Deck 13: Correlation and Linear Regression

Question 1

The coefficient of determination is the square root of the coefficient of correlation.

Answer 1

False

Question 2

If the coefficient of determination is expressed as a percent, its value is between 0% and 100%.

Answer 2

True

Question 3

In plotting paired data in a scatter diagram, the dependent variable scaled on the ___________________.

Answer 3

Y or vertical axis

Question 4

The strength of the correlation between two variables depends on the sign of the coefficient of correlation.

Question 5

The regression equation is used to estimate a value of the dependent variable Y based on a selected value of the independent variable X.

Question 6

One assumption underlying linear regression is that the Y values are statistically dependent. This means that in selecting a sample, the Y values chosen, for a particular X value, depend on the Y values for any other X value.

Question 7

The hypothesis to test the slope of a regression equation is H₀: $\alpha$ = 0.

Question 8

If there is absolutely no relationship between two variables, what will Pearson's r equal? _____

Question 9

The coefficient of determination is the proportion of total variation in Y that is explained by X.

Question 10

If the coefficient of determination is 0.81, what is the coefficient of correlation? ______

Question 11

An economist is interested in predicting the unemployment rate based on gross domestic product. Since the economist is interested in predicting unemployment, the independent variable is gross domestic product.

Question 12

Correlation analysis is a statistical technique used to measure the strength of the relationship between two variables.

Question 13

A scatter diagram is a graph that portrays the correlation between a dependent variable and an independent variable.

Question 14

A confidence interval can be determined for the mean value of Y for a given value of X.

Question 15

The least squares technique minimizes the sum of the squares of the vertical distances between the actual Y values and the predicted values of Y.

Question 16

The values of a and b in the regression equation are called the regression coefficients.

Question 17

In regression analysis, error is defined as ( - Y).

Question 18

If the coefficient of correlation is 0.80, what is the coefficient of determination? ______

Question 19

How do we designate the population correlation coefficient? _____

Question 20

The standard error of estimate measures the accuracy of a prediction.

Question 21

What is the range of values that the coefficient of determination can assume? _____ and ______

Question 22

If the value of r is -0.96, what does this indicate about the dependent variable as the independent variable increases? ___________

Question 23

What is the value of the correlation coefficient if there is perfect correlation? ___________

Question 24

Approximately what percent of the values lie within two standard errors of the regression line? ________

Question 25

Perfect correlation means that the scatter diagram will appear as a _____________________.

Question 26

A chart that shows the relationship between a dependent variable and an independent variable is called a ______________________.

Question 27

What is the best model to describe a linear relationship between two variables? ________________________

Question 28

What do the coefficient of correlation and the slope of the regression line always have in common? __________________

Question 29

What is the proportion of explained variation called? ________________

Question 30

A random sample of 15 homes that recently sold is obtained. The correlation between the area of the home, in square feet, and the selling price is 0.40. We want to test the null hypothesis that the correlation in the population is less than or equal to zero versus the alternate that it is greater than zero. The rejection region will fall in the ________ tail of a t distribution.

Question 31

What is the general form of the regression equation? _____________

Question 32

If the correlation between sales and advertising is +0.6, what percent of the variation in sales can be attributed to advertising? ______

Question 33

If the coefficient of correlation is -0.81, what is the coefficient of determination? _______

Question 34

What is the technique used to predict or estimate the value of the dependent variable Y based on a selected value of an independent variable X called? __________________________

Question 35

What principle is applied when calculating the regression coefficients? _________________

Question 36

An assumption of linear regression states that for each value of X, there is a group of Y values that are statistically __________________ and normally distributed about the regression line.

Question 37

What principle minimizes the sum of the squares of the vertical deviations about the line? _______________

Question 38

What is the direction of a regression line if its slope equals zero, indicating a lack of a relationship? ____________________

Question 39

The standard error of the estimate measures the scatter or dispersion of the observed values around a ___________________.

Question 40

What type of correlation designates an inverse relationship between two variables? ___________________

Question 41

The Pearson product-moment correlation coefficient, r, requires that variables are measured with:

A) An interval or ratio scale.
B) An ordinal or ratio scale.
C) A nominal or ordinal scale.
D) A nominal or ratio scale.

