Deck 14: Linear Correlation and Simple Linear Regression Analysis

Question 1

In simple regression analysis the error terms are assumed to be independent and normally distributed with zero mean and constant variance.

Answer 1

True

Question 2

One of the major uses of residual analysis is to test some of the assumptions underlying regression.

Answer 2

True

Question 3

For the regression line, y = 21 − 5x, 21 is the y-intercept of the line.

Answer 3

True

Question 4

The process of constructing a mathematical model or function that can be used to predict or determine one variable by another variable is called regression analysis.

Question 5

In regression, the predictor variable is called the dependent variable.

Question 6

The difference between the actual y value and the predicted y value found using a regression equation is called the residual.

Question 7

The coefficient of determination is the proportion of variability of the dependent variable (y) accounted for or explained by the independent variable (x).

Question 8

The proportion of variability of the dependent variable (y) accounted for or explained by the independent variable (x) is called the coefficient of correlation.

Question 9

Correlation is a measure of the degree of linear relationship between two variables.

Question 10

Data points that lie apart from the rest of the points are called deviants.

Question 11

In a simple regression the coefficient of correlation is the square root of the coefficient of determination.

Question 12

The slope of the regression line, y = 21 − 5x, is 5.

Question 13

The strength of a linear relationship in simple linear regression change if the units of the data are converted, say from feet to inches.

Question 14

If the correlation coefficient between two variables is -1, it means that the two variables are $\textbf{ not }$ related.

Question 15

In regression, the variable that is being predicted is usually referred to as the independent variable.

Question 16

One of the assumptions of simple regression analysis is that the error terms are exponentially distributed

Question 17

The slope of the regression line, y = 21 − 5x, is 21.

Question 18

In the simple regression model, y = 21 − 5x, if the coefficient of determination is 0.81, we can say that the coefficient of correlation between y and x is 0.90.

Question 19

The first step in simple regression analysis usually is to construct a scatter plot.

Question 20

The range of admissible values for the coefficient of determination is −1 to +1.

Question 21

From the following scatter plot, we can say that between Y and X there is ___.

A) perfect positive correlation
B) virtually no correlation
C) positive correlation
D) negative correlation
E) perfect negative correlation

Question 22

The numerical value of the coefficient of determination must be ___.

A) between -1 and +1
B) between -1 and 0
C) between 0 and 1
D) equal to SSE/(n - 2)
E) between -100 and +100

Question 23

In regression analysis, R-squared is also called the ___.

A) residual
B) coefficient of determination
C) coefficient of correlation
D) standard error of the estimate
E) sum of squares of regression

Question 24

From the following scatter plot, we can say that between Y and X there is ___.

A) perfect positive correlation
B) virtually no correlation
C) positive correlation
D) negative correlation
E) perfect negative correlation

Question 25

The standard error of the estimate, denoted s_e, is the square root of the sum of the squares of the vertical distances between the actual y values and the predicted values of y.

Question 26

Regression output from Excel software includes an ANOVA table.

Question 27

According to the following graphic, X and Y have ___.

A) strong negative correlation
B) virtually no correlation
C) strong positive correlation
D) moderate negative correlation
E) weak negative correlation

Question 28

Prediction intervals get narrower as we extrapolate outside the range of the data.

Question 29

The variability in the estimated slope is smaller when the x values are more spread out.

Question 30

If there is positive correlation between two sets of numbers, then ___.

A) r = 0
B) r < 0
C) r > 0
D) SSE =1
E) MSE = 1

Question 31

According to the following graphic, X and Y have ___.

A) strong negative correlation
B) virtually no correlation
C) strong positive correlation
D) moderate negative correlation
E) weak negative correlation

Question 32

Given x, a 95% prediction interval for a single value of y is always wider than a 95% confidence interval for the average value of y.

Question 33

The numerical value of the coefficient of correlation must be ___.

A) between -1 and +1
B) between -1 and 0
C) between 0 and 1
D) equal to SSE/(n - 2)
E) between 0 and -1

Question 34

Regression output from Excel software directly shows the regression equation.

Question 35

If there is perfect negative correlation between two sets of numbers, then ___.

A) r = 0
B) r = -1
C) r = +1
D) SSE =1
E) MSE = 1

Question 36

A t test is used to determine whether the coefficients of the regression model are significantly different from zero.

Question 37

If x and y in a regression model are totally unrelated, ___.

A) the correlation coefficient would be -1
B) the coefficient of determination would be 0
C) the coefficient of determination would be 1
D) the SSE would be 0
E) the MSE would be 0s

Question 38

Regression methods can be pursued to estimate trends that are linear in time.

Question 39

From the following scatter plot, we can say that between Y and X there is ___.

A) perfect positive correlation
B) virtually no correlation
C) positive correlation
D) negative correlation
E) perfect negative correlation

Question 40

The proportion of variability of the dependent variable accounted for or explained by the independent variable is called the ___.

A) sum of squares error
B) coefficient of correlation
C) coefficient of determination
D) covariance
E) regression sum of squares

Question 41

If a scatter plot of variables X and Y shows a trend that can be summarized to a large degree by a straight line with slope 0.8 and y-intercept 0.2 (i.e., Y = 0.2 + 0.8X), then the correlation coefficient between X and Y is ___.

