Deck 12: Simple Linear Regression

Question 1

In a regression analysis, the error term ε is a random variable with a mean or expected value of

A) zero
B) one
C) any positive value
D) any value

Answer 1

A

Question 2

In regression analysis, the unbiased estimate of the variance is

A) coefficient of correlation
B) coefficient of determination
C) mean square error
D) slope of the regression equation

Answer 2

C

Question 3

In regression analysis, the model in the form y = β₀ + β₁x + ε is called

A) regression equation
B) correlation equation
C) estimated regression equation
D) regression model

Answer 3

D

Question 4

In a simple regression analysis where Y is a dependent and X an independent variable), if the Y intercept is positive, then

A) there is a positive correlation between X and Y
B) if X is increased, Y must also increase
C) if Y is increased, X must also increase
D) None of these alternatives is correct.

Question 5

In the following estimated regression equation $\widehat { y }$ = b? + b?x

A) b? is the slope
B) b? is the intercept
C) b? is the slope
D) None of these alternatives is correct.

Question 6

Regression analysis is a statistical procedure for developing a mathematical equation that describes how

A) one independent and one or more dependent variables are related
B) several independent and several dependent variables are related
C) one dependent and one or more independent variables are related
D) None of these alternatives is correct.

Question 7

In regression analysis, which of the following is not a required assumption about the error term ε?

A) The expected value of the error term is one.
B) The variance of the error term is the same for all values of X.
C) The values of the error term are independent.
D) The error term is normally distributed.

Question 8

The interval estimate of the mean value of y for a given value of x is

A) prediction interval estimate
B) confidence interval estimate
C) average regression
D) x versus y correlation interval

Question 9

The model developed from sample data that has the form of $\widehat { y }$ = b? + b?x is known as

A) regression equation
B) correlation equation
C) estimated regression equation
D) regression model

Question 10

A regression analysis between sales Y in $1000) and advertising X in dollars) resulted in the following equation $\hat { Y }$ = 30,000 + 4 X
The above equation implies that an

A) increase of $4 in advertising is associated with an increase of $4,000 in sales
B) increase of $1 in advertising is associated with an increase of $4 in sales
C) increase of $1 in advertising is associated with an increase of $34,000 in sales
D) increase of $1 in advertising is associated with an increase of $4,000 in sales

Question 11

The value of the coefficient of correlation R)

A) can be equal to the value of the coefficient of determination R²)
B) can never be equal to the value of the coefficient of determination R²)
C) is always smaller than the value of the coefficient of determination
D) is always larger than the value of the coefficient of determination

Question 12

If the coefficient of determination is a positive value, then the coefficient of correlation

A) must also be positive
B) must be zero
C) can be either negative or positive
D) must be larger than 1

Question 13

The coefficient of determination

A) cannot be negative
B) is the square root of the coefficient of correlation
C) is the same as the coefficient of correlation
D) can be negative or positive

Question 14

The standard error is the

A) t-statistic squared
B) square root of SSE
C) square root of SST
D) square root of MSE

Question 15

In regression analysis, the variable that is being predicted is the

A) dependent variable
B) independent variable
C) intervening variable
D) is usually x

Question 16

The equation that describes how the dependent variable y) is related to the independent variable x) is called

A) the correlation model
B) the regression model
C) correlation analysis
D) None of these alternatives is correct.