Question 42

Which of the following statements regarding the coefficient of correlation is true?

A) It ranges from 0.0 to +1.0 inclusive.
B) It tests for a relationship between two variables.
C) A value of 0.00 indicates two variables are related.
D) It is calculated as the square of the slope.

Question 43

Which value of r indicates a stronger correlation than 0.40?

A) -0.30
B) -0.50
C) +0.38
D) 0

Question 44

If the correlation coefficient between two variables equals zero, what can be said of the variables X and Y?

A) Not related
B) Dependent on each other
C) Highly related
D) X causes Y

Question 45

If we reject the null hypothesis that tests a population correlation coefficient, what can we conclude about the correlation in the population?

A) It is zero
B) It could be zero
C) It is not zero
D) It equals the computed sample correlation

Question 46

What is the chart called when the paired data (the dependent and independent variables) are plotted?

A) Scatter diagram
B) Bar chart
C) Pie chart
D) Histogram

Question 47

If the correlation between two variables is close to one, the association is

A) significant.
B) moderate.
C) insignificant.
D) none.

Question 48

If r = 0.65, what does the coefficient of determination equal?

A) 0.1945
B) 0.4225
C) 0.5778
D) 0.8061

Question 49

In the regression equation, what does the letter "b" represent?

A) Y intercept
B) Slope of the line
C) Any value of the independent variable that is selected
D) Value of Y when X = 0

Question 50

In the regression equation, what does the letter "X" represent?

A) Y intercept
B) Slope of the line
C) The independent variable
D) The dependent variable

Question 51

A hypothesis test is conducted at the .05 level of significance to test whether or not the population correlation is zero. If the sample consists of 25 observations and the correlation coefficient is 0.60, what is the computed value of the test statistic?

A) 1.96
B) 2.07
C) 2.94
D) 3.60

Question 52

What is the range of values for the coefficient of determination?

A) -1 to +1 inclusive
B) -100% to +100% inclusive
C) -100% to 0% inclusive
D) 0% to 100% inclusive

Question 53

What is the null hypothesis to test the significance of the slope in a regression equation?

A) H₀: $\beta$ = 0
B) H₀: $\beta$ $\neq$ 0
C) H₀: $\beta$$\le$ 0
D) H₀: $\beta$$\ge$

Question 54

In the regression equation, what does the letter "Y" represent?

A) Y intercept
B) Slope of the line
C) The independent variable
D) The dependent variable

Question 55

In the regression equation, what does the letter "a" represent?

A) Y intercept
B) Slope of the line
C) Any value of the independent variable that is selected
D) Error

Question 56

What is the variable used to predict the value of another called?

A) Independent variable
B) Dependent variable
C) Correlation variable
D) Variable of determination

Question 57

What does a coefficient of correlation of 0.70 infer?

A) Almost no correlation because 0.70 is close to 1.0
B) 70% of the variation in one variable is explained by the other
C) Coefficient of determination is 0.49
D) Coefficient of nondetermination is 0.30

Question 58

What does the coefficient of determination equal if r = 0.89?

A) 0.9412
B) 0.0121
C) 0.7921
D) 0.1100

Question 59

What can we conclude if the coefficient of determination is 0.94?

A) The strength of the relationship is 0.94.
B) The direction of relationship is positive.
C) 94% of total variation of one variable is explained by variation in the other variable.
D) The direction of the relationship is negative.

Question 60

What is the range of values for a coefficient of correlation?

A) 0 to +1.0
B) -3 to +3 inclusive
C) -1.0 to +1.0 inclusive
D) Unlimited range

Question 61

Which of the following is true about the standard error of estimate?

A) It is a measure of the accuracy of the prediction
B) It is based on squared vertical deviations between Y and X
C) It can be negative
D) It is calculated using the regression mean square

Question 62

Which of the following is NOT a difference between a confidence interval and a prediction interval?

