Deck 12: Simple Linear Regression

Question 1

Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained. = 500 + 4x 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

Answer 1

$900,000

Question 2

Application of the least squares method results in values of the y intercept and the slope that minimizes the sum of the squared deviations between the

A)observed values of the independent variable and the predicted values of the independent variable
B)actual values of the independent variable and predicted values of the dependent variable
C)observed values of the dependent variable and the predicted values of the dependent variable
D)None of these answers is correct.

Answer 2

observed values of the dependent variable and the predicted values of the dependent variable

Question 3

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

Answer 3

is the dependent variable

Question 4

A measure of the strength of the relationship between two variables is the

A)coefficient of determination
B)slope b₁ of the estimated regression line
C)standard error of the estimate
D)correlation coefficient

Question 5

The least squares criterion is

A)
B)
C)
D)

Question 6

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

A)confidence interval
B)prediction interval
C)residual interval
D)correlation interval

Question 7

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 answers is correct.

Question 8

Regression analysis was applied between sales (in $1,000) and advertising (in $100), and the following regression function was obtained. = 80 + 6.2x 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 9

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)All of these answers are correct.

Question 10

A procedure used for finding the equation of a straight line that provides the best approximation for the relationship between the independent and dependent variables is the

A)correlation analysis
B)mean squares method
C)least squares method
D)most squares method

Question 11

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 unit of currency
C)can be any units
D)can not be in dollars

Question 12

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the

A)correlation coefficient
B)standard error of the estimate
C)coefficient of determination
D)confidence interval estimate

Question 13

A regression analysis between demand (y in 1000 units) and price (x in dollars) resulted in the following equation =9 - 3x 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 14

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)there is a negative correlation between x and y
C)if x is increased, y must also increase
D)None of these answers is correct.

Question 15

In a residual plot against x that does not suggest we should challenge the assumptions of our regression model, we would expect to see

A)a horizontal band of points centered near zero
B)a widening band of points
C)a band of points having a slope consistent with that of the regression equation
D)a parabolic band of points

Question 16

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)None of these answers is correct.

Question 17

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

A)dependent variable
B)independent variable
C)intervening variable
D)None of these answers is correct.

Question 18

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the

A)standard error
B)residual
C)prediction interval
D)variance

Question 19

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 answers is correct.

Question 20

As the goodness of fit for the estimated regression equation increases,

A)the absolute value of the regression equation's slope increases
B)the value of the regression equation's y intercept decreases
C)the value of the coefficient of determination increases
D)the value of the correlation coefficient increases

Question 21

SSE can never be

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

Question 22

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

A)much larger than 1, if the correlation is positive
B)much smaller than 1, if the correlation is negative
C)either much larger than 1 or much smaller than 1
D)None of these answers is correct.

Question 23

If the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the estimated regression equation is

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

Question 24

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)All of the above can be computed.

Question 25

In a regression 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 26

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

A)0.6000
B)0.1666
C)1.6666
D)0.3750

Question 27

If the coefficient of determination 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 28

In simple linear regression, r² is the

A)estimated regression equation
B)coefficient of correlation
C)sum of the squared residuals
D)coefficient of determination

Question 29

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 this 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 30

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 31

Which of the following is correct?

A)SSE = SSR +SST
B)SSR = SSE +SST
C)SST =SSR + SSE
D)SST= (SSR)²

Question 32

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 33

In a regression analysis if r² = 1, then

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

Question 34

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 35

It is possible for the coefficient of determination to be

A)larger than 1
B)less than one
C)less than zero
D)All of these answers are correct, depending on the situation under consideration.

Question 36

A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation = 50,000 + 6x The above equation implies that an

A)increase of $6 in advertising is associated with an increase of $6,000 in sales
B)increase of $1 in advertising is associated with an increase of $6 in sales
C)increase of $1 in advertising is associated with an increase of $56,000 in sales
D)increase of $1 in advertising is associated with an increase of $6,000 in sales

Question 37

If a data set has SST = 2,000 and SSE =800, then the coefficient of determination is

A)0.4
B)0.6
C)0.5
D)0.8

Question 38

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 39

If the coefficient of correlation is 0.4, the percentage of variation in the dependent variable explained by the estimated regression equation

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

Question 40

A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation =50,000 - 8x 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 increase of $8,000 in sales
C)increase of $1 in price is associated with a decrease of $42,000 in sales
D)increase of $1 in price is associated with a decrease of $8000 in sales

Question 41

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

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

Question 42

Exhibit 12-1
A regression analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x).


-Refer to Exhibit 12-1. The point estimate of y when x = 20 is

A)0
B)31
C)9
D)-9

Question 43

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 44

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

A)is 0.6561
B)must be 0.9
C)must be positive
D)None of these answers is correct.

Question 45

Data points having high leverage are often

A)residuals
B)sum of squares error
C)influential
D)None of the other answers is correct.

Question 46

Exhibit 12-2
You are given the following information about y and x.

Refer to Exhibit 12-2. The least squares estimate of b₀ equals

A)-7.647
B)-1.3
C)21.4
D)16.41176

Question 47

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

A)must also be positive
B)can be either negative or positive
C)can be zero
D)None of these answers is correct.