Question 17

The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, Ey) = β₀ + β₁x, is known as

A) regression equation
B) correlation equation
C) estimated regression equation
D) regression model

Question 18

In a regression analysis the standard error is determined to be 4. In this situation the MSE

A) is 2
B) is 16
C) depends on the sample size
D) depends on the degrees of freedom

Question 19

If only MSE is known, you can compute the

A) r square
B) coefficient of determination
C) standard error
D) all of these alternatives are correct

Question 20

The interval estimate of an individual value of y for a given value of x is

A) prediction interval estimate
B) confidence interval estimate
C) average regression
D) x versus y correlation interval

Question 21

In a regression and correlation analysis if R² = 1, then

A) SSE must also be equal to one
B) SSE must be equal to zero
C) SSE can be any positive value
D) SSE must be negative

Question 22

Larger values of R² imply that the observations are more closely grouped about the

A) average value of the independent variables
B) average value of the dependent variable
C) least squares line
D) origin

Question 23

SSE can never be

A) larger than SST
B) smaller than SST
C) equal to 1
D) equal to zero

Question 24

If the coefficient of correlation is a positive value, then the regression equation

A) must have a positive slope
B) must have a negative slope
C) could have either a positive or a negative slope
D) must have a positive y intercept

Question 25

In a regression analysis, the coefficient of correlation is 0.16. The coefficient of determination in this situation is

A) 0.4000
B) 0.0256
C) 4
D) 2.56

Question 26

The coefficient of correlation

A) is the square of the coefficient of determination
B) is the square root of the coefficient of determination
C) is the same as r-square
D) can never be negative

Question 27

In a regression analysis, the regression equation is given by y = 12 - 6x. If SSE = 510 and SST = 1000, then the coefficient of correlation is

A) -0.7
B) +0.7
C) 0.49
D) -0.49

Question 28

In regression analysis, the independent variable is

A) used to predict other independent variables
B) used to predict the dependent variable
C) called the intervening variable
D) the variable that is being predicted

Question 29

Correlation analysis is used to determine

A) the equation of the regression line
B) the strength of the relationship between the dependent and the independent variables
C) a specific value of the dependent variable for a given value of the independent variable
D) None of these alternatives is correct.

Question 30

If the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the variation in the independent variable is

A) 0.80%
B) 80%
C) 0.64%
D) 64%

Question 31

In a regression analysis, the variable that is being predicted

A) must have the same units as the variable doing the predicting
B) is the independent variable
C) is the dependent variable
D) usually is denoted by x

Question 32

If there is a very weak correlation between two variables, then the coefficient of determination must be

A) much larger than 1, if the correlation is positive
B) much smaller than -1, if the correlation is negative
C) much larger than one
D) None of these alternatives is correct.

Question 33

In regression analysis, if the independent variable is measured in pounds, the dependent variable

A) must also be in pounds
B) must be in some unit of weight
C) cannot be in pounds
D) can be any units

Question 34

In a regression analysis, the coefficient of determination is 0.4225. The coefficient of correlation in this situation is

A) 0.65
B) 0.1785
C) any positive value
D) any value

Question 35

In simple linear regression analysis, which of the following is not true?

A) The F test and the t test yield the same conclusion.
B) The F test and the t test may or may not yield the same conclusion.
C) The relationship between X and Y is represented by means of a straight line.
D) The value of F = t2.

Question 36

In a regression and correlation analysis if R² = 1, then

A) SSE = SST
B) SSE = 1
C) SSR = SSE
D) SSR = SST

Question 37

If the coefficient of determination is equal to 1, then the coefficient of correlation

A) must also be equal to 1
B) can be either -1 or +1
C) can be any value between -1 to +1
D) must be -1

Question 38

In regression and correlation analysis, if SSE and SST are known, then with this information the

A) coefficient of determination can be computed
B) slope of the line can be computed
C) Y intercept can be computed
D) x intercept can be computed

Question 39

Regression analysis was applied between demand for a product Y) and the price of the product X), and the following estimated regression equation was obtained. $\hat { Y }$ = 120 - 10 X
Based on the above estimated regression equation, if price is increased by 2 units, then demand is expected to

A) increase by 120 units
B) increase by 100 units
C) increase by 20 units
D) decease by 20 units

Question 40

In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is

A) 0.6667
B) 0.6000
C) 0.4000
D) 1.5000

Question 41

A least squares regression line

A) may be used to predict a value of y if the corresponding x value is given
B) implies a cause-effect relationship between x and y
C) can only be determined if a good linear relationship exists between x and y
D) None of these alternatives is correct.

Question 42

If a data set has SSR = 400 and SSE = 100, then the coefficient of determination is

A) 0.10
B) 0.25
C) 0.40
D) 0.80

Question 43

Compared to the confidence interval estimate for a particular value of y in a linear regression model), the interval estimate for an average value of y will be

A) narrower
B) wider
C) the same
D) None of these alternatives is correct.

Question 44

A regression analysis between sales in $1000) and price in dollars) resulted in the following equation = 60 - 8X
$\hat { Y }$ The above equation implies that an

A) increase of $1 in price is associated with a decrease of $8 in sales
B) increase of $8 in price is associated with an decrease of $52,000 in sales
C) increase of $1 in price is associated with a decrease of $52 in sales
D) increase of $1 in price is associated with a decrease of $8000 in sales

Question 45

If the coefficient of correlation is -0.4, then the slope of the regression line

A) must also be -0.4
B) can be either negative or positive
C) must be negative
D) must be 0.16

Question 46

It is possible for the coefficient of determination to be

A) larger than 1
B) less than one
C) less than -1
D) None of these alternatives is correct.

Question 47

If the coefficient of correlation is 0.90, then the coefficient of determination

A) is also 0.9
B) is either 0.81 or -0.81
C) can be either negative or positive
D) must be 0.81

Question 48

If two variables, x and y, have a strong linear relationship, then

A) there may or may not be any causal relationship between x and y
B) x causes y to happen
C) y causes x to happen
D) None of these alternatives is correct.

Question 49

A regression analysis between demand Y in 1000 units) and price X in dollars) resulted in the following equation = 9 - 3X
$\hat { Y }$ The above equation implies that if the price is increased by $1, the demand is expected to

A) increase by 6 units
B) decrease by 3 units
C) decrease by 6,000 units
D) decrease by 3,000 units

Question 50

In a regression analysis if SST = 4500 and SSE = 1575, then the coefficient of determination is

A) 0.35
B) 0.65
C) 2.85
D) 0.45

Question 51

In a regression analysis if SST = 500 and SSE = 300, then the coefficient of determination is

A) 0.20
B) 1.67
C) 0.60
D) 0.40

Question 52

In regression analysis if the dependent variable is measured in dollars, the independent variable

A) must also be in dollars
B) must be in some units of currency
C) can be any units
D) cannot be in dollars

Question 53

If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on these data is

A) 0
B) 1
C) either 1 or -1, depending upon whether the relationship is positive or negative
D) could be any value between -1 and 1

Question 54

If there is a very strong correlation between two variables then the coefficient of determination must be

A) much larger than 1, if the correlation is positive
B) much smaller than -1, if the correlation is negative
C) any value larger than 1
D) None of these alternatives is correct.

Question 55

If the coefficient of correlation is a negative value, then the coefficient of determination

A) must also be negative
B) must be zero
C) can be either negative or positive
D) must be positive

Question 56

The coefficient of correlation

A) is the square of the coefficient of determination
B) is the square root of the coefficient of determination
C) is the same as r-square
D) can never be negative

Question 57

Regression analysis was applied between sales in $1000) and advertising in $100) and the following regression function was obtained. = 500 + 4 X
$\hat { Y }$ Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales in dollars) is

A) $900
B) $900,000
C) $40,500
D) $505,000

Question 58

If the coefficient of determination is 0.81, the coefficient of correlation

A) is 0.6561
B) could be either + 0.9 or - 0.9
C) must be positive
D) must be negative

Question 59

Regression analysis was applied between sales in $10,000) and advertising in $100) and the following regression function was obtained. = 50 + 8 X
$\hat { Y }$ Based on the above estimated regression line if advertising is $1,000, then the point estimate for sales in dollars) is

