Deck 4: B: Numerical Descriptive Techniques

Question 1

If the coefficient of correlation r = -.81,the standard deviations of x and y are 20 and 25,respectively,then cov(x,y)must be -405.0.

Answer 1

True

Question 2

The advantage that the coefficient of correlation has over the covariance is that the former has a set lower and upper limit.

Answer 2

True

Question 3

If $\sum x _ { i } = 7587$ , $\sum y _ { i } = 7106.4$ ,n = 12,and the slope equals 0.5,then the y-intercept of the least squares line is b₀ = 276.08.

Answer 3

True

Question 4

If the coefficient of correlation r = 0,then there can be no linear relationship between the dependent variable y and the independent variable x.

Question 5

If the standard deviation of x is 18,the covariance of x and y is 120,the coefficient r = 0.90,then the standard deviation of y is 54.87.

Question 6

Three measures of the linear relationship between x and y are the coefficient of correlation,the coefficient of determination,and the coefficient of variation.

Question 7

The Y-intercept,b₀,of the least squares line $\hat { y } = b _ { 0 } + b _ { 1 } x$ represents the:

A) estimated average value of Y when X = 0.
B) estimated average change in Y per unit change in X.
C) predicted value of Y.
D) variation around the sample regression line.

Question 8

A perfect straight line sloping upward would produce a correlation coefficient value of 1.0.

Question 9

If the correlation coefficient r = 1.00,then all the observations must fall exactly on:

A) a straight line with a slope that equals 1.00.
B) a straight line with a negative slope.
C) a straight line with a positive slope.
D) a horizontal straight line with a zero slope.

Question 10

The variance is a measure of the linear relationship between two variables.

Question 11

If the coefficient of correlation r = $\pm$ 1,then the best-fit linear equation will actually include all of the observations.

Question 12

Assuming a linear relationship between X and Y,if the coefficient of correlation (r)equals -0.75,this means that:

A) there is very weak correlation.
B) the slope b₁ is = -0.75.
C) the value of X is always greater than the value of Y.
D) None of these choices are true.

Question 13

The coefficient of correlation r is a number that indicates the direction and the strength of the linear relationship between the dependent variable y and the independent variable x.

Question 14

If the standard deviations of x and y are 12.5 and 10.8,respectively,and the covariance is 118.8,then the coefficient of correlation r is 0.88.

Question 15

When the standard deviation is expressed as a percentage of the mean,the result is the coefficient of correlation.

Question 16

Generally speaking,if two variables are unrelated (as one increases,the other shows no pattern),the covariance will be:

A) a large positive number.
B) a large negative number.
C) a positive or negative number close to zero.
D) None of these choices.

Question 17

If the coefficient of correlation r = 0,then there can be no relationship whatsoever between the dependent variable y and the independent variable x.

Question 18

Generally speaking,if two variables are unrelated,the covariance will be a number close to zero.

Question 19

The slope b₁ of the least squares line $\hat { y } = b _ { 0 } + b _ { 1 } x$ represents the:

A) predicted value of Y when X = 0.
B) estimated average change in Y per unit change in X.
C) predicted value of Y.
D) variation around the regression line.

Question 20

If the covariance of x and y is 26.16 and the standard deviation of x is 32.7,then the slope of the least squares line is b₁ =.80.

Question 21

Longevity and Salary
A sample of eight observations of variables x (years of experience)and y (salary in $1,000s)is shown below:

{Longevity and Salary Narrative} Draw the scatter diagram and plot the least squares line.

Question 22

If cov(x,y)= 20, $s _ { x } ^ { 2 } = 16$ and $s _ { y } ^ { 2 } = 49$ then the sample coefficient of correlation r is:

A) 1.400
B) 0.026
C) 0.714
D) None of these choices.

Question 23

Which of the following is a property of the slope,b₁?

A) The slope equals one if X and Y have the same variance.
B) The slope has the same sign as r,the coefficient of correlation.
C) The slope equals one if r equals one.
D) All of these choices are true.

Question 24

The method used to find the best fitting line through the observations is called the ____________________ method.

Question 25

The ____________________ of a linear relationship is hard to interpret from the covariance,but it is easy to interpret from the correlation.

Question 26

The ____________________ of the correlation indicates the direction of a linear relationship.

Question 27

Longevity and Salary
A sample of eight observations of variables x (years of experience)and y (salary in $1,000s)is shown below:

{Longevity and Salary Narrative}
a.
Calculate and interpret the covariance between x and y.
b.
Give a possible reason that the covariance is negative.

Question 28

Longevity and Salary
A sample of eight observations of variables x (years of experience)and y (salary in $1,000s)is shown below:

{Longevity and Salary Narrative} Determine the least squares line,and use it to estimate the value of y for x = 6.

Question 29

In the equation of the least squares line, ,b₀ is the ____________________ and b₁ is the ____________________.

Question 30

When two variables x and y are linearly related,it does not necessarily mean that x ____________________ y.

Question 31

Which of the following is a property of r,the coefficient of correlation?

A) r always lies between 0 and 1.
B) r has no units.
C) If you switch the values of X and Y,the sign of r changes.
D) All of these choices are true.

Question 32

Which of the following are measures of the linear relationship between two variables?

A) The covariance
B) The coefficient of correlation
C) The variance
D) Both a and b

Question 33

The coefficient of determination is the percentage of variation in the ____________________ variable that is explained by the variation in the ____________________ variable.

Question 34

The strength of the linear relationship between two interval variables can be measured by the:

A) coefficient of variation.
B) coefficient of correlation.
C) slope of the regression line.
D) Y-intercept.

Question 35

The y-intercept of the least squares line is the point on the line when ________________ = 0.

Question 36

The ____________________ measures the margin of relative change in the dependent variable.

Question 37

A perfect straight line sloping downward would produce a correlation coefficient equal to:

A) +1.0
B) -1.0
C) 0.0
D) Cannot tell from the information given.

Question 38

The denominator in the calculation of the sample covariance,cov (x,y),is:

A) n -2
B) n - 1
C) n
D) 2n - 1

Question 39

The magnitude of the correlation measures the ____________________ of a linear relationship.