# Quiz 13: Simple Linear Regression

Statistics

Q 1Q 1

A simple regression model contains:
A)two independent variables
B)two dependent variables
C)one independent and one dependent variable
D)more than one independent variable

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Multiple Choice

C

Q 2Q 2

A linear regression:
A)gives a relationship between two variables that can be described by a line
B)gives a relationship between two variables that cannot be described by a line
C)gives a relationship between three variables that can be described by a line
D)contains only two variables

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Multiple Choice

A

Q 3Q 3

In a regression model,the y-intercept is the:
A)point where the y-axis intersects the x-axis
B)point where the regression line intersects the y-axis
C)point where the x-axis intersects the y-axis
D)value of y when x is equal to 1

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Multiple Choice

B

Q 4Q 4

In a regression model,the slope represents the:
A)point where the y-axis intersects the x-axis
B)change in y due to a one unit change in x
C)point where the x-axis intersects the y-axis
D)change in the independent variable due to a one unit change in the dependent variable

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Multiple Choice

Q 5Q 5

In the equation ,y is the:
A)independent variable
B)slope of the line
C)dependent variable
D)y-intercept

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Multiple Choice

Q 6Q 6

In the equation ,x is the:
A)independent variable
B)slope of the line
C)dependent variable
D)y-intercept

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Multiple Choice

Q 7Q 7

In the equation ,2 is the:
A)independent variable
B)slope of the line
C)dependent variable
D)y-intercept

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Multiple Choice

Q 8Q 8

In the equation ,6 is the:
A)independent variable
B)slope of the line
C)dependent variable
D)y-intercept

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Multiple Choice

Q 9Q 9

In the equation ,120 is the:
A)value of y when x is equal to 1
B)point where the line intersects the x-axis
C)change in y due to a one-unit change in x
D)point where the line intersects the y-axis

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Multiple Choice

Q 10Q 10

In the equation ,17 is the:
A)value of y when x is equal to 1
B)point where the line intersects the x-axis
C)change in y due to a one-unit change in x
D)change in x due to a one-unit change in y

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Multiple Choice

Q 11Q 11

The model is a:
A)probabilistic model
B)nonlinear model
C)stochastic model
D)deterministic model

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Multiple Choice

Q 12Q 12

The regression model is:
A)a probabilistic model
B)a nonlinear model
C)an exact relationship
D)a deterministic model

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Multiple Choice

Q 13Q 13

In the regression model ,A and B are the:
A)sample statistics
B)random variables
C)population parameters
D)omitted variables

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Multiple Choice

Q 14Q 14

In the regression model , is the:
A)slope of the regression line
B)random error term
C)y-intercept
D)missing variable

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Multiple Choice

Q 15Q 15

In the regression model ,x is the:
A)dependent variable
B)independent variable
C)error term
D)missing variable

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Multiple Choice

Q 16Q 16

In the regression model ,y is the:
A)dependent variable
B)independent variable
C)error term
D)missing variable

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Multiple Choice

Q 17Q 17

In a regression model,the random error term is included to capture the effects of the:
A)independent variable
B)dependent variable
C)missing variables and random variation
D)deterministic relationship

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Multiple Choice

Q 18Q 18

In the regression model ,a and b are the:
A)estimates of the population parameters A and B
B)random variables
C)population parameters
D)omitted variables

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Multiple Choice

Q 19Q 19

In the regression model ,a and b are the:
A)sample statistics
B)random variables
C)population parameters
D)omitted variables

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Multiple Choice

Q 20Q 20

In the regression model , is the:
A)actual value of y
B)predicted value of y
C)value of y when a and b are zero
D)missing value of y

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Multiple Choice

Q 21Q 21

We construct a scatter diagram by:
A)scattering the values of x over the values of y
B)scattering the values of y over the values of x
C)plotting the paired values of x and y
D)plotting the values of the population parameters A and B

