the exam. Find the standard error of estimate,  , given that  
A) 8.912
B) 7.913
C) 9.875
D) 6.305

Accepted Answer

The answer of The data below are the final exam...

Question 9

The data below are the number of absences and the final grades of 9 randomly selected students in an engineering class. Find the standard error of estimate,  , given that  
A) 3.876
B) 4.531
C) 1.798
D) 2.160

Accepted Answer

The answer of The data below are the number of...

Question 10

Test the claim, at the ? = 0.05 level of significance, that a linear relation exists between the two variables, for the data below, given that  = -2.5x.

Accepted Answer

The answer of Test the claim, at the ? =...

Question 11

Test the claim, at the ? = 0.01 level of significance, that a linear relation exists between the two variables, for the data below, given that

Accepted Answer

The answer of Test the claim, at the ? =...

Question 12

Test the claim, at the ? = 0.10 level of significance, that a linear relation exists between the two variables, for the data below, given that

Accepted Answer

The answer of Test the claim, at the ? =...

Question 13

A breeder of thoroughbred horses wishes to model the relationship between the gestation period and the length of life of a horse. The breeder believes that the two variables may follow a linear trend. The information in the table was supplied to the breeder from various thoroughbred stables across the state. Test the claim, at the ? =0.05 level of significance, that a linear relation exists between the gestation period and the length of life of a horse.

Accepted Answer

The answer of A breeder of thoroughbred horses wishes to...

Question 14

If a hypothesis test of the linear relation between the explanatory and the response variable is of the type where  :  = 0,  :  > 0, then we are testing the claim that
A) no linear relationship exists.
B) a relationship exist without regard to the sign of the slope.
C) the slope of the least square regression model is positive.
D) the slope of the least squares regression model is negative.

Accepted Answer

The answer of If a hypothesis test of the linear...

Question 15

Construct a 95% confidence interval about the slope of the true least-squares regression line, for the data below, given that  = -2.5x. 
A) (-6.226, 1.226)
B) (-3.630, -1.370)
C) (-4.165, -0.835)
D) (-3.731, -1.269)

Accepted Answer

The answer of Construct a 95% confidence interval about the...

Question 16

Construct a 99% confidence interval about the slope of the true least-squares regression line, for the data below, given that  
A) (1.787, 2.407)
B) (1.749, 2.445)
C) (1.738, 2.456)
D) ( -1.177, 5.371)

Accepted Answer

The answer of Construct a 99% confidence interval about the...

Question 17

Construct a 90% confidence interval about the slope of the true least-squares regression line, for the data below, for the data below, given that  
A) (-1.979, -1.791)
B) (-2.008, -1.762)
C) (-2.010, -1.760)
D) (-3.025, -0.745)

Accepted Answer

The answer of Construct a 90% confidence interval about the...

Question 18

The data below are the ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults.Construct a 95% confidence interval about the slope of the true least-squares regression line, for the data below, given that  
A) (-8.443, 11.419)
B) (1.098, 1.877)
C) (1.175, 1.801)
D) (1.108, 1.868)

Accepted Answer

The answer of The data below are the ages and...

Question 19

A breeder of Thoroughbred horses wishes to model the relationship between the gestation period and the length of life of a horse. The breeder believes that the two variables may follow a linear trend. The information in the table was supplied to the breeder from various thoroughbred stables across the state. Construct a 90% confidence interval about the slope of the true least-squares regression line.

Accepted Answer

The answer of A breeder of Thoroughbred horses wishes to...

Question 20

Construct a 95% confidence interval about the mean value of y, given x = -3.5,  = 2.097x - 0.552 and  
A) (-8.921,-6.862)
B) (-12.142 ,-6.475)
C) (-4.598 ,-1.986)
D) (-10.367, -5.417)

Accepted Answer

The answer of Construct a 95% confidence interval about the...

Quiz 14: Inference of the Least-Squares Regression Model

One of the requirements for conducting inference on the least-squares regression model is that the

The least-squares regression model for one explanatory variable is given by the equation

Find the standard error of estimate, , for the data below, given that = 2x + 1.

Find the standard error of estimate, , for the data below, given that = -2.5x.

Find the standard error of estimate, , for the data below, given that

Find the standard error of estimate, , for the data below, given that

Find the standard error of estimate, , for the data below, given that

The data below are the final exam scores of 10 randomly selected engineering students and the number of hours they slept the night before the exam. Find the standard error of estimate, , given that

The data below are the number of absences and the final grades of 9 randomly selected students in an engineering class. Find the standard error of estimate, , given that

Test the claim, at the ? = 0.05 level of significance, that a linear relation exists between the two variables, for the data below, given that = -2.5x.

Test the claim, at the ? = 0.01 level of significance, that a linear relation exists between the two variables, for the data below, given that

Test the claim, at the ? = 0.10 level of significance, that a linear relation exists between the two variables, for the data below, given that

If a hypothesis test of the linear relation between the explanatory and the response variable is of the type where : = 0, : > 0, then we are testing the claim that

Construct a 95% confidence interval about the slope of the true least-squares regression line, for the data below, given that = -2.5x.

Construct a 99% confidence interval about the slope of the true least-squares regression line, for the data below, given that

Construct a 90% confidence interval about the slope of the true least-squares regression line, for the data below, for the data below, given that

The data below are the ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults.Construct a 95% confidence interval about the slope of the true least-squares regression line, for the data below, given that

Construct a 95% confidence interval about the mean value of y, given x = -3.5, = 2.097x - 0.552 and