Deck 12: Simple Regression Analysis and Correlation

Question 1

The slope of the regression line, y = 21 − 8x, is 8.

Answer 1

False

Question 2

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

Answer 2

False

Question 3

The slope of the regression line, y = 21 − 8x, is 21.

Answer 3

False

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

For the regression line, y = 21 − 8x, 21 is the y intercept of the line.

Question 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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 17

In the simple regression model, y = 21 − 8x, if the coefficient of determination is 0.81, we can say that the coefficient of correlation between y and x is 0.90.

Question 18

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

Question 19

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

Question 20

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 21

A cost accountant is developing a regression model to predict the total cost of producing a batch of car seats as a function of batch size (the number of seats produced in one lot or batch).The dependent variable is ___.

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

Question 22

A cost accountant is developing a regression model to predict the total cost of producing a batch of car seats as a linear function of batch size (the number of seats 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 23

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 24

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

A)y = 2.16 + 1.37x
B)y = 1.37 + 2.16x
C)y = 0.69 + 0.57x
D)y = 0.57 + 0.69x
E)y = 0.57 - 0.69x

Question 25

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

A)2.36
B)2.16
C)0.68
D)0.57
E)1.37

Question 26

For following scatter plot and regression line, at x = 65 the residual is ___.

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

Question 27

In the regression equation, y = 75.65 + 0.80x, the intercept is ___.

A)0.80
B)75.65
C)1.00
D)0.00
E)-0.80

Question 28

A cost accountant is developing a regression model to predict the total cost of producing a batch of car seats as a linear function of batch size (the number of seats 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 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

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 31

Consider the following scatter plot and regression line.At x = 17, the residual (error term)is ___.

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

Question 32

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 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

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 35

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 36

A cost accountant is developing a regression model to predict the total cost of producing a batch of car seats as a function of batch size (the number of seats produced in one lot or batch).The explanatory variable is ___.

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

Question 37

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 38

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

A)1.36
B)2.16
C)0.68
D)0.57
E)2.36

Question 39

In the regression equation, y = 75.65 + 0.80x, the slope is ___.

A)0.80
B)75.65
C)1.00
D)0.00
E)-0.80

Question 40

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

A)heteroscedasticity
B)homoscedasticity
C)residuals
D)linearity
E)non-normality

Question 41

A researcher has developed a regression model from fifteen pairs of data points.He wants to test to determine 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 42

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 43

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 44

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 45

In a regression analysis if SST = 200 and SSR = 200, r² = ___.

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

Question 46

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 47

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 48

For a certain data set the regression equation is y = 21 - 8x.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 49

A researcher has developed a regression model from fourteen pairs of data points.He wants to test to determine 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 50

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 51

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 52

A manager wishes to predict the annual cost (y)of an automobile based on the number of kilometres (x)driven.The following model was developed: y = 1,550 + .36x.If a car is driven 20,000 kilometres, the predicted cost is ___.

A)7,200
B)5,650
C)8,750
D)2,270
E)6,750

Question 53

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 54

A manager wishes to predict the annual cost (y)of an automobile based on the number of kilometres (x)driven.The following model was developed: y = 1,550 + 0.36x.If a car is driven 15,000 kilometres, the predicted cost is ___.

A)2090
B)3850
C)7400
D)6950
E)5400

Question 55

For a certain data set the regression equation is y = 2 + 3.5x.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 3

Question 56

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 57

A manager wishes to predict the annual cost (y)of an automobile based on the number of kilometres (x)driven.The following model was developed: y = 1,550 + 0.36x.If a car is driven 30,000 kilometres, the predicted cost is ___.

A)10,800
B)12,350
C)2,630
D)9,250
E)10,250

Question 58

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 59

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 60

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 61

Abby Kuntz, a market specialist at the market research firm of Saez, Gann, and Spitz, is analyzing household budget data collected by her firm.Abby's dependent variable is monthly household expenditures on groceries (in $'s), and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: 11eb6c3a_ec61_fde9_ad81_59fe2eaa383b_TB8417_00 The correlation coefficient between the two variables in this regression is ___.

A)0.682478
B)-0.83
C)0.83
D)-0.68
E)1.0008

s), and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: The correlation coefficient between the two variables in this regression is ___. A)0.682478 B)-0.83 C)0.83 D)-0.68 E)1.0008 " class="answers-bank-image d-block" loading="lazy" > The correlation coefficient between the two variables in this regression is ___.

A)0.682478
B)-0.83
C)0.83
D)-0.68
E)1.0008

s), and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: The correlation coefficient between the two variables in this regression is ___. A)0.682478 B)-0.83 C)0.83 D)-0.68 E)1.0008 " class="answers-bank-image d-block" loading="lazy" > 11eb6c3a_ec61_fde9_ad81_59fe2eaa383b_TB8417_00 The correlation coefficient between the two variables in this regression is ___.

A)0.682478
B)-0.83
C)0.83
D)-0.68
E)1.0008

Question 62

Abby Kuntz, a market specialist at the market research firm of Saez, Gann, and Spitz, is analyzing household budget data collected by her firm.Abby's dependent variable is monthly household expenditures on groceries (in $'s), and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables. 11eb6c3a_ec62_731f_ad81_5b97fdcd3d3e_TB8417_00 For a household with $50,000 annual income, Abby's model predicts monthly grocery expenditures of ___.

A)$150.35
B)$50.35
C)$1,959.29
D)$128.65
E)$1286.50

s), and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables. For a household with $50,000 annual income, Abby's model predicts monthly grocery expenditures of ___. A)$150.35 B)$50.35 C)$1,959.29 D)$128.65 E)$1286.50 " class="answers-bank-image d-block" loading="lazy" > For a household with $50,000 annual income, Abby's model predicts monthly grocery expenditures of ___.

A)$150.35
B)$50.35
C)$1,959.29
D)$128.65
E)$1286.50

s), and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables. For a household with $50,000 annual income, Abby's model predicts monthly grocery expenditures of ___. A)$150.35 B)$50.35 C)$1,959.29 D)$128.65 E)$1286.50 " class="answers-bank-image d-block" loading="lazy" > 11eb6c3a_ec62_731f_ad81_5b97fdcd3d3e_TB8417_00 For a household with $50,000 annual income, Abby's model predicts monthly grocery expenditures of ___.

A)$150.35
B)$50.35
C)$1,959.29
D)$128.65
E)$1286.50

Question 63

Alan Nip, market analyst for Clear Sound Mart, is analyzing the relation between heavy metal CD sales and the size of the teenage population.He gathers data from six sales districts.Alan's dependent variable is annual heavy metal CD sales (in $1,000,000's), and his independent variable is teenage population (in 1,000's).Regression analysis of the data yielded the following tables: Alan's sample size is ___.

A)2
B)4
C)6
D)8
E)10

Question 64

Louis Tang, a cost accountant at Prime Plastics, Inc.(PPI), is analyzing the manufacturing costs of a moulded plastic telephone handset produced by PPI.Louis's independent variable is production lot size (in 1,000's of units), and his dependent variable is the total cost of the lot (in $100's).Regression analysis of the data yielded the following tables: Using $\alpha$ = 0.05, Louis should ___.

A)increase the sample size
B)suspend judgment
C)not reject H₀: $\beta$ ₁ = 0
D)reject H₀: $\beta$ ₁ = 0
E)do not reject H₀: $\beta$ ₀ = 0

Question 65

Louis Tang, a cost accountant at Prime Plastics, Inc.(PPI), is analyzing the manufacturing costs of a moulded plastic telephone handset produced by PPI.Louis's independent variable is production lot size (in 1,000's of units), and his dependent variable is the total cost of the lot (in $100's).Regression analysis of the data yielded the following tables: The correlation coefficient between Louis's variables is ___.

A)-0.73
B)0.73
C)0.28
D)-0.28
E)0.00

Question 66

Louis Tang, a cost accountant at Prime Plastics, Inc.(PPI), is analyzing the manufacturing costs of a moulded plastic telephone handset produced by PPI.Louis's independent variable is production lot size (in 1,000's of units), and his dependent variable is the total cost of the lot (in $100's).Regression analysis of the data yielded the following tables: Louis's regression model is ___.

