Question 1

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 coefficient of determination (R-squared) is the percentage of variation in the dependent variable that is explained by the independent variable. In this case, the R-squared value is 0.57, which means that approximately 57 percent of the variation in the y variable is explained by the independent variable(s).

Question 2

Use the following regression results to answer the question below.  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 3

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 negative correlation coefficient of -0.73 indicates an inverse relationship between vitamin A consumption and cancer rate. This means that as vitamin A consumption increases, cancer rate decreases. Therefore, choice A is the correct interpretation of the correlation coefficient.

Question 4

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

Accepted Answer

The sample size is typically represented by the "n" value, which is missing in the output. However, we can see that there are 9 observations for the variable "Y", which suggests that the sample size is 9. Therefore, the best choice is C.

Question 5

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

The correlation coefficient only measures linear relationships between variables and cannot indicate the presence or strength of a curvilinear relationship. A scatter plot would be necessary to visually observe the curvature in the relationship.

Question 6

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

This is known as a spurious correlation, where the association between two variables appears to be related, but in reality, there is no actual causal link between them.

Question 7

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 8

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 9

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 10

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

Since we are testing the hypothesis at an alpha level of .05, we need to find the critical value for a t-distribution with 13 degrees of freedom (n-2=15-2=13). Using a t-table or calculator, we find that the critical value is t=1.7709 for a two-tailed test. Therefore, the best choice is D.

Question 11

Use the following regression results to answer the question below.  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-value = 0.205 is greater than 0.05
B)The slope does not differ significantly from 0 because p-value = 0.205 is greater than 0.05
C)The slope differs significantly from 0 because p-value = 0.003 is less than 0.05
D)The slope does not differ significantly from 0 because p-value = 0.003 is less than 0.05

Accepted Answer

To conduct a hypothesis test of the slope using a 0.05 level of significance, we need to compare the p-value with the significance level (0.05). In this case, the p-value for the slope is 0.003, which is less than 0.05. Therefore, we can reject the null hypothesis and conclude that the slope differs significantly from 0. Option C is the correct choice.

Question 12

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

Since the p-value is not given, we cannot directly compare it to the significance level of 0.05. Therefore, we need to use the critical value approach. The sample size is too small (n=15) to assume normality, so we need to use a t-distribution with df = n-2 = 13. The critical t-value for a two-tailed test with alpha = 0.05 and df = 13 is 2.160 (from a t-table or calculator). The calculated t-value for the correlation coefficient (using a t-test formula or calculator) is 0.748. Since 0.748 is less than 2.160 (in absolute value), we fail to reject the null hypothesis that the population correlation coefficient is zero. Therefore, we conclude that based on the sample data, there is not enough evidence to conclude that the true correlation is different from zero.

Question 13

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 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 of normality for the distribution of error terms is typically included in the assumptions for simple linear regression, but the statement in choice B about the distribution being skewed left or right is not a necessary assumption. The other three choices are all commonly included as assumptions for the simple linear regression model.

Question 15

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

A correlation coefficient of -0.70 indicates a strong negative linear relationship between the two variables. Option A is incorrect because a positive linear relationship would correspond to a positive correlation coefficient. Option C is incorrect because correlation coefficients do not measure cause and effect relationships. Option D is incorrect because an upward sloping scatter diagram would indicate a positive linear relationship.

Question 16

Which of the following statements is correct?
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

The answer of Which of the following statements is correct?
A)A...

Question 17

Use the following regression results to answer the question below.  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 18

Use the following regression results to answer the question below.  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 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 appropriate null hypothesis to test whether the population correlation is zero? A)H₀ : r = 0.0 B)H₀ : ρ = 0.0 C)H₀ : μ = 0.0 D)H₀ : ρ ≠ 0

Accepted Answer

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

Question 20

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 between the x and y variables.
B) This statement is also true, as a negative correlation implies that as x increases, y decreases. Thus, the regression slope coefficient will also be negative.
C) This statement is true, as a significant correlation between the dependent and the independent variable indicates that there is a relationship between the two, which can be used to build a significant regression model for predicting y given x.
Therefore, all the given statements (A, B, and C) are true with respect to a simple linear regression model.

Quiz 14: Introduction to Linear Regression and Correlation Analysis

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?

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

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:

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 pair of variables have a strong curvilinear relationship,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?

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. In conducting a hypothesis test of the slope using a 0.05 level of significance,which of the following is correct?

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:

Which of the following is NOT an assumption for the 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?

Which of the following statements is correct?

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

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

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?

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