A) 0.8, and there is a causal relation between X and Y (either X causes Y or Y causes X)
B) 0.2, and there is a causal relation between X and Y (either X causes Y or Y causes X)
C) 0.8, but there is no causal relation between X and Y
D) 0.2, but there is no causal relation between X and Y
E) 0.8, and there may be a causal relation between X and Y, but not necessarily

Question 42

A quality manager is developing a regression model to predict the total number of defects as a function of the day of week the item is produced. Production runs are done 10 hours a day, 7 days a week. The dependent variable is ___.

A) day of week
B) production run
C) percentage of defects
D) number of defects
E) number of production runs

Question 43

If the correlation coefficient between variables X and Y is roughly zero, then ___.

A) Y is independent of X
B) Y is dependent on X
C) there is a linear correlation between Y and X
D) Y is not necessarily independent of X
E) Y is caused by X.

Question 44

Consider the following scatter plot and regression line. At x = 50, the residual (error term) is ___.

A) positive
B) zero
C) negative
D) imaginary
E) unknown

Question 45

The coefficient of correlation in a simple regression analysis is = -0.6. The coefficient of determination for this regression would be ___.

A) 0.6
B) -0.6 or +0.6
C) 0.13
D) -0.36
E) 0.36

Question 46

A cost accountant is developing a regression model to predict the total cost of producing a batch of printed circuit boards as a linear function of batch size (the number of boards produced in one lot or batch). The intercept of this model is the ___.

A) batch size
B) unit variable cost
C) fixed cost
D) total cost
E) total variable cost

Question 47

The following data is to be used to construct a regression model: The value of the intercept is ___.

A) 16.49
B) 1.19
C) 1.43
D) 0.75
E) 1.30

Question 48

Given a set of paired data, {X, Y}, if Y is independent of X, you would expect that the correlation coefficient is ___.

A) negative
B) zero
C) positive
D) any value between −1.0 and 1.0
E) any value between −0.5 and 0.5

Question 49

For the following scatter plot and regression line, at x = 35 the residual is ___.

A) positive
B) zero
C) negative
D) imaginary
E) unknown

Question 50

In the regression equation, y = 54.78 + 1.45x, the x-intercept is ___.

A) 1.45
B) −1.45
C) 54.78
D) −54.78
E) −37.8

Question 51

A regression line minimizes the sum of the squared error values. This means that the regression line minimizes the sum of ___ from each point in the scatter point to the regression line.

A) the squares of the distances
B) the squares of the horizontal distances (differences in the x-coordinates)
C) the squares of the vertical distances (differences in the x-coordinates)
D) the squares of the horizontal distances (differences in the y-coordinates)
E) the squares of the vertical distances (differences in the y-coordinates)

Question 52

The following data is to be used to construct a regression model: The regression equation is ___.

A) y = 16.49 + 1.43x
B) y = 1.19 + 0.91x
C) y = 1.19 + 0.75x
D) y = 0.75 + 0.18x
E) y = 0.91 + 4.06x

Question 53

A cost accountant is developing a regression model to predict the total cost of producing a batch of printed circuit boards as a linear function of batch size (the number of boards produced in one lot or batch). The slope of the accountant's model is ___.

A) batch size
B) unit variable cost
C) fixed cost
D) total cost
E) total variable cost

Question 54

In the regression equation, y = 54.78 + 1.45x, the intercept is ___.

A) 1.45
B) -1.45
C) 54.78
D) -54.78
E) 0.00

Question 55

In the regression equation, y = 49.56 + 0.97x, the slope is ___.

A) 0.97
B) 49.56
C) 1.00
D) 0.00
E) -0.97

Question 56

For a certain data set the regression equation is y = 37 + 13x. The correlation coefficient between y and x in this data set ___.

A) must be 0
B) is negative
C) must be 1
D) is positive
E) must be 3

Question 57

For a certain data set the regression equation is y = 29 - 5x. The correlation coefficient between y and x in this data set ___.

A) must be 0
B) is negative
C) must be 1
D) is positive
E) must be >1

Question 58

Suppose you compute the correlation coefficient between two variables, X and Y, and obtain a value of 0.55. Then you realize that all the values for both variables have been corrupted in a way that their actual sign has been changed (positive values were turned into negative values and vice versa; only the signs have been changed). Then the actual, corrected value of the correlation coefficient ___.

A) is −0.55
B) remains unchanged
C) changes but there is not enough information to determine the correct value
D) is 0
E) is 0.50

Question 59

The following data is to be used to construct a regression model: The value of the slope is ___.

A) 16.49
B) 1.19
C) 1.43
D) 0.75
E) 1.30

Question 60

A quality manager is developing a regression model to predict the total number of defects as a function of the day of week the item is produced. Production runs are done 10 hours a day, 7 days a week. The explanatory variable is ___.

A) day of week
B) production run
C) percentage of defects
D) number of defects
E) number of production runs

Question 61

Which of the following assertions is true about the regression line?

