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

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

Answer 2

True

Question 3

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.

Answer 3

True

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

In regression analysis, error is defined as .

Question 9

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

Question 10

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 11

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

Question 12

If the coefficient of correlation is -0.81, the coefficient of determination is ______.

Question 13

If the coefficient of correlation is 0.80, the coefficient of determination is _____.

Question 14

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

Question 15

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

Question 16

One assumption underlying linear regression is that the X values are normally distributed.

Question 17

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

Question 18

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 19

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

Question 20

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

Question 21

For an inverse relationship between two variables, the sign of the correlation coefficient is __________________.

Question 22

The ___________ method determines the equation of a line that minimizes the sum of the squares of the vertical deviations about the line.

Question 23

_______________ 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.

Question 24

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

Question 25

The coefficient of correlation and the slope of the regression line always have their __________ in common.

Question 26

A random sample of 15 recent home sales was selected to test the hypothesis that the area of a home, in square feet, and the selling price are positively correlated. The rejection region will fall in the ________ tail of a t distribution.

Question 27

If the correlation between sales and advertising is +0.6, _____% of the variation in sales can be attributed to advertising.

Question 28

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

A)A scatter diagram
B)A bar chart
C)A pie chart
D)A histogram

Question 29

The best model to describe a linear relationship between two variables is the _______________________.

Question 30

The minimum and maximum values of the coefficient of determination are ________.

Question 31

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

Question 32

If the slope of a regression line is zero, the orientation of the regression line is _________, which indicates a lack of a relationship.

Question 33

A chart that shows the relationship between a continuous dependent variable and a continuous independent variable is called a ____________.

Question 34

The _______________ principle is applied when calculating the regression coefficients.

Question 35

If the sample correlation coefficient, r, is -0.96, the dependent variable ________ as the independent variable increases.

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

Approximately ______% of the observations lies within two standard errors of the regression line.

Question 38

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

A)It ranges from 0.0 to +1.0 inclusive.
B)It describes the 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 39

The proportion of explained variation is called the _______________.

Question 40

In regression analysis, what is the predictor variable called?

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

Question 41

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? Round to two decimal places.

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

Question 42

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

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

Question 43

If we reject the null hypothesis, H₀: , what can we conclude about the population correlation coefficient?

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

Question 44

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

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

Question 45

The Pearson product-moment correlation coefficient, r, requires that variables be 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 46

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

A)Strong
B)Moderate
C)Weak
D)Zero

Question 47

Which value of r indicates a stronger correlation than 0.40?

A)-0.30
B)-0.80
C)+0.38
D)0

Question 48

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 49

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

A)H₁: β = 0
B)H₁: β ≠ 0
C)H₁: β ≤ 0
D)H₁: β ≥ 0

Question 50

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

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

Question 51

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)π-statistic

Question 52

What does a coefficient of correlation of 0.70 infer?

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

Question 53

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

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

Question 54

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

A)The variables are not related.
B)The variables are dependent on each other.
C)The variables are highly related.
D)X causes Y.

Question 55

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

A)H₀: β = 0
B)H₀: β ≠ 0
C)H₀: β ≤ 0
D)H₀: β ≥ 0

Question 56

If the coefficient of determination is 0.94, what can we say about the relationship between two variables?

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

Question 57

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

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

Question 58

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 59

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

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

Question 60

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

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

Question 61

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. What is the independent variable?

A)Salesperson
B)Number of contacts
C)Amount of sales
D)Sales manager

Question 62

What is the general form of the regression equation?

A)Ŷ = ab
B)Ŷ = a+(bX)
C)Ŷ = (a+b)X
D)Ŷ = abX

Question 63

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 64

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression analysis shows the following results: What is the Y-intercept of the linear equation?

A)-12.201
B)2.195
C)-1.860
D)12.505

Question 65

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 = -2.560
B)z = +2.639
C)t = +2.560
D)t = +2.639

Question 66

Which of the following are the same between a confidence interval and a prediction interval?

A)The formulas are the same.
B)They both use the standard error of estimate.
C)They both provide a confidence interval for the mean.
D)A confidence interval and prediction interval are the same width.

Question 67

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 critical value to test the significance of the slope at the 0.05 significance level?

A)z = ±1.96
B)t = ±2.179
C)t = ±2.145
D)t = +2.145

Question 68

Which of the following are true assumptions underlying linear regression? (1) For each value of X, there is a group of Y values that 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

Question 69

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 70

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

A)It is the slope of the line.
B)It is the Y intercept.
C)It is the predicted value of Y, given a specific X value.
D)It is the value of Y when X = 0.

Question 71

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 72

A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. What is the dependent variable?

A)Salesperson
B)Number of contacts
C)Amount of sales dollars
D)Sales manager

Question 73

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 74

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 = -0.960

Question 75

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 76

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 r² and the confidence interval uses r
D)No difference

Question 77

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

A)When X = 0, Y = 10.
B)X increases by 10 for each unit increase in Y.
C)Y increases by 10, for each unit increase in X.
D)It is the error of estimation.

Question 78

What is the variable used to predict another variable called?

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

Question 79

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 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 = ±3.707

Question 80

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