Question 48

The numerical value of the coefficient of determination

A)is always larger than the coefficient of correlation
B)is always smaller than the coefficient of correlation
C)is negative if the coefficient of determination is negative
D)can be larger or smaller than the coefficient of correlation

Question 49

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

A)The expected value of the error term is zero.
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)All are required assumptions about the error term.

Question 50

A data point (observation) that does not fit the trend shown by the remaining data is called a(n)

A)residual
B)outlier
C)point estimate
D)None of the other answers is correct.

Question 51

Exhibit 12-1
A regression analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x).

Refer to Exhibit 12-1. The least squares estimate of b₀ equals

A)1
B)-1
C)5.5
D)11

Question 52

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 answers is correct.

Question 53

Exhibit 12-1
A regression analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x).

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

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

Question 54

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)Not enough information is given.

Question 55

Exhibit 12-1
A regression analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x).

Refer to Exhibit 12-1. The sample correlation coefficient equals

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

Question 56

An observation that has a strong effect on the regression results is called a(n)

A)residual
B)sum of squares error
C)influential observation
D)None of the other answers is correct.

Question 57

Exhibit 12-1
A regression analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x).

Refer to Exhibit 12-1. The least squares estimate of b₁ equals

A)1
B)-1
C)5.5
D)11

Question 58

Exhibit 12-2
You are given the following information about y and x.

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

A)-0.99705
B)-0.9941
C)0.9941
D)0.99705

Question 59

Exhibit 12-2
You are given the following information about y and x.

Refer to Exhibit 12-2. The least squares estimate of b₁ equals

A)-0.7647
B)-0.13
C)21.4
D)16.412

Question 60

Exhibit 12-2
You are given the following information about y and x.

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

A)-86.667
B)-0.99705
C)0.9941
D)0.99705

Question 61

Exhibit 12-4
The following information regarding a dependent variable (Y) and an independent variable (X) is provided.
SSE = 6
SST = 16
Refer to Exhibit 12-4. The coefficient of correlation is

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

Question 62

Exhibit 12-6
You are given the following information about y and x.

Refer to Exhibit 12-6. The least squares estimate of b₀ equals

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

Question 63

Exhibit 12-6
You are given the following information about y and x.

Refer to Exhibit 12-6. The coefficient of determination equals

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

Question 64

Exhibit 12-5
You are given the following information about y and x.

Refer to Exhibit 12-5. The point estimate of y when x = 10 is

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

Question 65

Exhibit 12-3
Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained.

Refer to Exhibit 12-3. 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 66

Exhibit 12-4
The following information regarding a dependent variable (Y) and an independent variable (X) is provided.
SSE = 6
SST = 16
Refer to Exhibit 12-4. The coefficient of determination is

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

Question 67

Exhibit 12-6
You are given the following information about y and x.

Refer to Exhibit 12-6. The sample correlation coefficient equals

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

Question 68

Exhibit 12-5
You are given the following information about y and x.

Refer to Exhibit 12-5. The sample correlation coefficient equals

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

Question 69

Exhibit 12-6
You are given the following information about y and x.

Refer to Exhibit 12-6. The least squares estimate of b₁ equals

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

Question 70

Exhibit 12-3
Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained.

Refer to Exhibit 12-3. The t statistic for testing the significance of the slope is

A)1.80
B)1.96
C)6.709
D)0.555

Question 71

Exhibit 12-5
You are given the following information about y and x.

Refer to Exhibit 12-5. The coefficient of determination equals

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

Question 72

Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable).

a.Develop the least squares estimated regression equation.
b.At 95% confidence, perform a t test and determine whether or not the slope is significantly different from zero.
c.Perform an F test to determine whether or not the model is significant. Let   0.05.
d.Compute the coefficient of determination.

Question 73

Exhibit 12-4
The following information regarding a dependent variable (Y) and an independent variable (X) is provided.
SSE = 6
SST = 16
Refer to Exhibit 12-4. The least squares estimate of the slope is

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

Question 74

Exhibit 12-3
Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained.

Refer to Exhibit 12-3. The F statistic computed from the above data is

A)3
B)45
C)48
D)Not enough information is given to answer this question.

Question 75

Exhibit 12-5
You are given the following information about y and x.

Refer to Exhibit 12-5. The least squares estimate of b₀ (intercept)equals

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

Question 76

Exhibit 12-4
The following information regarding a dependent variable (Y) and an independent variable (X) is provided.
SSE = 6
SST = 16
Refer to Exhibit 12-4. The MSE is

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

Question 77

Exhibit 12-3
Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained.


-Refer to Exhibit 12-3. The critical F value at $\alpha$ =0.05 is

A)3.59
B)3.68
C)4.45
D)4.54

Question 78

Exhibit 12-3
Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained.


-Refer to Exhibit 12-3. Using $\alpha$ =0.05, the critical t value for testing the significance of the slope is

A)1.753
B)2.131
C)1.746
D)2.120

Question 79

Exhibit 12-4
The following information regarding a dependent variable (Y) and an independent variable (X) is provided.
SSE = 6
SST = 16
Refer to Exhibit 12-4. The least squares estimate of the Y intercept is

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

Question 80

Exhibit 12-5
You are given the following information about y and x.

Refer to Exhibit 12-5. The least squares estimate of b₁ (slope) equals

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