Question 1

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)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.

Accepted Answer

The null hypothesis would be that the population correlation coefficient is equal to zero. Since the sample correlation coefficient is 0.235, there is not enough evidence to reject the null hypothesis at the 0.05 significance level and conclude that the true correlation is different from zero. This means that choice (A) and (D) are incorrect. Choice (C) is also incorrect because the sample correlation coefficient cannot be equal to zero if the calculated test statistic falls outside of the rejection region.

Question 2

In analyzing the relationship between two variables,a scatter plot can be used to detect which of the following?
A)A positive linear relationship
B)A curvilinear relationship
C)A negative linear relationship
D)All of the above

Accepted Answer

A scatter plot can detect all three types of relationships between two variables - positive linear, negative linear, and curvilinear.

Question 3

Which of the following statements are incorrect?
A)A scatter plot showing two variables with a positive linear relationship will have all points on a straight line.
B)The stronger the linear relationship between two variables,the closer the correlation coefficient will be to 1.0.
C)Two variables that are uncorrelated with one another may still be related in a nonlinear manner.
D)All of the above are correct.

Accepted Answer

This statement is incorrect. Nonlinear relationships between variables can still exist even if they are uncorrelated.

Question 4

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?
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.

Accepted Answer

The test statistic for testing whether the true population correlation coefficient is equal to zero can be calculated using the formula $t = r\sqrt{\frac{n-2}{1-r^2}}$, where $r$ is the sample correlation and $n$ is the sample size. Substituting $r = 0.468$ and $n = 30$ into the formula gives $t \approx 2.80$. The level of significance is not needed to calculate the test statistic value.

Question 5

Use the following regression results to answer the question below.  ANOVA   In conducting a hypothesis test of the slope using a 0.05 level of significance,which of the following is correct?
A)The slope differs significantly from 0 because p = 0.205 is greater then 0.05.
B)The slope does not differ significantly from 0 because p = 0.205 is greater then 0.05.
C)The slope differs significantly from 0 because p = 0.003 is less then 0.05.
D)The slope does not differ significantly from 0 because p = 0.003 is less then 0.05.

Accepted Answer

In hypothesis testing, we compare the p-value to the level of significance (α) to determine the statistical significance of our test. Here, the p-value for the slope is given as 0.003, which is less than the level of significance of 0.05. Hence, we reject the null hypothesis and conclude that the slope is significantly different from 0. Therefore, the correct choice is C.

Question 6

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

Accepted Answer

The answer of A study was done in which the...

Question 7

Which of the following statements is true with respect to a simple linear regression model?
A)The percent of variation in the dependent variable that is explained by the regression model is equal to the square of the correlation coefficient between the x and y variables.
B)If the correlation coefficient between the x and y variables is negative,the sign on the regression slope coefficient will also be negative.
C)If the correlation between the dependent and the independent variable is determined to be significant,the regression model for y given x will also be significant.
D)All of the above are true.

Accepted Answer

A) This statement is true as the coefficient of determination (r-squared) is equal to the square of the correlation coefficient (r).
B) This statement is also true as the regression slope coefficient measures the direction and strength of the relationship between x and y variables. If the correlation is negative, the regression slope will also be negative.
C) This statement is true as the significance of the correlation implies that there is a linear relationship between the variables, and therefore, the regression model for predicting y given x will also be significant.

Question 8

If the population correlation between two variables is determined to be -0.70,which of the following is known to be true?
A)There is a positive linear relationship between the two variables.
B)There is a fairly strong negative linear relationship between the two variables.
C)An increase in one of the variables will cause the other variable to decline by 70 percent.
D)The scatter diagram for the two variables will be upward sloping from left to right.

Accepted Answer

The negative sign indicates a negative linear relationship, and the magnitude of -0.70 indicates a fairly strong correlation (closer to -1). Option A is incorrect because the negative sign contradicts a positive linear relationship. Option C is incorrect because correlation does not indicate causation, and it does not mean that a change in one variable will cause a proportional change in the other. Option D is incorrect because the negative sign indicates a downward sloping scatter diagram.

Question 9

Use the following regression results to answer the question below.  ANOVA   Which of the following is true?
A)x explains about 88.5 percent of the variation in y.
B)y explains about 88.5 percent of the variation in x.
C)x explains about 78.4 percent of the variation in y.
D)y explains about 78.4 percent of the variation in x.

Accepted Answer

The answer of Use the following regression results to answer...

Question 10

Assume that a medical research study found a correlation of -0.73 between consumption of vitamin A and the cancer rate of a particular type of cancer.This could be interpreted to mean:
A)the more vitamin A consumed,the lower a person's chances are of getting this type of cancer.
B)the less vitamin A consumed,the lower a person's chances are of getting this type of cancer.
C)the more vitamin A consumed,the higher a person's chances are of getting this type of cancer.
D)vitamin A causes this type of cancer.

Accepted Answer

A correlation of -0.73 means that there is a negative association between consumption of vitamin A and the cancer rate - meaning that as consumption of vitamin A increases, the cancer rate decreases. Therefore, choice A is the correct interpretation.

