Deck 13: Linear Regression and Correlation

Question 1

A coefficient of correlation,r,close to 0 (say,0.08)shows that the relationship between two variables is quite weak.

Answer 1

True

Question 2

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

Answer 2

False

Question 3

The two variables in a correlation analysis are called the dependent and response variables.

Answer 3

False

Question 4

The coefficient of correlation,r,is often referred to as Spearman's rho.

Question 5

If the coefficient of correlation is -0.90,the coefficient of determination is -0.81.

Question 6

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

Question 7

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

Question 8

The coefficient of correlation r is often referred to as the Pearson product-moment correlation coefficient.

Question 9

If the coefficient of correlation is -0.50,the coefficient of determination is +0.25.

Question 10

A correlation coefficient equal to -1 or +1 indicates perfect correlation.

Question 11

Correlation coefficients of -0.91 and +0.91 represent relationships between two variables that have equal strength but different directions.

Question 12

A coefficient of correlation of -0.96 indicates a very weak negative correlation.

Question 13

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 14

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

Question 15

Pearson's product-moment correlation coefficient,r,requires that the data be interval or ratio scaled,such as incomes and weights.

Question 16

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

Question 17

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

Question 18

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

Question 19

If the coefficient of correlation is 0.68,the coefficient of determination is 0.4624.

Question 20

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

Question 21

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 22

A regression equation is a mathematical equation that defines the relationship between two variables.

Question 23

Pearson's coefficient of correlation can be used if the data is nominally scaled.

Question 24

The coefficient of determination is equal to or greater than zero.

Question 25

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 26

A t test is used to test the significance of the coefficient of correlation.

Question 27

To test the significance of Pearson's r,we use the standard normal z distribution.

Question 28

When testing the strength of the relationship between two variables,the alternate hypothesis is:

Question 29

In regression analysis,we expect prediction error or ( - Y)does not equal zero.

Question 30

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 31

In order to visualize the regression equation line,we can draw a scatter diagram.

Question 32

The technique used to measure the strength of the relationship between two variables using the coefficient of correlation and the coefficient of determination is called regression analysis.

Question 33

The standard error of estimate is used to construct confidence intervals when the sample size is large and the scatter about the regression line is somewhat normally distributed.

Question 34

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

Question 35

The least squares principle is used to determine the best-fitting line.

Question 36

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

Question 37

Trying to predict weekly sales with a standard error of estimate of $1,955,we would conclude that 68 percent of the predictions would not be off more than $1,955,95 percent would not be off by more $3,910,and 99.7 percent would not be off by more than $5,865.

Question 38

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

Question 39

One assumption underlying linear regression is that for each value of X there is a group of Y values that is normally distributed.

Question 40

When testing the strength of the relationship between two variables,the null hypothesis is:

Question 41

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 42

In regression analysis,there is no difference in the width of a confidence interval and the width of a predictor interval.

Question 43

When analyzing a curvilinear relationship between dependent and independent variables,a transformation of the data is necessary.

Question 44

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 45

When analyzing data with regression,a transformation is necessary when the relationship between the dependent and independent variables is linear.

Question 46

A mathematical transformation can be used to change a curvilinear relationship between two variables to a linear relationship.

Question 47

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 48

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)All of these are correct

Question 49

Which value of r indicates a stronger correlation than 0.40?

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

Question 50

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

A)It ranges from -1.0 to +1.0 inclusive
B)It measures the strength of the relationship between two variables
C)A value of 0.00 indicates two variables are not related
D)All of these

Question 51

The smaller the samples,the smaller the standard error of estimate.

Question 52

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

Question 53

Explained variation equals total variation minus unexplained variation.

Question 54

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

A)strong.
B)moderate.
C)weak.
D)none.

Question 55

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

A)Strength of relationship is 0.94.
B)Direction of relationship is positive.
C)94% of total variation of one variable is explained by variation in the other variable.
D)A and B are correct.

Question 56

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 57

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

A)0.194
B)0.423
C)0.577
D)0.806

Question 58

A confidence interval is narrower than a prediction interval because a confidence interval estimates a mean Y instead of an individual Y for a given X.

Question 59

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

A)0.94
B)0.89
C)0.79
D)0.06

Question 60

The least squares method assumes the relationship between the dependent and independent variables is linear.

Question 61

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

A)Y intercept
B)For each unit increased in Y,X increases by 10
C)For each unit increased in X,Y increases by 10
D)None of these

Question 62

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)all of these.

Question 63

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 64

In regression analysis,a transformation is used when.

A)the confidence interval is wider than a prediction interval.
B)two variables are not independent.
C)the relationship between dependent and independent variables is not linear.
D)the correlation is near zero.

Question 65

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
C)It cannot be negative
D)All of these

Question 66

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)None of these

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

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

A)the Y intercept.
B)for each unit increase in X,Y increases by 20.
C)for each unit increase in Y,X increases by 20.
D)none of these.

Question 69

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 70

What is the general form of the regression equation?

A) = ab
B) = a + bX
C) = a - bX
D) = abX

Question 71

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 72

In the equation = a + bX,what is ?

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 73

A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of the sales.To verify this belief,the following data was collected: What is the dependent variable?

A)Salesperson
B)Number of contacts
C)Amount of sales
D)All the above

Question 74

Given the least squares regression equation, = 1202 + 1,133X,when X = 3,what does equal?

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

Question 75

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 straight line of regression;and/or 3)the standard deviations of these normal distributions are equal?

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

Question 76

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 77

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 78

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)none of these.

Question 79

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 80

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

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