A) The addition of "1" under the radical for the prediction interval.
B) A confidence interval uses the standard error of estimate and a prediction interval does not.
C) A prediction interval refers to a specific case.
D) A confidence interval is narrower than a prediction interval.

Question 63

The regression equation is Ŷ = 30 + 2.56X, the sample size is 14, and the standard error of the slope is 0.97. What is the test statistic to test the significance of the slope?

A) z = -2.56
B) z = 2.639
C) t = 2.56
D) t = 2.639

Question 64

Given the least squares regression equation, Ŷ = 1,202 + 1,133X, when X = 3, what does Ŷ equal?

A) 5,734
B) 8,000
C) 4,601
D) 4,050

Question 65

If all the plots on a scatter diagram lie on a straight line, what is the standard error of estimate?

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

Question 66

In regression, the difference between the confidence interval and prediction interval formulas is

A) the prediction interval is the square root of the confidence interval.
B) the addition of "1" to the quantity under the radical sign.
C) the prediction interval uses and the confidence interval uses r.
D) no difference.

Question 67

What is the variable used to predict another variable called?

A) Independent variable
B) Dependent variable
C) Important variable
D) Causal variable

Question 68

The regression equation is ? = 29.29 - 0.96X, the sample size is 8, and the standard error of the slope is 0.22. What is the critical value to test the significance of the slope at the 0.01 significance level?

A) z = 2.576
B) t = 3.707
C) t = 3.355
D) t = $\pm$ 3.707

Question 69

Based on the regression equation, we can

A) predict the value of the dependent variable given a value of the independent variable.
B) predict the value of the independent variable given a value of the dependent variable.
C) measure the association between two variables.
D) measure cause and effect.

Question 70

What is the test statistic to test the significance of the slope in a regression equation?

A) z-statistic
B) F-statistic
C) t-statistic
D) $\pi$ -statistic

Question 71

In the least squares equation, Ŷ = 10 + 20X the value of 20 indicates

A) the Y intercept increases by 20 units for each unit increase in X.
B) that Y increases by 20 units for each unit increase in X.
C) that X increases by 20 units for each unit increase in Y.
D) the error in prediction.

Question 72

Assume the least squares equation is Ŷ = 10 + 20X. What does the value of 10 in the equation indicate?

A) Y intercept
B) X increases by 10 for each unit increase in Y
C) Y increases by 10, for each unit increase in X
D) Error

Question 73

What is the general form of the regression equation?

A) Ŷ= ab
B)
C)
D) Ŷ= abX

Question 74

The regression equation is ? = 30 + 2.56X, the sample size is 14, and the standard error of the slope is 0.97. What is the critical value to test the significance of the slope at the 0.05 significance level?

A) z = $\pm$ 1.96
B) t = $\pm$ 2.179
C) t = $\pm$ 2.145
D) t = +2.145

Question 75

What is the alternate hypothesis to test the significance of the slope in a regression equation?

A) H₁:  = 0 H₁:   0
C) H₁:   0
D) H₁:  0

Question 76

What are the degrees of freedom used to test the significance of the slope in a regression equation?

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

Question 77

The regression equation is Ŷ = 29.29 - 0.96X, the sample size is 8, and the standard error of the slope is 0.22. What is the test statistic to test the significance of the slope?

A) z = -4.364
B) z = 4.364
C) t = -4.364
D) t = -0.96

Question 78

In the equation Ŷ = a + bX, what is Ŷ?

A) Slope of the line
B) Y intercept
C) Predicted value of Y, given a specific X value
D) Value of Y when X = 0

Question 79

When comparing the 95% confidence and prediction intervals for a given regression analysis,

A) the confidence interval is wider than a prediction interval.
B) the confidence interval is narrower than a prediction interval.
C) there is no difference between confidence and prediction intervals.
D) the prediction interval has a higher level of confidence.

Question 80

Which of the following are true assumptions underlying linear regression? 1) For each value of X, there is a group of Y values which is normally distributed. 2) The means of these normal distributions of Y values all lie on the regression line. 3) The standard deviations of these normal distributions are equal.

A) Only (1)
B) Only (2)
C) Only (3)
D) All of them