Question 11

Use the following regression results to answer the question below.  ANOVA   How many observations were involved in this regression?
A)7
B)8
C)9
D)10

Accepted Answer

The answer of Use the following regression results to answer...

Question 12

The following regression output is available.Notice that some of the values are missing.  Given this information,what percent of the variation in the y variable is explained by the independent variable?
A)About 75 percent
B)Approximately 57 percent
C)Can't be determined without having the actual data available.
D)About 25 percent

Accepted Answer

The value of R-squared is 0.569, which means approximately 57 percent of the variation in the y variable is explained by the independent variable.

Question 13

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

Accepted Answer

To test the null hypothesis that there is no positive relationship between the number of miles driven and the age of the driver, we can use a t-test for correlation coefficients with n-2 degrees of freedom. At an alpha level of .05 and with 13 degrees of freedom (15-2), the critical value for a one-tailed test is 1.7709. Therefore, the appropriate critical value is D.

Question 14

Which of the following is NOT an assumption for the simple linear regression model?
A)The individual error terms are statistically independent.
B)The distribution of the error terms will be skewed left or right depending on the shape of the dependent variable.
C)The error terms have equal variances for all values of the independent variable.
D)The mean of the dependent variable value for all levels of x can be connected by a straight line.

Accepted Answer

The assumption that the distribution of the error terms will be skewed left or right depending on the shape of the dependent variable is not a valid assumption for the simple linear regression model. The assumption that the error terms are statistically independent, have equal variances for all values of the independent variable, and that the mean of the dependent variable value for all levels of x can be connected by a straight line are all valid assumptions for the simple linear regression model.

Question 15

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,and assuming that the test is to be performed at the .05 level of significance,which of the following is the correct test statistic?
A)t = 1.4812
B)t = 1.7709
C)z = 2.114
D)t = 1.74

Accepted Answer

The correct test statistic for testing the significance of a correlation coefficient, r, with a sample size of n is given by the formula $t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$. Using the given sample correlation coefficient, r = .38, and the sample size, n = 15, the calculation yields a t-value close to 1.4812, making option A the correct choice.

Question 16

If a pair of variables have a strong curvilinear relationship,which of the following is true?
A)The correlation coefficient will be able to indicate that curvature is present.
B)A scatter plot will not be needed to indicate that curvature is present.
C)The correlation coefficient will not be able to indicate the relationship is curved.
D)The correlation coefficient will be equal to zero.

Accepted Answer

Correlation coefficients only measure linear relationships between variables. They cannot detect curvilinear relationships. Therefore, even if there is a strong curvilinear relationship between two variables, the correlation coefficient will not be able to indicate it.

Question 17

Use the following regression results to answer the question below.  ANOVA   Which of the following is true?
A)The correlation between x and y must be approximately 0.8851.
B)The correlation between x and y must be approximately -0.8851.
C)The correlation between x and y must be approximately 0.7835.
D)The correlation between x and y must be approximately -0.7835.

Accepted Answer

The answer of Use the following regression results to answer...

Question 18

The term that is given when two variables are correlated but there is no apparent connection between them is:
A)spontaneous correlation.
B)random correlation.
C)spurious correlation.
D)linear correlation.

Accepted Answer

A spurious correlation is a statistical relationship between two variables that occurs when there is no causal connection between them. It is often caused by a common underlying factor that influences both variables, leading to a false impression of correlation between them.

Question 19

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 the test statistic for testing whether the true population correlation is equal to zero?
A)t = 0.245
B)t = 1.76
C)t = 2.1604
D)t = 0.872

Accepted Answer

The answer of A recent study of 15 shoppers showed...

Question 20

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 the appropriate null hypothesis to test whether the population correlation is zero? A)H_o : r = 0.0 B)H_o : ρ = 0.0 C)H_o : μ = 0.0 D)H_o : ρ ≠ 0

Accepted Answer

The answer of A recent study of 15 shoppers showed...

Quiz 14: Introduction to Linear Regression and Correlation Analysis

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?

In analyzing the relationship between two variables,a scatter plot can be used to detect which of the following?

Which of the following statements are incorrect?

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?

Use the following regression results to answer the question below. ANOVA In conducting a hypothesis test of the slope using a 0.05 level of significance,which of the following is correct?

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:

Which of the following statements is true with respect to a simple linear regression model?

If the population correlation between two variables is determined to be -0.70,which of the following is known to be true?

Use the following regression results to answer the question below. ANOVA Which of the following is true?

Assume that a medical research study found a correlation of -0.73 between consumption of vitamin A and the cancer rate of a particular type of cancer.This could be interpreted to mean:

Use the following regression results to answer the question below. ANOVA How many observations were involved in this regression?

The following regression output is available.Notice that some of the values are missing. Given this information,what percent of the variation in the y variable is explained by the independent variable?

Which of the following is NOT an assumption for the simple linear regression model?

If a pair of variables have a strong curvilinear relationship,which of the following is true?

Use the following regression results to answer the question below. ANOVA Which of the following is true?

The term that is given when two variables are correlated but there is no apparent connection between them is:

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 the test statistic for testing whether the true population correlation is equal to zero?

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 the appropriate null hypothesis to test whether the population correlation is zero?