A) $8,050
B) $130
C) $130,000
D) $1,300,000

Question 60

If the coefficient of correlation is 0.4, the percentage of variation in the dependent variable explained by the variation in the independent variable

A) is 40%
B) is 16%.
C) is 4%
D) can be any positive value

Question 61

Exhibit 12-2
You are given the following information about y and x.
$\begin{array}{cc}\text { Dependent Variable Y) }&\text { Independent Variable } \mathbf{X} \text { ) }\\5 & 1 \\4 & 2 \\3 & 3 \\2 & 4 \\1 & 5\end{array}$

-Refer to Exhibit 12-2. The sample correlation coefficient equals

A) 0
B) +1
C) -1
D) -0.5

Question 62

Regression analysis was applied between sales Y in $1,000) and advertising X in $100), and the following estimated regression equation was obtained. $\hat { Y }$ = 80 + 6.2 X
Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales in dollars) is

A) $62,080
B) $142,000
C) $700
D) $700,000

Question 63

Exhibit 12-1
The following information regarding a dependent variable Y) and an independent variable X) is provided.
$\begin{array} { l l } Y&X\\4&2\\3&1\\4&4\\6&3\\8&5\end{array}$ SSE = 6
SST = 16

-Refer to Exhibit 12-1. The least squares estimate of the Y intercept is

A) 1
B) 2
C) 3
D) 4

Question 64

Exhibit 12-1
The following information regarding a dependent variable Y) and an independent variable X) is provided.
$\begin{array} { l l } Y&X\\4&2\\3&1\\4&4\\6&3\\8&5\end{array}$ SSE = 6
SST = 16

-Refer to Exhibit 12-1. The coefficient of determination is

A) 0.7096
B) - 0.7906
C) 0.625
D) 0.375

Question 65

Exhibit 12-1
The following information regarding a dependent variable Y) and an independent variable X) is provided.
$\begin{array} { l l } Y&X\\4&2\\3&1\\4&4\\6&3\\8&5\end{array}$ SSE = 6
SST = 16

-Refer to Exhibit 12-1. The MSE is

A) 1
B) 2
C) 3
D) 4

Question 66

Exhibit 12-4
Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained.
= 12 + 1.8 x
$\hat { Y }$ n = 17
SSR = 225
SSE = 75
Sb? = 0.2683

-Refer to Exhibit 12-4. Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales in dollars) is

A) $66,000
B) $5,412
C) $66
D) $17,400

Question 67

Exhibit 12-1
The following information regarding a dependent variable Y) and an independent variable X) is provided.
$\begin{array} { l l } Y&X\\4&2\\3&1\\4&4\\6&3\\8&5\end{array}$ SSE = 6
SST = 16

-Refer to Exhibit 12-1. The least squares estimate of the slope is

A) 1
B) 2
C) 3
D) 4

Question 68

Exhibit 12-2
You are given the following information about y and x.
$\begin{array}{cc}\text { Dependent Variable Y) }&\text { Independent Variable } \mathbf{X} \text { ) }\\5 & 1 \\4 & 2 \\3 & 3 \\2 & 4 \\1 & 5\end{array}$

-Refer to Exhibit 12-2. The coefficient of determination equals

A) 0
B) -1
C) +1
D) -0.5

Question 69

Exhibit 12-2
You are given the following information about y and x.
$\begin{array}{cc}\text { Dependent Variable Y) }&\text { Independent Variable } \mathbf{X} \text { ) }\\5 & 1 \\4 & 2 \\3 & 3 \\2 & 4 \\1 & 5\end{array}$

-Refer to Exhibit 12-2. The least squares estimate of b? intercept)equals

A) 1
B) -1
C) 6
D) 5

Question 70

Exhibit 12-4
Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained.
= 12 + 1.8 x
$\hat { Y }$ n = 17
SSR = 225
SSE = 75
Sb? = 0.2683

