Question 1

Recently,an automobile insurance company performed a study of a random sample of 15 of its customers to determine if there is a positive relationship between the number of miles driven and the age of the driver.The sample correlation coefficient is r = .38.Given this information,which of the following is appropriate critical value for testing the null hypothesis at an alpha = .05 level?

Accepted Answer

A) t = 2.6104 
B) t = 1.7613 
C) t = 1.7531 
D) t = 1.7709

Question 2

Two variables have a correlation coefficient that is very close to zero.This means that there is no relationship between the two variables.

Accepted Answer

A) True 
 B)False

Question 3

In a regression analysis situation,the standard error of the slope is:

Accepted Answer

A) a measure of the variation in the regression slope from sample to sample. 
B) equal to the square root of the standard error of the estimate. 
C) a measure of the amount of change in y that will occur for a one-unit change in x. 
D) All of the above.

Question 4

A study was recently performed by the Internal Revenue Service to determine how much tip income waiters and waitresses should make based on the size of the bill at each table.A random sample of bills and resulting tips were collected.These data are shown as follows:  Based upon these data,what is the approximate predicted value for tips if the total bill is $100?

Accepted Answer

A) $15.55 
B) $20.61 
C) $26.03 
D) $12.88

Question 5

If two variables are spuriously correlated,it means that the correlation coefficient between them is near zero.

Accepted Answer

A) True 
 B)False

Question 6

State University recently randomly sampled seven students and analyzed grade point average (GPA)and number of hours worked off-campus per week.The following data were observed:  In regression model with HOURS as the independent variable has an R-square equal to approximately .46.

Accepted Answer

A) True 
 B)False

Question 7

A correlation coefficient computed from a sample of data values selected from a population is called a statistic and is subject to sampling error.

Accepted Answer

A) True 
 B)False

Question 8

A bank is interested in determining whether its customers' checking balances are linearly related to their savings balances.A sample of n = 20 customers was selected and the correlation was calculated to be +0.40.If the bank is interested in testing to see whether there is a significant linear relationship between the two variables using a significance level of .05,the correct null and alternative hypotheses to test are:

Accepted Answer

A) True 
 B)False

Question 9

The following regression output was generated based on a sample of utility customers.The dependent variable was the dollar amount of the monthly bill and the independent variable was the size of the house in square feet.  Based on this regression output,what is the 95 percent confidence interval estimate for the population regression slope coefficient?

Accepted Answer

A) Approximately -0.0003 ----- +0.0103 
B) About -0.0082 ----- +0.0188 
C) Approximately -32.76 ----- +32.79 
D) None of the above.

Question 10

A recent study of 15 shoppers showed that the correlation between the time spent in the store and the dollars spent was 0.235.Using a significance level equal to 0.05,which of the following is true?

Accepted Answer

A) The null hypothesis that the population mean is equal to zero should be rejected and we should conclude that the true correlation is not equal to zero. 
B) Based on the sample data there is not enough evidence to conclude that the true correlation is different from zero. 
C) The sample correlation coefficient could be zero since the test statistic does not fall in the rejection region. 
D) The null hypothesis should be rejected because the test statistic exceeds the critical value.

Question 11

The National Football League has performed a study in which the total yards gained by teams in games was used as an independent variable to explain the variation in total points scored by teams during games.The points scored ranged from 0 to 57 and the yards gained ranged from 187 to 569.The following regression model was determined:  = 12.3 + .12x. Given this model,which of the following statements is true?

Accepted Answer

A) The average points scored for teams who gain zero yards during a game is -12.3 points. 
B) The average yards gained will increase by .12 for every additional point scored. 
C) The average change in points scored for each increase of one yard will be 0.12. 
D) The average number of points scored per game is 12.3.

Question 12

A study was done in which the high daily temperature and the number of traffic accidents within the city were recorded.These sample data are shown as follows:  Given this data the sample correlation is:

Accepted Answer

A) -0.57. 
B) 0.64. 
C) 1.54. 
D) 0.57.