A) The regression line is also called the least cubes line and is found minimizing the sum of the cubes of the residuals.
B) It is found minimizing the sum of the residuals squared, but-even though it would be unnecessarily complicated-it could also be found minimizing the sum of the residuals cubed.
C) Depending on the data, some regression lines could have only positive residuals.
D) Depending on the data, some regression lines could have all residuals equal to zero.
E) Depending on the data, some regression lines could have only negative residuals.

Question 62

The following residuals plot indicates ___.

A) a nonlinear relation
B) a nonconstant error variance
C) the simple regression assumptions are met
D) the sample is biased
E) a random sample

Question 63

A simple regression model resulted in a sum of squares of error of 125 (i.e., SSE = 125), and the standard error is 3.95. This model is for ___ pairs of data.

A) 8
B) 9
C) 10
D) 11
E) 12

Question 64

Suppose for a given data set the regression equation is: y = 54.78 + 1.45x, and the point (0.00, 24.78) is in the data set. The residual for this point is ___.

A) 24.78
B) −24.78
C) 0.00
D) 30.00
E) −30.00

Question 65

A simple regression model developed for 12 pairs of data resulted in a sum of squares of error, SSE = 246. The standard error of the estimate is ___.

A) 24.6
B) 4.96
C) 20.5
D) 4.53
E) 12.3

Question 66

A simple regression model developed for ten pairs of data resulted in a sum of squares of error, SSE = 125. The standard error of the estimate is ___.

A) 12.5
B) 3.5
C) 15.6
D) 3.95
E) 25

Question 67

The assumptions underlying simple regression analysis include ___.

A) the error terms are exponentially distributed
B) the error terms have unequal variances
C) the model is nonlinear
D) the error terms are dependent
E) the error terms are independent

Question 68

The assumption of constant error variance in regression analysis is called ___.

A) heteroscedasticity
B) homoscedasticity
C) residuals
D) linearity
E) nonnormality

Question 69

In the regression equation, y = 2.164 + 1.3657x, n = 6, the mean of x is 8.667, S_xx= 89.333 and S_e= 3.44. A 95% confidence interval for the average of y when x = 8 is ___.

A) (9.13, 17.05)
B) (2.75, 23.43)
C) (10.31, 15.86)
D) (3.56, 22.62)
E) (12.09, 14.09)

Question 70

A researcher has developed the regression equation y = 2.164 + 1.3657x, where n = 6, the mean of x is 8.667, S_xx = 89.333, and S_e = 3.44. The researcher wants to test if the slope is significantly positive, and he chooses a significance level of 0.05. The observed t value is ___.

A) 3.752
B) 3.852
C) 3.972
D) 3.985
E) 3.995

Question 71

A researcher has developed the regression equation y = 2.164 + 1.3657x, where n = 6, the mean of x is 8.667, S_xx = 89.333, and S_e = 3.44. The researcher wants to test if the slope is significantly positive, and he chooses a significance level of 0.05. The critical t value is ___.

A) 2.776
B) 2.132
C) 2.015
D) 1.943
E) 1.782

Question 72

A standard deviation of the error of the regression model is called the ___.

A) coefficient of determination
B) sum of squares of error
C) standard error of the estimate
D) R-squared
E) coefficient of correlation

Question 73

One of the assumptions made in simple regression is that ___.

A) the error terms are exponentially distributed
B) the error terms have unequal variances
C) the model is linear
D) the error terms are dependent
E) the model is nonlinear

Question 74

A simple regression model for 10 pair of data resulted in a standard error of 3.95 (i.e., S_e = 3.95), and the sum of squares of error (SSE) is ___.

A) 187.23
B) 171.63
C) 156.03
D) 140.42
E) 124.82

Question 75

The total of the squared residuals is called the ___.

A) coefficient of determination
B) sum of squares of error
C) standard error of the estimate
D) R-squared
E) coefficient of correlation

Question 76

A researcher has developed a regression model from 26 pairs of data points. He wants to test if the slope is significantly different from zero. He uses a two? tailed test and ɑ = 0.01. The degrees of freedom for the critical table t value is ___.

A) 23
B) 24
C) 26
D) 25
E) 27

Question 77

One of the assumptions made in simple regression is that ___.

A) the error terms are normally distributed
B) the error terms have unequal variances
C) the model is nonlinear
D) the error terms are dependent
E) the error terms are all equal

Question 78

A researcher has developed a regression model from fourteen pairs of data points. He wants to test if the slope is significantly different from zero. He uses a two? tailed test and ɑ = 0.01. The critical table t value is ___.

A) 2.650
B) 3.012
C) 3.055
D) 2.718
E) 2.168

Question 79

The following residuals plot indicates ___.

A) a nonlinear relation
B) a nonconstant error variance
C) the simple regression assumptions are met
D) the sample is biased
E) the sample is random

Question 80

A researcher has developed a regression model from fifteen pairs of data points. He wants to test if the slope is significantly different from zero. He uses a two?tailed test and ɑ = 0.10. The critical table t value is ___.

A) 1.771
B) 1.350
C) 1.761
D) 2.145
E) 2.068