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Multiple Choice

Q 22Q 22

The value of y obtained for an element from a survey is the:
A)predicted value of y
B)estimated value of y
C)actual value of y
D)residual

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Multiple Choice

Q 23Q 23

The random error for the sample regression model,denoted by e,is equal to the:
A)predicted value of y minus the estimated value of y
B)estimated value of y minus the predicted value of y
C)actual value of y minus the predicted value of y
D)actual value of y minus the actual value of x

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Multiple Choice

Q 24Q 24

For a regression model,the error sum of squares,denoted by SSE,is equal to the sum of the:
A)errors
B)squares of errors
C)squares of y values
D)squares of the difference between x and y values

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Multiple Choice

Q 25Q 25

The least squares method minimizes the:
A)difference between the y and x values
B)sum of the errors
C)sum of the squares of errors
D)sum of the y values

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Multiple Choice

Q 26Q 26

The value of :
A)is always negative
B)is always non-negative
C)is always positive
D)can be negative,zero,or positive

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Multiple Choice

Q 27Q 27

The value of :
A)is always negative
B)is always non-negative
C)is always positive
D)can be negative,zero,or positive

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Multiple Choice

Q 28Q 28

Given that 875 and 275,the value of b in the regression of y on x,rounded to two decimal places,is:

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Short Answer

Q 29Q 29

Given that 968 and -915,the value of b in the regression of y on x,rounded to two decimal places,is:

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Short Answer

Q 30Q 30

For a data set on x and y,the value of is 979, is -1,538,the mean of the x values is 88 ,and the mean of the y values is 55.The value of a in the regression of y on x,rounded to two decimal places,is:

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Short Answer

Q 31Q 31

For a data set on x and y,the value of is 831, is 386,the mean of the x values is 9 ,and the mean of the y values is 48.The value of a in the regression of y on x,rounded to two decimal places,is:

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Short Answer

Q 32Q 32

Use the following to answer questions 32-34:
The table shown below gives six pairs of x and y values.
-The values of and ,rounded to three decimal places,are:

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Essay

Q 33Q 33

Use the following to answer questions 32-34:
The table shown below gives six pairs of x and y values.
-For the regression of y on x,the values of a and b,rounded to two decimal places,are:

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Short Answer

Q 34Q 34

Use the following to answer questions 32-34:
The table shown below gives six pairs of x and y values.
-Using the regression of y on x,the predicted value of y for x = 17,rounded to two decimal places,is:

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Short Answer

Q 35Q 35

Use the following to answer questions 35-37:
The table shown below gives seven pairs of x and y values.
-The values of and ,rounded to three decimal places,are:

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Essay

Q 36Q 36

Use the following to answer questions 35-37:
The table shown below gives seven pairs of x and y values.
-For the regression of y on x,the values of a and b,rounded to two decimal places,are:

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Short Answer

Q 37Q 37

Use the following to answer questions 35-37:
The table shown below gives seven pairs of x and y values.
-Using the regression of y on x,the predicted value of y for x = 14,rounded to two decimal places,is:

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Short Answer

Q 38Q 38

Use the following to answer questions 38-42:
The following table lists the monthly incomes (in hundreds of dollars)and the monthly rents paid (in hundreds of dollars)by a sample of six families.
-The values of and ,rounded to three decimal places,are:

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Essay

Q 39Q 39

Use the following to answer questions 38-42:
The following table lists the monthly incomes (in hundreds of dollars)and the monthly rents paid (in hundreds of dollars)by a sample of six families.
-For the regression of y on x,the values of a and b,rounded to two decimal places,are:

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Short Answer

Q 40Q 40

Use the following to answer questions 38-42:
The following table lists the monthly incomes (in hundreds of dollars)and the monthly rents paid (in hundreds of dollars)by a sample of six families.
-Using the regression of monthly rent paid on monthly income,the predicted value of monthly rent paid by a family with a monthly income of $3,000,rounded to the nearest dollar,is:

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Short Answer

Q 41Q 41

Suppose we have information on the monthly incomes and the monthly rents paid by a sample of families.In the regression of monthly rent paid on the monthly income for these data,the value of a will represent:
A)the point where this regression line will intersect the y-axis
B)the point where this regression line will intersect the x-axis
C)an increase in the monthly rent paid by a family due to a $100 increase in income
D)an increase in the income of a family due to a $100 increase in the monthly rent

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Multiple Choice

Q 42Q 42

Suppose we have information on the monthly incomes and the monthly rents paid by a sample of families.In the regression of monthly rent paid on the monthly income for these data,the value of b will represent:
A)the point where this regression line will intersect the y-axis
B)the point where this regression line will intersect the x-axis
C)an increase in the monthly rent paid by a family due to a $100 increase in income
D)an increase in the income of a family due to a $100 increase in the monthly rent

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Multiple Choice

Q 43Q 43

Use the following to answer questions 43-47:
The following table lists the ages (in years)and the prices (in thousands of dollars)by a sample of six houses.
-The values of and ,rounded to three decimal places,are:

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Essay

Q 44Q 44

Use the following to answer questions 43-47:
The following table lists the ages (in years)and the prices (in thousands of dollars)by a sample of six houses.
-For the regression of price on age,the estimated values of A and B,rounded to two decimal places,are:

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Essay

Q 45Q 45

Use the following to answer questions 43-47:
The following table lists the ages (in years)and the prices (in thousands of dollars)by a sample of six houses.
-Using the regression of house value on age,the predicted value of a house that 16 years old,rounded to the nearest dollar,is:

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Short Answer

Q 46Q 46

Suppose we have information on the ages (in years)and the prices of a sample of houses.In the regression of price on age for these data,the value of a will represent:
A)the point where this regression line will intersect the y-axis
B)the point where this regression line will intersect the x-axis
C)an decrease in the age of a house due to a $1,000 increase in its price
D)an decrease in the price of a house due to a one year increase in its age

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Multiple Choice

Q 47Q 47

Suppose we have information on the ages (in years)and the prices of a sample of houses.In the regression of price on age for these data,the value of b will represent:
A)the point where this regression line will intersect the y-axis
B)the point where this regression line will intersect the x-axis
C)an decrease in the age of a house due to a $1,000 increase in its price
D)an decrease in the price of a house due to a one year increase in its age

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Multiple Choice

Q 48Q 48

An assumption of the regression model is that the random error term has a mean equal to:
A)zero for each x
B)one for each x
C)the value of each x
D)zero for each y

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Multiple Choice

Q 49Q 49

An assumption of the regression model is that the distribution of errors is
A)binomial
B)rectangular
C)normal
D)bimodal

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Multiple Choice

Q 50Q 50

The regression model assumes that the spread of points around the regression line is:
A)different for all values of x
B)different for all values of y
C)similar for all values of y
D)similar for all values of x

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Multiple Choice

Q 51Q 51

The degrees of freedom for a simple linear regression of sample size n are:
A)n - 1
B)n - 2
C)n - 3
D)2n - 1

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Multiple Choice

Q 52Q 52

The coefficient of determination represents the proportion of:
A)SSE (error sum of squares)that the regression model explains
B)SSR (regression sum of squares)that the regression model explains
C)SST (total sum of squares)that the regression model explains
D)SSR (regression sum of squares)that the regression model does not explain

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Multiple Choice

Q 53Q 53

The value of :
A)is always negative
B)is always nonnegative
C)is always positive
D)can be negative,positive,or zero

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Multiple Choice

Q 54Q 54

The value of the coefficient of determination is always:
A)less than 1
B)greater than 1
C)in the range zero to 1
D)between -1 and 1

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Multiple Choice

Q 55Q 55

The total sum of squares (SST)is always equal to the:
A)regression sum of squares plus the error sum of squares
B)regression sum of squares minus the error sum of squares
C)error sum of squares minus the regression sum of squares
D)regression sum of squares divided by the error sum of squares

