chapter 13 and 14: mcq from assignments

Question 1

In simple regression analysis, if the correlation coefficient is a positive value, then

a) the y-intercept must also be a positive value
b) the least squares regression equation could have either a positive or a negative slope
c) the slope of the regression line must also be positive
d) the coefficient of determination can be either positive or negative, depending on the value of the slope
e) the standard error of estimate can have either a positive or a negative value

Answer 1

c) the slope of the regression line must also be positive

Question 2

When using simple linear regression, we would like to use confidence intervals for the ___________ and prediction intervals for the ___________ at a given value of x.

a) mean y-value, individual y-value
b) Individual y-value, mean y-value
c) y-intercept, mean y-intercept
d) slope, mean sloped

Answer 2

a) mean y-value, individual y-value

Question 3

In simple regression analysis, the quantity E (Y^-Y-)^2 is called the __________ sum of squares.

a) total
b) error
c) unexplained
d) explained

Answer 3

d) explained

Question 4

The standard error of the estimate (standard error) is the estimated standard deviation of the distribution of the independent variable (X) for all values of the dependent variable (Y).

a) true
b) false

why?

Answer 4

b) false

Standard error is the standard deviation of the population of the error terms

Question 5

what is the standard error?

Answer 5

the standard deviation of the population of the error terms

Question 6

A simple regression analysis with 20 observations would yield ________ degrees of freedom error and _________degrees of freedom total.

a) 19, 20
b) 18, 19
c) 1, 20
d) 18, 20
e) 1, 19

why?

Answer 6

b) 18, 19

Degrees of freedom for the error are calculated as N − (K + 1),

where N is the number of observations and K is the number of independent variables, so 20 − (1 + 1) = 18 df-error.

The df-total is N − 1 = 19

Question 7

how do you calculate he degrees of freedom of error

Answer 7

N − (K + 1)

Question 8

The simple linear regression (least squares method) minimizes

a) SSxx.
b) SSyy.
c) SSE.
d) total variation.
e) the explained variation

Answer 8

c) SSE.

Question 9

In simple regression analysis,

the standard error is ___________ greater than the standard deviation of y values.

a) sometimes
b) never
c) always

Answer 9

b) never

Question 10

The least squares regression line minimizes the sum of the

a) absolute deviations between actual and predicted Y values.
b) squared differences between actual and predicted X values.
c) absolute deviations between actual and predicted X values.
d) squared differences between actual and predicted Y values.
e) differences between actual and predicted Y values.

Answer 10

d) squared differences between actual and predicted Y values.

Question 11

The strength of the relationship between two quantitative variables can be measured by

a) the slope of a simple linear regression equation.
b) the coefficient of determination.
c) both the coefficient of correlation and the coefficient of determination.
d) the y-intercept of the simple linear regression equation.
e) the coefficient of correlation.

Answer 11

c) both the coefficient of correlation and the coefficient of determination.

Question 12

The estimated simple linear regression equation minimizes the sum of the squared deviations between each value of Y and the line.

a) True
b) False

Answer 12

a) True

Question 13

The estimated simple linear regression equation minimizes what?

Answer 13

the squared deviations between each value of Y and the line

Question 14

In simple linear regression analysis,

we assume that the variance of the independent variable (X) is equal to the variance of the dependent variable (Y).

a) True
b) False

why?

Answer 14

b) False

The model assumptions of a simple linear regression are:

independence of the error terms

constant variation of the error terms.

Question 15

why is the variance of the independent variable X not equal to the variance of the independent variable Y?

Answer 15

because of the assumptions of a simple linear regression which are in this case:

independence of the error terms

constant variation of the error terms

Question 16

The range for r2 is between 0 and 1, and the range for r is between ____________.

a) There is no limit for r.
b) −1 and 0
c) 0 and 1
d) -1 and 1

Answer 16

d) -1 and 1

Question 17

The correlation coefficient may assume any value between

a) 0 and 8.
b) −1 and 0.
c) 0 and 1.
d) −1 and 1.
e) −∞ and ∞.

Answer 17

d) −1 and 1.

Question 18

In a simple linear regression model,

the slope term is the change in the mean value of y associated with _____________ in x.

a) a corresponding increase
b) a one-unit increase
c) no change
d) a variable change

Answer 18

b) a one-unit increase

Question 19

The least squares simple linear regression line minimizes the sum of the vertical deviations between the line and the data points.

a) True
b) False

why?

Answer 19

b) False

The least squares simple linear regression line minimizes the sum of the squared deviations

Question 20

what does the east squares simple linear regression line minimizes what?

Answer 20

the sum of the squared deviations

Question 21

For a given data set, value of X, and confidence level,

if all the other factors are constant,

the confidence interval for the mean value of Y will ___________ be wider than the corresponding prediction interval for the individual value of Y.

a) always
b) sometimes
c) never

Answer 21

c) never

Question 22

The _____ distribution is used for testing the significance of the slope term.

a) r
b) z
c) r2
d) t

Answer 22

d) t

Question 23

After plotting the data points on a scatter diagram,

we have observed an inverse relationship between the independent variable (X) and the dependent variable (Y).

Therefore, we can expect both the sample ___________ and the sample _____________ to be negative values.

a) slope, correlation coefficient
b) intercept, slope
c) slope, coefficient of determination
d) slope, standard error of estimate
e) intercept, correlation coefficient

Answer 23

a) slope, correlation coefficient

Question 24

A significant positive correlation between X and Y implies that changes in X cause Y to change.

a) True
b) False

Answer 24

b) False

Correlation does not assume or imply causation

Question 25

does correlation = causation?

Answer 25

nah boy

Question 26

The ___________ the r2 and the __________ the s (standard error),

the stronger the relationship between the dependent variable and the independent variable.

a) lower, lower
b) higher, higher
c) higher, lower
d) lower, higher

Answer 26

c) higher, lower

Question 27

In a simple linear regression model,

the intercept term is the mean value of y when x equals _____.

a) 1
b) 0
c) −1
d) y

Answer 27

b) 0

Question 28

The slope of the simple linear regression equation represents the average change in the value of the dependent variable per unit change in the independent variable (X).

a) True
b) False

Answer 28

a) True

Question 29

in a simple linear regression analysis,

the correlation coefficient (r) and the slope (b) ___________ have the same sign.

a) always
b) sometimes
c) never

Answer 29

a) always