-Refer to Exhibit 12-4. The F statistic computed from the above data is

A) 3
B) 45
C) 48
D) 50

Question 71

Exhibit 12-1
The following information regarding a dependent variable Y) and an independent variable X) is provided.
$\begin{array} { l l } Y&X\\4&2\\3&1\\4&4\\6&3\\8&5\end{array}$ SSE = 6
SST = 16

-Refer to Exhibit 12-1. The coefficient of correlation is

A) 0.7906
B) - 0.7906
C) 0.625
D) 0.375

Question 72

Exhibit 12-3
You are given the following information about y and x.
$\begin{array}{cc}\text { Dependent Variable Y) }&\text { Independent Variable } \mathbf{X} \text { ) }\\12 & 4 \\3 & 6 \\7 & 2 \\6 & 4\end{array}$

-Refer to Exhibit 12-3. The coefficient of determination equals

A) -0.4364
B) 0.4364
C) -0.1905
D) 0.1905

Question 73

If the coefficient of correlation is a positive value, then

A) the intercept must also be positive
B) the coefficient of determination can be either negative or positive, depending on the value of the slope
C) the regression equation could have either a positive or a negative slope
D) the slope of the line must be positive

Question 74

Exhibit 12-4
Regression analysis was applied between sales data Y in $1,000s) and advertising data x in $100s) and the following information was obtained.
= 12 + 1.8 x
$\hat { Y }$ n = 17
SSR = 225
SSE = 75
Sb? = 0.2683

-Refer to Exhibit 12-4. To perform an F test, the p-value is

A) less than .01
B) between .01 and .025
C) between .025 and .05
D) between .05 and 0.1

Question 75

Exhibit 12-3
You are given the following information about y and x.
$\begin{array}{cc}\text { Dependent Variable Y) }&\text { Independent Variable } \mathbf{X} \text { ) }\\12 & 4 \\3 & 6 \\7 & 2 \\6 & 4\end{array}$

-Refer to Exhibit 12-3. The sample correlation coefficient equals

A) -0.4364
B) 0.4364
C) -0.1905
D) 0.1905

Question 76

If the coefficient of determination is 0.9, the percentage of variation in the dependent variable explained by the variation in the independent variable

A) is 0.90%
B) is 90%.
C) is 81%
D) 0.81%

Question 77

Exhibit 12-3
You are given the following information about y and x.
$\begin{array}{cc}\text { Dependent Variable Y) }&\text { Independent Variable } \mathbf{X} \text { ) }\\12 & 4 \\3 & 6 \\7 & 2 \\6 & 4\end{array}$

-Refer to Exhibit 12-3. The least squares estimate of b? equals

A) 1
B) -1
C) -11
D) 11

Question 78

Exhibit 12-3
You are given the following information about y and x.
$\begin{array}{cc}\text { Dependent Variable Y) }&\text { Independent Variable } \mathbf{X} \text { ) }\\12 & 4 \\3 & 6 \\7 & 2 \\6 & 4\end{array}$

-Refer to Exhibit 12-3. The least squares estimate of b? equals

A) 1
B) -1
C) -11
D) 11

Question 79

Exhibit 12-2
You are given the following information about y and x.
$\begin{array}{cc}\text { Dependent Variable Y) }&\text { Independent Variable } \mathbf{X} \text { ) }\\5 & 1 \\4 & 2 \\3 & 3 \\2 & 4 \\1 & 5\end{array}$

-Refer to Exhibit 12-2. The least squares estimate of b? slope) equals

A) 1
B) -1
C) 6
D) 5

Question 80

Exhibit 12-2
You are given the following information about y and x.
$\begin{array}{cc}\text { Dependent Variable Y) }&\text { Independent Variable } \mathbf{X} \text { ) }\\5 & 1 \\4 & 2 \\3 & 3 \\2 & 4 \\1 & 5\end{array}$

-Refer to Exhibit 12-2. The point estimate of y when x = 10 is

A) -10
B) 10
C) -4
D) 4