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Multiple Choice

Q 56Q 56

The coefficient of determination is equal to the:
A)total sum of squares divided by the regression sum of squares
B)error sum of squares divided by the regression sum of squares
C)regression sum of squares divided by the total sum of squares
D)error sum of squares divided by the total sum of squares

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Multiple Choice

Q 57Q 57

One way to measure the quality of the regression model is to inspect the value of the:
A)constant term
B)coefficient on x
C)coefficient of determination
D)mean of x

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Multiple Choice

Q 58Q 58

Use the following to answer questions 58-59:
For a sample of 22 values of x and y, 746, 254,and b = 1.36.
-The standard deviation of errors for the regression of y on x,rounded to three decimal places,is:

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Short Answer

Q 59Q 59

Use the following to answer questions 58-59:
For a sample of 22 values of x and y, 746, 254,and b = 1.36.
-The coefficient of determination for the regression of y on x,rounded to three decimal places,is:

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Short Answer

Q 60Q 60

Use the following to answer questions 60-61:
For a sample of 19 values of x and y, 294, 502,and b = 0.27.
-The standard deviation of errors for the regression of y on x,rounded to three decimal places,is:

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Short Answer

Q 61Q 61

Use the following to answer questions 60-61:
For a sample of 19 values of x and y, 294, 502,and b = 0.27.
-The coefficient of determination for the regression of y on x,rounded to three decimal places,is:

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Short Answer

Q 62Q 62

Use the following to answer questions 62-63:
For a sample of 17 values of x and y, 127, -99,and b = -0.91.
-The standard deviation of errors for the regression of y on x,rounded to three decimal places,is:

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Short Answer

Q 63Q 63

Use the following to answer questions 62-63:
For a sample of 17 values of x and y, 127, -99,and b = -0.91.
-The coefficient of determination for the regression of y on x,rounded to three decimal places,is:

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Short Answer

Q 64Q 64

Use the following to answer questions 64-65:
The table shown below gives six pairs of x and y values.
-The standard deviation of errors for the regression of y on x,rounded to three decimal places,is:

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Short Answer

Q 65Q 65

Use the following to answer questions 64-65:
The table shown below gives six pairs of x and y values.
-The coefficient of determination for the regression of y on x,rounded to three decimal places,is:

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Short Answer

Q 66Q 66

Use the following to answer questions 66-67:
The following table lists the monthly incomes (in hundreds of dollars)and the monthly rents paid (in hundreds of dollars)by a sample of six families.
-The standard deviation of errors for the regression of monthly rent on monthly income,rounded to three decimal places,is:

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Short Answer

Q 67Q 67

Use the following to answer questions 66-67:
The following table lists the monthly incomes (in hundreds of dollars)and the monthly rents paid (in hundreds of dollars)by a sample of six families.
-The coefficient of determination for the regression of y on x,rounded to three decimal places,is:

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Short Answer

Q 68Q 68

Use the following to answer questions 68-69:
The following table lists the ages (in years)and the prices (in thousands of dollars)by a sample of six houses.
-The standard deviation of errors for the regression of y on x,rounded to three decimal places,is:

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Short Answer

Q 69Q 69

Use the following to answer questions 68-69:
The following table lists the ages (in years)and the prices (in thousands of dollars)by a sample of six houses.
-The coefficient of determination for the regression of y on x,rounded to three decimal places,is:

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Short Answer

Q 70Q 70

The slope,b,of the regression line:
A)is a point estimator of the slope of the population regression line
B)possesses no sampling distribution
C)will have the same value for all samples taken from the population
D)is not affected by the elements taken from the population

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Multiple Choice

Q 71Q 71

For a data set of x and y values,the value of = 266 and the standard deviation of errors for the regression of y on x is 8.875.The standard deviation of the sampling distribution of b,rounded to three decimal places,is:

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Short Answer

Q 72Q 72

For a data set of x and y values,the value of = 944 and the standard deviation of errors for the regression of y on x is 72.937.The standard deviation of the sampling distribution of b,rounded to three decimal places,is:

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Short Answer

Q 73Q 73

For a data set of x and y values,the value of = 66 and the standard deviation of errors for the regression of y on x is 4.345.The standard deviation of the sampling distribution of b,rounded to three decimal places,is:

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Short Answer

Q 74Q 74

Use the following to answer questions 74-76:
For a data set of 10 values of x and y,the value of = 86,the standard deviation of errors for the regression of y on x is 3.662,and the value of b is 3.00.
For the purpose of running a hypothesis test,the null hypothesis is that the slope of the population regression line of y on x is zero and the alternative hypothesis is that the slope of this population regression line is different from zero.The significance level is 5%.
-The 95% confidence interval for the slope,B,of the population regression line is:

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Essay

Q 75Q 75

What are the critical values of t?
A)-2.306 and 2.306
B)-2.228 and 2.228
C)-1.812 and 1.812
D)-1.860 and 1.860

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Multiple Choice

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Short Answer

Q 77Q 77

Use the following to answer questions 77-79:
For a data set of 8 values of x and y,the value of = 180,the standard deviation of errors for the regression of y on x is 9.237,and the value of b is -6.28.
For the purpose of running a hypothesis test,the null hypothesis is that the slope of the population regression line of y on x is zero and the alternative hypothesis is that the slope of this population regression line is less than zero.The significance level is 1%.
-The 99% confidence interval for the slope,B,of the population regression line is:

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Essay

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Multiple Choice

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Short Answer

Q 80Q 80

Use the following to answer questions 80-82:
For a data set of 15 values of x and y,the value of = 313,the standard deviation of errors for the regression of y on x is 8.347,and the value of b is 1.78.
For the purpose of running a hypothesis test,the null hypothesis is that the slope of the population regression line of y on x is zero and the alternative hypothesis is that the slope of this population regression line is greater than zero.The significance level is 5%.
-The 90% confidence interval for the slope,B,of the population regression line is:

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Essay

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Multiple Choice

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Short Answer

Q 83Q 83

Use the following to answer questions 83-85:
The following table lists the monthly incomes (in hundreds of dollars)and the monthly rents paid (in hundreds of dollars)by a sample of six families.
-The 99% confidence interval for the slope,B,of the population regression line is:

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Essay

Q 84Q 84

The null hypothesis is that the slope of the population regression line of monthly rent on monthly income is zero and the alternative hypothesis is that the slope of this population regression line is greater than zero.The significance level is 1%.What is the critical value of t?
A)3.747
B)3.143
C)3.365
D)4.032

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Multiple Choice

Q 85Q 85

The null hypothesis is that the slope of the population regression line of monthly rent on monthly income is zero and the alternative hypothesis is that the slope of this population regression line is greater than zero.The significance level is 1%.What is the value of the test statistic,t,rounded to three decimal places?

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Short Answer

Q 86Q 86

Use the following to answer questions 86-88:
The following table lists the ages (in years)and the prices (in thousands of dollars)by a sample of six houses.
-The 95% confidence interval for the slope,B,of the population regression line of price on age is:

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Essay

Q 87Q 87

The null hypothesis is that the slope of the population regression line of price on age is zero and the alternative hypothesis is that the slope of this population regression line is less than zero.The significance level is 5%.What is the critical value of t?
A)-2.015
B)-2.132
C)-1.943
D)-2.447

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Multiple Choice

Q 88Q 88

The null hypothesis is that the slope of the population regression line of price on age is zero and the alternative hypothesis is that the slope of this population regression line is less than zero.The significance level is 5%.What is the value of the test statistic,t,rounded to three decimal places?