A)y = -0.358 + 3.996x
B)y = 0.358 + 3.996x
C)y = -3.996 + 0.358x
D)y = 3.996 - 0.358x
E)y = 3.996 + 0.358x

Question 67

Alan Nip, market analyst for Clear Sound Mart, is analyzing the relation between heavy metal CD sales and the size of the teenage population.He gathers data from six sales districts.Alan's dependent variable is annual heavy metal CD sales (in $1,000,000's), and his independent variable is teenage population (in 1,000's).Regression analysis of the data yielded the following tables. The numerical value of the correlation coefficient between the CD sales and the size of teenage population is ___.

A)0.969785
B)0.940483
C)0.224675
D)-0.14156
E)1.000000

Question 68

Abby Kuntz, a market specialist at the market research firm of Saez, Gann, and Spitz, is analyzing household budget data collected by her firm.Abby's dependent variable is monthly household expenditures on groceries (in $'s), and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables. $\alpha$ = 0.05, Abby should ___.

A)reject H₀: $\beta$ ₁ = 0
B)not reject H₀: $\beta$ ₁ = 0
C)increase the sample size
D)suspend judgment
E)reject H₀: $\beta$ ₀ = 0

s), and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables. Using \alpha = 0.05, Abby should ___. A)reject H₀: \beta ₁ = 0 B)not reject H₀: \beta ₁ = 0 C)increase the sample size D)suspend judgment E)reject H₀: \beta ₀ = 0 " class="answers-bank-image d-block" loading="lazy" > 11eb6c3a_ec62_4c0d_ad81_ff858582a93a_TB8417_00 Using $\alpha$ = 0.05, Abby should ___.

A)reject H₀: $\beta$ ₁ = 0
B)not reject H₀: $\beta$ ₁ = 0
C)increase the sample size
D)suspend judgment
E)reject H₀: $\beta$ ₀ = 0

s), and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables. Using \alpha = 0.05, Abby should ___. A)reject H₀: \beta ₁ = 0 B)not reject H₀: \beta ₁ = 0 C)increase the sample size D)suspend judgment E)reject H₀: \beta ₀ = 0 " class="answers-bank-image d-block" loading="lazy" > Using $\alpha$ = 0.05, Abby should ___.

A)reject H₀: $\beta$ ₁ = 0
B)not reject H₀: $\beta$ ₁ = 0
C)increase the sample size
D)suspend judgment
E)reject H₀: $\beta$ ₀ = 0

s), and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables. Using \alpha = 0.05, Abby should ___. A)reject H₀: \beta ₁ = 0 B)not reject H₀: \beta ₁ = 0 C)increase the sample size D)suspend judgment E)reject H₀: \beta ₀ = 0 " class="answers-bank-image d-block" loading="lazy" > 11eb6c3a_ec62_4c0d_ad81_ff858582a93a_TB8417_00 Using $\alpha$ = 0.05, Abby should ___.

A)reject H₀: $\beta$ ₁ = 0
B)not reject H₀: $\beta$ ₁ = 0
C)increase the sample size
D)suspend judgment
E)reject H₀: $\beta$ ₀ = 0

Question 69

Louis Tang, a cost accountant at Prime Plastics, Inc.(PPI), is analyzing the manufacturing costs of a moulded plastic telephone handset produced by PPI.Louis's independent variable is production lot size (in 1,000's of units), and his dependent variable is the total cost of the lot (in $100's).Regression analysis of the data yielded the following tables: For a lot size of 10,000 handsets, Louis' model predicts total cost will be ___.

A)$4,031.80
B)$757.60
C)$3,960.20
D)$354.01
E)$1873.077

Question 70

Alan Nip, market analyst for Clear Sound Mart, is analyzing the relation between heavy metal CD sales and the size of the teenage population.He gathers data from six sales districts.Alan's dependent variable is annual heavy metal CD sales (in $1,000,000's), and his independent variable is teenage population (in 1,000's).Regression analysis of the data yielded the following tables: For a sales district with 20,000 teenagers, Alan's model predicts annual CD sales of ___.

A)$1,947.08
B)$2,104.04
C)$2,103,900
D)$1,962,340
E)$2,908,089

Question 71

Alan Nip, market analyst for Clear Sound Mart, is analyzing the relation between heavy metal CD sales and the size of the teenage population.He gathers data from six sales districts.Alan's dependent variable is annual heavy metal CD sales (in $1,000,000's), and his independent variable is teenage population (in 1,000's).Regression analysis of the data yielded the following tables: Using $\alpha$ = 0.05, Alan should ___.