Question 13

In a study of 30 customers' utility bills in which the monthly bill was the dependent variable and the number of square feet in the house is the independent variable,the resulting regression model is  = 23.40 + 0.4x.Based on this model,the expected utility bill for a customer with a home with 2,300 square feet is approximately $92.00.

Accepted Answer

A) True 
 B)False

Question 14

The difference between a scatter plot and a scatter diagram is that the scatter plot has the independent variable on the x-axis while the independent variable is on the Y-axis in a scatter diagram.

Accepted Answer

A) True 
 B)False

Question 15

When the correlation coefficient for the two variables was -0.23,it implies that the two variables are not correlated because the correlation coefficient cannot be negative.

Accepted Answer

A) True 
 B)False

Question 16

A bank is interested in determining whether its customers' checking balances are linearly related to their savings balances.A sample of n = 20 customers was selected and the correlation was calculated to be +0.40.If the bank is interested in testing to see whether there is a significant linear relationship between the two variables using a significance level of 0.05,the value of the test statistic is approximately t = 1.8516.

Accepted Answer

A) True 
 B)False

Question 17

Consider the following partially completed computer printout for a regression analysis where the dependent variable is the price of a personal computer and the independent variable is the size of the hard drive.  Based on the information provided,what percentage of the variation in the price of the personal computers is accounted for by the regression model using hard drive capacity as the independent variable?

Accepted Answer

A) About 82 percent 
B) About 67 percent 
C) 217.75 
D) About 66 percent

Question 18

The following regression output is available.Notice that some of the values are missing.  Given this information,what was the sample size used in the study?

Accepted Answer

A) 8 
B) 18 
C) 9 
D) 16

Question 19

If a sample of n = 30 people is selected and the sample correlation between two variables is r = 0.468,what is the test statistic value for testing whether the true population correlation coefficient is equal to zero?

Accepted Answer

A) About t = 2.80 
B) About t = -.3.01 
C) t = 2.0484 
D) Can't be determined without knowing the level of significance for the test.

Question 20

State University recently randomly sampled seven students and analyzed grade point average (GPA)and number of hours worked off-campus per week.The following data were observed:  If the university wished to test the claim that the correlation between hours worked and GPA is negative,the following null and alternative hypotheses would be appropriate:  : ρ < 0.0  : ρ ≥ 0.0

Accepted Answer

A) True 
 B)False

Exam 14: Introduction to Linear Regression and Correlation Analysis

Two variables have a correlation coefficient that is very close to zero.This means that there is no relationship between the two variables.

In a regression analysis situation,the standard error of the slope is:

If two variables are spuriously correlated,it means that the correlation coefficient between them is near zero.

State University recently randomly sampled seven students and analyzed grade point average (GPA)and number of hours worked off-campus per week.The following data were observed: In regression model with HOURS as the independent variable has an R-square equal to approximately .46.

A correlation coefficient computed from a sample of data values selected from a population is called a statistic and is subject to sampling error.

A recent study of 15 shoppers showed that the correlation between the time spent in the store and the dollars spent was 0.235.Using a significance level equal to 0.05,which of the following is true?

A study was done in which the high daily temperature and the number of traffic accidents within the city were recorded.These sample data are shown as follows: Given this data the sample correlation is:

The difference between a scatter plot and a scatter diagram is that the scatter plot has the independent variable on the x-axis while the independent variable is on the Y-axis in a scatter diagram.

When the correlation coefficient for the two variables was -0.23,it implies that the two variables are not correlated because the correlation coefficient cannot be negative.

The following regression output is available.Notice that some of the values are missing. Given this information,what was the sample size used in the study?

If a sample of n = 30 people is selected and the sample correlation between two variables is r = 0.468,what is the test statistic value for testing whether the true population correlation coefficient is equal to zero?