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Short Answer

Q 89Q 89

The value of the correlation coefficient is always:
A)in the range 0 to 1
B)less than zero
C)in the range -1 to 1
D)greater than zero

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Multiple Choice

Q 90Q 90

A perfect positive correlation means:
A)the points in a scatter diagram lie on an upward sloping line
B)the points in a scatter diagram lie on a downward sloping line
C)r is equal to -1
D)r is equal to 0

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Multiple Choice

Q 91Q 91

A perfect negative correlation means:
A)the points in a scatter diagram lie on an upward sloping line
B)the points in a scatter diagram lie on a downward sloping line
C)r is equal to 1
D)r is equal to 0

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Multiple Choice

Q 92Q 92

A strong positive correlation means:
A)the points in a scatter diagram lie on an upward sloping line
B)the points in a scatter diagram lie on a downward sloping line
C)r is close to 1
D)r is close to -1

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Multiple Choice

Q 93Q 93

A strong negative correlation means:
A)the points in a scatter diagram lie on an upward sloping line
B)the points in a scatter diagram lie on a downward sloping line
C)r is close to -1
D)r is close to 1

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Multiple Choice

Q 94Q 94

A weak positive correlation means:
A)the points in a scatter diagram are very close to an upward sloping line
B)the points in a scatter diagram are very close to a downward sloping line
C)r is positive and close to zero
D)r is close to 1

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Multiple Choice

Q 95Q 95

A weak negative correlation means:
A)the points in a scatter diagram are very close to an upward sloping line
B)the points in a scatter diagram are very close to a downward sloping line
C)r is negative and close to zero
D)r is close to -1

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Multiple Choice

Q 96Q 96

The value of the correlation coefficient is zero if the points in a scatter diagram:
A)lie on an upward sloping line
B)lie on a downward sloping line
C)are scattered all over the diagram
D)are close to the regression line

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Multiple Choice

Q 97Q 97

Given that = 276, = 183,and = 153,what is the value of the correlation coefficient,rounded to three decimal places?

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Short Answer

Q 98Q 98

Given that = 853, = 642,and = 314,what is the value of the correlation coefficient,rounded to three decimal places?

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Short Answer

Q 99Q 99

Given that = 241, = 326,and = -71,what is the value of the correlation coefficient,rounded to three decimal places?

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Short Answer

Q 100Q 100

Use the following to answer question 100:
The following table lists the monthly incomes (in hundreds of dollars)and the monthly rents paid (in hundreds of dollars)by a sample of six families.
-Chapter 100.What is the value of the correlation coefficient?

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Short Answer

Q 101Q 101

Use the following to answer question 101:
The following table lists the ages (in years)and the prices (in thousands of dollars)by a sample of six houses.
-What is the value of the correlation coefficient?

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Short Answer

Q 102Q 102

Use the following to answer questions 102-103:
The following table lists the monthly incomes (in hundreds of dollars)and the monthly rents paid (in hundreds of dollars)by a sample of six families.
-What is the 99% confidence interval for the mean monthly rent of all families with a monthly income of $2500,rounded to the nearest penny?

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Essay

Q 103Q 103

Use the following to answer questions 102-103:
The following table lists the monthly incomes (in hundreds of dollars)and the monthly rents paid (in hundreds of dollars)by a sample of six families.
-What is the 99% confidence interval for the mean monthly rent of a randomly selected family with a monthly income of $2500,rounded to the nearest penny?

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Essay

Q 104Q 104

Use the following to answer questions 104-105:
The following table lists the ages (in years)and the prices (in thousands of dollars)by a sample of six houses.
-What is the 90% confidence interval for the average price of all 16-year old homes,rounded to the nearest dollar?

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Essay

Q 105Q 105

Use the following to answer questions 104-105:
The following table lists the ages (in years)and the prices (in thousands of dollars)by a sample of six houses.
-What is the 90% confidence interval for the average price of all 16-year old homes,rounded to the nearest dollar?

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Essay