A)increase the sample size
B)not reject H₀: $\beta$ ₁ = 0
C)reject H₀: $\beta$ ₁ = 0
D)suspend judgment
E)reject H₀: $\beta$ ₀ = 0

Question 72

Abby Kuntz, a market specialist at the market research firm of Saez, Gann, and Spitz, is analyzing household budget data collected by her firm.Abby's dependent variable is monthly household expenditures on groceries (in $'s), and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: 11eb6c3a_ec62_24fb_ad81_a7111ecfb44e_TB8417_00 Abby's sample size (n)is ___.

A)8
B)10
C)11
D)20
E)12

s), and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: Abby's sample size (n)is ___. A)8 B)10 C)11 D)20 E)12 " class="answers-bank-image d-block" loading="lazy" > Abby's sample size (n)is ___.

A)8
B)10
C)11
D)20
E)12

s), and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: Abby's sample size (n)is ___. A)8 B)10 C)11 D)20 E)12 " class="answers-bank-image d-block" loading="lazy" > 11eb6c3a_ec62_24fb_ad81_a7111ecfb44e_TB8417_00 Abby's sample size (n)is ___.

A)8
B)10
C)11
D)20
E)12

Question 73

Alan Nip, market analyst for Clear Sound Mart, is analyzing the relation between heavy metal CD sales and the size of the teenage population.He gathers data from six sales districts.Alan's dependent variable is annual heavy metal CD sales (in $1,000,000's), and his independent variable is teenage population (in 1,000's).Regression analysis of the data yielded the following tables: Alan's regression model can be written as: ___.

A)y = 7.950352 - 0.48455x
B)y = -0.48455 + 7.950352x
C)y = -0.14156 + 0.105195x
D)y = 0.105195 - 0.14156x
E)y = 0.105195 + 0.14156x

Question 74

Abby Kuntz, a market specialist at the market research firm of Saez, Gann, and Spitz, is analyzing household budget data collected by her firm.Abby's dependent variable is monthly household expenditures on groceries (in $'s), and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: 11eb6c3a_ec61_d6d7_ad81_a936bb16aa64_TB8417_00 Abby's regression model is ___.

A)y = 39.15 + 2.79x
B)y = 39.15 - 1.79x
C)y = 1.79 + 39.15x
D)y = -1.79 + 39.15x
E)y = 39.15 + 1.79x

s), and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: Abby's regression model is ___. A)y = 39.15 + 2.79x B)y = 39.15 - 1.79x C)y = 1.79 + 39.15x D)y = -1.79 + 39.15x E)y = 39.15 + 1.79x " class="answers-bank-image d-block" loading="lazy" > Abby's regression model is ___.

A)y = 39.15 + 2.79x
B)y = 39.15 - 1.79x
C)y = 1.79 + 39.15x
D)y = -1.79 + 39.15x
E)y = 39.15 + 1.79x

s), and her independent variable is annual household income (in $1,000's).Regression analysis of the data yielded the following tables: Abby's regression model is ___. A)y = 39.15 + 2.79x B)y = 39.15 - 1.79x C)y = 1.79 + 39.15x D)y = -1.79 + 39.15x E)y = 39.15 + 1.79x " class="answers-bank-image d-block" loading="lazy" > 11eb6c3a_ec61_d6d7_ad81_a936bb16aa64_TB8417_00 Abby's regression model is ___.

A)y = 39.15 + 2.79x
B)y = 39.15 - 1.79x
C)y = 1.79 + 39.15x
D)y = -1.79 + 39.15x
E)y = 39.15 + 1.79x

Question 75

Louis Tang, a cost accountant at Prime Plastics, Inc.(PPI), is analyzing the manufacturing costs of a moulded plastic telephone handset produced by PPI.Louis's independent variable is production lot size (in 1,000's of units), and his dependent variable is the total cost of the lot (in $100's).Regression analysis of the data yielded the following tables: Louis's sample size (n)is ___.

A)13
B)14
C)12
D)24
E)1