Deck 12: Simple Regression Analysis and Correlation

Question 1

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

Answer 1

False

Question 2

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

Answer 2

True

Question 3

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

Answer 3

False

Question 4

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 5

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 6

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

Question 7

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

Question 8

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

Question 9

If the correlation coefficient between two variables is -1,it means that the two variables are not related.

Question 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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 15

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 16

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 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

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

Question 22

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 23

To determine whether the overall regression model is significant,the F-test is used.

Question 24

Regression output from Excel software includes an ANOVA table.

Question 25

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 26

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 27

Regression output from Minitab software includes an ANOVA table.

Question 28

Regression output from Excel software directly shows the regression equation.

Question 29

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 30

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 31

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

Question 32

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

Question 33

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 34

Regression output from Minitab software directly displays the regression equation.

Question 35

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 36

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 37

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

Question 38

The F-value to test the overall significance of a regression model is computed by dividing the sum of squares regression (SS_reg)by the sum of squares error (SS_err).

Question 39

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 40

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

Question 41

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 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

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 44

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 45

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 46

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 47

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 48

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

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

Question 49

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 50

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 51

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 52

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 53

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 54

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 55

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 56

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 57

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 58

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 59

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 60

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 61

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 $\alpha$ = 0.10.The critical table t value is _______.

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

Question 62

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 63

In a regression analysis if SST = 150 and SSR = 100,r ² = _________.

A) 0.82
B) 1.22
C) 1.50
D) 0.67
E) -1.00

Question 64

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 65

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% prediction interval for 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 66

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 67

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 68

A manager wishes to predict the annual cost (y)of an automobile based on the number of miles (x)driven. The following model was developed: y = 2,000 + 0.42x.If a car is driven 30,000 miles,the predicted cost is _____________.

A) 10,400
B) 14,600
C) 2,000
D) 32,000
E) 10,250

Question 69

A manager wishes to predict the annual cost (y)of an automobile based on the number of miles (x)driven. The following model was developed: y = 2,000 + 0.42x. If a car is driven 15,000 miles,the predicted cost is ____________.

A) 2,090
B) 17,000
C) 8,400
D) 8,300
E) 6,300

Question 70

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 71

The equation of the trend line for the data based on sales (in $1000)of a local restaurant over the years 2005-2010 is Sales= -265575+132.571 year.Using the trend line,the forecast sales for the year 2012 is ________

A) $1157.85
B) $1157850
C) $132571
D) $2673304
E) $1000327

Question 72

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 73

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 74

A manager wants to predict the cost (y)of travel for salespeople based on the number of days (x)spent on each sales trip.The following model has been developed: y = $400 + 120x.If a trip took 4 days,the predicted cost of the trip is _____________.

A) 480
B) 880
C) 524
D) 2080
E) 1080

Question 75

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 $\alpha$ = 0.01.The critical table t value is _______.

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

Question 76

In a regression analysis if SST = 200 and SSR = 200,r ² = _________.

A) 0.25
B) 0.75
C) 0.00
D) 1.00
E) -1.00

Question 77

A manager wants to predict the cost (y)of travel for salespeople based on the number of days (x)spent on each sales trip.The following model has been developed: y = $400 + 120x.If a trip took 3 days,the predicted cost of the trip is _____________.

A) 760
B) 360
C) 523
D) 1560
E) 1080

Question 78

A manager wishes to predict the annual cost (y)of an automobile based on the number of miles (x)driven. The following model was developed: y = 2,000 + 0.42x.If a car is driven 20,000 miles,the predicted cost is ____________.

A) 10,400
B) 20,000
C) 2,840
D) 6,200
E) 6,750

Question 79

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 80

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