Simple Linear Regression

Question 1

A numerical measure of linear association between two variables is the

Answer 1

covariance

Question 2

A numerical measure of linear association between two variables is the

Answer 2

correlation coefficient

Question 3

The coefficient of correlation

Answer 3

cannot be larger than 1

Question 4

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

Answer 4

zero

Question 5

The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = 0 + 1x, is known as

Answer 5

regression equation

Question 6

A regression analysis between sales (Y in $1000) and advertising (X in dollars) resulted in the following equation
Y hat= 30,000 + 4 X

Answer 6

increase of $1 in advertising is associated with an increase of $4,000 in sales

Question 7

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

Answer 7

None of these alternatives is correct.

Question 8

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

Answer 8

the regression model

Question 9

In a regression analysis, the variable that is being predicted

Answer 9

is the dependent variable

Question 10

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

Answer 10

increase of $1 in price is associated with a decrease of $8000 in sales

Question 11

A regression analysis between demand (Y in 1000 units) and price (X in dollars) resulted in the following equation
Y8 = 9 - 3X
The above equation implies that if the price is increased by $1, the demand is expected to

Answer 11

decrease by 3,000 units

Question 12

A least squares regression line

Answer 12

may be used to predict a value of y if the corresponding x value is given

Question 13

The coefficient of determination

Answer 13

cannot be negative

Question 14

The value of the coefficient of correlation (R)

Answer 14

can be equal to the value of the coefficient of determination (R2)

Question 15

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

Answer 15

0.65

Question 16

Correlation analysis is used to determine

Answer 16

the strength of the relationship between the dependent and the independent variables

Question 17

In a regression and correlation analysis if r squared = 1, then

Answer 17

SSR = SST

Question 18

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

Answer 18

0.6000

Question 19

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

Answer 19

must have a positive slope

Question 20

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

Answer 20

coefficient of determination can be computed

Question 21

SSE can never be

Answer 21

larger than SST

Question 22

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

Answer 22

must be positive

Question 23

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

Answer 23

there may or may not be any causal relationship between x and y

Question 24

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

Answer 24

1

Question 25

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

Answer 25

0.40

Question 26

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

Answer 26

is 16%.

Question 27

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

Answer 27

must be 0.81

Question 28

If the coefficient of correlation is a positive value, then

Answer 28

the slope of the line must be positive

Question 29

In regression analysis, which of the following is not a required assumption about the error term (backward 3)

Answer 29

The expected value of the error term is one.

Question 30

In regression analysis, the unbiased estimate of the variance is

Answer 30

mean square error

Question 31

If only MSE is known, you can compute the

Answer 31

standard error

Question 32

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

Answer 32

The F test and the t test may or may not yield the same conclusion.

Question 33

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

Answer 33

confidence interval estimate

Question 34

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. Y hat = 120 - 10 X Based on the above estimated regression equation, if price is increased by 2 units, then demand is expected to

Answer 34

decease by 20 units

Question 35

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

Answer 35

$900,000

Question 36

Regression analysis was applied between sales (Y in $1,000) and advertising (X in $100), and the following estimated regression equation was obtained. Y hat = 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

Answer 36

$700,000