Deck 13: Simple Linear Regression

Question 1

In the regression model ,y is the:

A)dependent variable
B)independent variable
C)error term
D)missing variable

Answer 1

dependent variable

Question 2

The regression model is:

A)a probabilistic model
B)a nonlinear model
C)an exact relationship
D)a deterministic model

Answer 2

a probabilistic model

Question 3

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

Answer 3

gives a relationship between two variables that can be described by a line

Question 4

In the equation ,6 is the:

A)independent variable
B)slope of the line
C)dependent variable
D)y-intercept

Question 5

In the equation ,y is the:

A)independent variable
B)slope of the line
C)dependent variable
D)y-intercept

Question 6

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

Question 7

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

Question 8

In the regression model ,a and b are the:

A)sample statistics
B)random variables
C)population parameters
D)omitted variables

Question 9

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

Question 10

The model is a:

A)probabilistic model
B)nonlinear model
C)stochastic model
D)deterministic model

Question 11

In the regression model , is the:

A)slope of the regression line
B)random error term
C)y-intercept
D)missing variable

Question 12

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

Question 13

In the equation ,x is the:

A)independent variable
B)slope of the line
C)dependent variable
D)y-intercept

Question 14

In the equation ,2 is the:

A)independent variable
B)slope of the line
C)dependent variable
D)y-intercept

Question 15

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

Question 16

In the regression model ,A and B are the:

A)sample statistics
B)random variables
C)population parameters
D)omitted variables

Question 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

Question 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

Question 19

In the regression model ,x is the:

A)dependent variable
B)independent variable
C)error term
D)missing variable

Question 20

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

Question 21

Use the following to answer questions :
The table shown below gives six pairs of x and y values.

The values of and ,rounded to three decimal places,are:

Question 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

Question 23

Use the following to answer questions :
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:

Question 24

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:

Question 25

Use the following to answer questions :
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:

Question 26

The value of :

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

Question 27

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

Question 28

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

Question 29

Use the following to answer questions :
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:

Question 30

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

Question 31

Use the following to answer questions :
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:

Question 32

Use the following to answer questions :
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:

Question 33

The value of :

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

Question 34

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

Question 35

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

Question 36

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

Question 37

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:

Question 38

Use the following to answer questions :
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:

Question 39

Use the following to answer questions :
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:

Question 40

Use the following to answer questions :
The table shown below gives seven pairs of x and y values.

The values of and ,rounded to three decimal places,are:

Question 41

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

Question 42

Use the following to answer questions :
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:

Question 43

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

Question 44

Use the following to answer questions :
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.

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

Question 45

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

Question 46

Use the following to answer questions :
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:

Question 47

The value of :

A)is always negative
B)is always nonnegative
C)is always positive
D)can be negative,positive,or zero

Question 48

Use the following to answer questions :
The following table lists the ages (in years)and the prices (in thousands of dollars)by a sample of six houses.

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

Question 49

Use the following to answer questions :
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:

Question 50

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

Question 51

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

Question 52

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

Question 53

Use the following to answer questions :
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:

Question 54

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

Question 55

An assumption of the regression model is that the distribution of errors is

A)binomial
B)rectangular
C)normal
D)bimodal

Question 56

Use the following to answer questions :
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:

Question 57

Use the following to answer questions :
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.

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

Question 58

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

Question 59

Use the following to answer questions :
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:

Question 60

Use the following to answer questions :
The following table lists the ages (in years)and the prices (in thousands of dollars)by a sample of six houses.

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

Question 61

Use the following to answer questions :
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:

Question 62

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:

Question 63

Use the following to answer questions :
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:

Question 64

Use the following to answer questions :
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:

Question 65

Use the following to answer questions :
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:

Question 66

Use the following to answer questions :
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%.
What is the value of the test statistic,t,rounded to three decimal places?

Question 67

Use the following to answer questions :
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:

Question 68

Use the following to answer questions :
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:

Question 69

Use the following to answer questions :
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:

Question 70

Use the following to answer questions :
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%.
What is the critical value of t?

A)-2.896
B)-2.998
C)-3.499
D)-3.143

Question 71

Use the following to answer questions :
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%.
What is the value of the test statistic,t,rounded to three decimal places?

Question 72

Use the following to answer questions :
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:

Question 73

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

Question 74

Use the following to answer questions :
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:

Question 75

Use the following to answer questions :
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:

Question 76

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:

Question 77

Use the following to answer questions :
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%.
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

Question 78

Use the following to answer questions :
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:

Question 79

Use the following to answer questions :
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:

Question 80

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: