Question 1

What is spurious correlation? Provide a real or hypothetical example where two variables might exhibit such a relationship.

Accepted Answer

Spurious correlation occurs whenever two

Question 2

For a given data set of (x,y)values,an infinite number of possible regression equations can be fitted to the corresponding scatter diagram,and each equation will have a unique combination of values for the y-intercept b0 and the slope b1.However,only one equation will be the "best fit" as defined by the least-squares criterion.

Accepted Answer

A) True 
 B)False

Question 3

Maintenance Costs
Data was collected to investigate the relationship between the age and annual maintenance costs for a one particular car.The table below shows the costs over the life of a seven-year old car.
 $$\begin{array} { | c | c } 
\hline \text { Year } & \text { Annual Maintenance Casts } \
\hline 1 & \$ 150 \
\hline 2 & \$ 210 \
\hline 3 & \$ 450 \
\hline 4 & \$ 490 \
\hline 5 & \$ 510 \
\hline 6 & \$ 1590 \
\hline 7 & \$ 160 \
\hline
\end{array}$$
-In testing the hypotheses $H _ { 0 } : \beta _ { 1 } = 0$ vs. $\mathrm { H } _ { 1 } : \beta _ { 1 } \neq 0$ ,what is the value of the test statistic?

Accepted Answer

The answer of Maintenance Costs
Data was collected to investigate the...

Question 4

Test the null hypothesis that the true population coefficient of correlation equals zero using the 0.05 significance level.

Accepted Answer

H₀: @#LAT-DLM& = 0 (There is no linear

Question 5

Salesperson
The general manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson.To examine this belief she records last month's sales (in $1,000s)and the years of experience of 10 randomly selected salespeople.These data are listed below.
 $$\begin{array} { | c | c | c | } 
\hline \text { Ealesperson } & \text { Years of Experience } & \text { Eales } \
\hline 1 & 0 & 7 \
\hline 2 & 2 & 9 \
\hline 3 & 10 & 20 \
\hline 4 & 3 & 15 \
\hline 5 & 8 & 18 \
\hline 0 & 5 & 14 \
\hline 7 & 12& 20 \
\hline 8 &7 & 17 \
\hline 9 &20 & 30 \
\hline 10 & 15& 25 \
\hline
\end{array}$$
-Determine the standard error of estimate. $5 _ { y . x }$ = ____________________
Describe what this statistic tells you about the regression line.

Accepted Answer

1.5724; Th

Question 6

If the total variation in y values is 200,and the variation explained by regression line is 180,then the coefficient of determination is equal to ____________________.

Accepted Answer

The answer of If the total variation in y values...

Question 7

If the coefficient of correlation is either ____________________ or ____________________,then the regression line will actually include all of the data points and the line will be a perfect fit.

Accepted Answer

The answer of If the coefficient of correlation is either...

Question 8

The assumption of equal standard deviations about the regression line is called _________________________.

Accepted Answer

The answer of The assumption of equal standard deviations about...

Question 9

A scatter diagram includes the data points:
(x = 2,y = 5),
(x = 4,y = 12),
(x = 6,y = 20),
(x = 8,y = 28),and
(x = 10,y = 30).
Two regression lines are proposed:
(1) $\hat { y }$ = -.6 + 3x
(2) $\hat { y }$ = -1 + 5 x
Using the least squares criterion,which of these regression lines is the better fit to the data? Why?

Accepted Answer

The residual sum of squares, @#LAT-DLM&

Question 10

GPA
The following table shows the grade point average (GPA)for 5 students along with their entrance exam scores for MBA programs (GMAT).Develop a model that would predict the GPA of a student based on their GMAT score.
 $$\begin{array} { | c | c | c } 
\hline \text { Student } & \text { CPA } & \text { GMAT } \
\hline 1 & 3.5 & 6.7 \
\hline 2 & 3.1 & 5.4 \
\hline 3 & 3.2 & 4.8 \
\hline 4 & 4.0 & 7.0 \
\hline 5 & 3.6 & 5.9 \
\hline 6 & 3.2 & 5.2 \
\hline 7 & 3.7 & 7.2 \
\hline
\end{array}$$
-Construct a 95% prediction interval for an individual y value when x = 6.5.

Accepted Answer

When x = 6.5, @#LAT-DLM& .Also t._025,5= 2.571

Question 11

In the sample regression line $\hat { y } = b _ { 0 } + b _ { 1 } x$ the term b0 is the y-intercept; this is the value of y where the line intersects the y-axis whenever x = 0.

Accepted Answer

A) True 
 B)False

Question 12

Household
The following data was collected by a particular company to determine if a relationship exists between the number of people in a household and weekly food expenditures.
 $$\begin{array} { | c | c | c } 
\hline \text { Househald } & \text { Number in Hausehald } & \text { Weakly Fadd Expenses } \
\hline 1 & 2 & \$ 95 \
\hline 2 & 3 & \$ 137 \
\hline 3 & 5 & \$ 165 \
\hline 4 & 2 & \$ 105 \
\hline 5 & 4 & \$ 227 \
\hline 6 & 4 & \$ 240 \
\hline 7 & 5 & \$ 185 \
\hline
\end{array}$$
-Calculate the coefficient of determination and interpret the results.

Accepted Answer

@#LAT-DLM& .This means that 50.8% of the

Question 13

GPA
The following table shows the grade point average (GPA)for 5 students along with their entrance exam scores for MBA programs (GMAT).Develop a model that would predict the GPA of a student based on their GMAT score.
 $$\begin{array} { | c | c | c } 
\hline \text { Student } & \text { CPA } & \text { GMAT } \
\hline 1 & 3.5 & 6.7 \
\hline 2 & 3.1 & 5.4 \
\hline 3 & 3.2 & 4.8 \
\hline 4 & 4.0 & 7.0 \
\hline 5 & 3.6 & 5.9 \
\hline 6 & 3.2 & 5.2 \
\hline 7 & 3.7 & 7.2 \
\hline
\end{array}$$
-Determine the standard error of estimate.

Accepted Answer

The answer of GPA
The following table shows the grade point...

Question 14

A regression analysis between sales (in $1000)and advertising (in $)resulted in the following least squares line: $\hat{y}$ = 80,000 + 5x.This implies that an:

Accepted Answer

A)  increase of $1 in advertising is expected to result in an increase of $5 in sales. 
B)  increase $5 in advertising is expected to result in an increase of $5,000 in sales. 
C)  increase of $1 in advertising is expected to result in an increase of $80,005 in sales. 
D)  increase of $1 in advertising is expected to result in an increase of $5,000 in sales. 
A)  increase of $1 in advertising is expected to result in an increase of $5 in sales. 
B)  increase $5 in advertising is expected to result in an increase of $5,000 in sales. 
C)  increase of $1 in advertising is expected to result in an increase of $80,005 in sales. 
D)  increase of $1 in advertising is expected to result in an increase of $5,000 in sales.

Question 15

Consider the following data values of variables x and y
 $$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline \mathbf { x } & 5 & 4 & 3 & 6 & 9 & 8 & 10 \
\hline \mathbf { y } & 7 & \mathbf { g } & 10 & 5 & 2 & 3 & 1 \
\hline
\end{array}$$   What does the scatter diagram tell you about the relationship between x and y?

Accepted Answer

The relationship bet

Question 16

In the sample regression line, $\hat { y } = b _ { 0 } + b _ { 1 } x$ what does the cap (^)over the y indicate?

Accepted Answer

The (^)indicates that @#LAT-DLM& is the

Question 17

Unemployed
The data below are for the number of unemployed persons (in millions)and the federal unemployment insurance payments (in billions of dollars)for the years 1978 - 1985.Some economists state that these two variables are positively related.
 $\begin{array}{|l|l|l|l|l|l|l|l|l}
\hline \text { Year } & \mathbf{1 9 7 8} & \mathbf{1 9 7 9} & \mathbf{1 9 8 0} & \mathbf{1 9 8 1} & \mathbf{1 9 8 2} & \mathbf{1 9 8 3} & \mathbf{1 9 8 4} & \mathbf{1 9 8 5} \
\hline \text { Federal Unemployment Insurance Payments } & 11.8 & 10.7 & 18.0 & 19.7 & 23.7 & 31.5 & 18.4 & 16.8 \
\hline \text { Number of Unemployed Persons } & 6.2 & 6.1 & 7.6 & 8.3 & 10.7 & 10.7 & 8.5 & 8.3
\end{array}$

-Calculate the estimated standard deviation of the slope.

Accepted Answer

The answer of Unemployed
The data below are for the number...

Question 18

Unemployed
The data below are for the number of unemployed persons (in millions)and the federal unemployment insurance payments (in billions of dollars)for the years 1978 - 1985.Some economists state that these two variables are positively related.
 $\begin{array}{|l|l|l|l|l|l|l|l|l}
\hline \text { Year } & \mathbf{1 9 7 8} & \mathbf{1 9 7 9} & \mathbf{1 9 8 0} & \mathbf{1 9 8 1} & \mathbf{1 9 8 2} & \mathbf{1 9 8 3} & \mathbf{1 9 8 4} & \mathbf{1 9 8 5} \
\hline \text { Federal Unemployment Insurance Payments } & 11.8 & 10.7 & 18.0 & 19.7 & 23.7 & 31.5 & 18.4 & 16.8 \
\hline \text { Number of Unemployed Persons } & 6.2 & 6.1 & 7.6 & 8.3 & 10.7 & 10.7 & 8.5 & 8.3
\end{array}$

-Use these data to develop a scatter diagram for these data.

Accepted Answer

The answer of Unemployed
The data below are for the number...

Question 19

Household
The following data was collected by a particular company to determine if a relationship exists between the number of people in a household and weekly food expenditures.
 $$\begin{array} { | c | c | c } 
\hline \text { Househald } & \text { Number in Hausehald } & \text { Weakly Fadd Expenses } \
\hline 1 & 2 & \$ 95 \
\hline 2 & 3 & \$ 137 \
\hline 3 & 5 & \$ 165 \
\hline 4 & 2 & \$ 105 \
\hline 5 & 4 & \$ 227 \
\hline 6 & 4 & \$ 240 \
\hline 7 & 5 & \$ 185 \
\hline
\end{array}$$
-Construct a 95% confidence interval for the mean weekly food expense when the number in household equals 3.

Accepted Answer

When x = 3, @#LAT-DLM& .Also t._025,5 = 2.571.

Question 20

Simple linear regression requires that the scales of measurement be expressed in either:

Accepted Answer

A)  nominal or ordinal. 
B)  ordinal or ratio. 
C)  interval or ratio. 
D)  nominal or ratio. 
E)  nominal or interval. 
A)  nominal or ordinal. 
B)  ordinal or ratio. 
C)  interval or ratio. 
D)  nominal or ratio. 
E)  nominal or interval.

What is spurious correlation? Provide a real or hypothetical example where two variables might exhibit such a relationship.

Test the null hypothesis that the true population coefficient of correlation equals zero using the 0.05 significance level.

If the total variation in y values is 200,and the variation explained by regression line is 180,then the coefficient of determination is equal to ____________________.

If the coefficient of correlation is either or ,then the regression line will actually include all of the data points and the line will be a perfect fit.

The assumption of equal standard deviations about the regression line is called _________________________.

In the sample regression line $\hat { y } = b _ { 0 } + b _ { 1 } x$ the term b₀ is the y-intercept; this is the value of y where the line intersects the y-axis whenever x = 0.

A regression analysis between sales (in $1000)and advertising (in $)resulted in the following least squares line: $\hat{y}$ = 80,000 + 5x.This implies that an:

In the sample regression line, $\hat { y } = b _ { 0 } + b _ { 1 } x$ what does the cap (^)over the y indicate?

Simple linear regression requires that the scales of measurement be expressed in either:

A Preview of Business Statistics

Visual Description of Data

Statistical Description of Data

Data Collection and Sampling Methods

Probability: Review of Basic Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Estimation From Sample Data

Hypothesis Tests Involving a Sample Mean or Proportion

Hypothesis Tests Involving Two Sample Means

Analysis of Variance Tests

Chi-Square Applications

Nonparametric Methods

Multiple Regression and Correlation

Model Building

Models for Time Series and Forecasting

Decision Theory

Total Quality Management

Filters

Exam 15: Simple Linear Regression and Correlation

What is spurious correlation? Provide a real or hypothetical example where two variables might exhibit such a relationship.

Test the null hypothesis that the true population coefficient of correlation equals zero using the 0.05 significance level.

If the total variation in y values is 200,and the variation explained by regression line is 180,then the coefficient of determination is equal to ____________________.

If the coefficient of correlation is either ____________________ or ____________________,then the regression line will actually include all of the data points and the line will be a perfect fit.

The assumption of equal standard deviations about the regression line is called _________________________.

In the sample regression line y^=b0+b1x\hat { y } = b _ { 0 } + b _ { 1 } xy^​=b0​+b1​x the term b0 is the y-intercept; this is the value of y where the line intersects the y-axis whenever x = 0.

A regression analysis between sales (in $1000)and advertising (in $)resulted in the following least squares line: y^\hat{y}y^​ = 80,000 + 5x.This implies that an:

Consider the following data values of variables x and y 5 4 3 6 9 8 10 7 10 5 2 3 1 What does the scatter diagram tell you about the relationship between x and y?

In the sample regression line, y^=b0+b1x\hat { y } = b _ { 0 } + b _ { 1 } xy^​=b0​+b1​x what does the cap (^)over the y indicate?

Simple linear regression requires that the scales of measurement be expressed in either:

A Preview of Business Statistics

Visual Description of Data

Statistical Description of Data

Data Collection and Sampling Methods

Probability: Review of Basic Concepts

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Estimation From Sample Data

Hypothesis Tests Involving a Sample Mean or Proportion

Hypothesis Tests Involving Two Sample Means

Analysis of Variance Tests

Chi-Square Applications

Nonparametric Methods

Multiple Regression and Correlation

Model Building

Models for Time Series and Forecasting

Decision Theory

Total Quality Management

Filters

If the coefficient of correlation is either or ,then the regression line will actually include all of the data points and the line will be a perfect fit.

In the sample regression line $\hat { y } = b _ { 0 } + b _ { 1 } x$ the term b₀ is the y-intercept; this is the value of y where the line intersects the y-axis whenever x = 0.

A regression analysis between sales (in $1000)and advertising (in $)resulted in the following least squares line: $\hat{y}$ = 80,000 + 5x.This implies that an:

In the sample regression line, $\hat { y } = b _ { 0 } + b _ { 1 } x$ what does the cap (^)over the y indicate?