Question 1

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

Accepted Answer

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

Question 2

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?

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 3

Which of the following statements is correct?

Accepted Answer

Two variables can have a nonlinear relationship even if they are uncorrelated, meaning the correlation coefficient is zero.

Question 4

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

Accepted Answer

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

Question 5

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

The answer of Recently, an automobile insurance company performed a...

Question 6

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

With a correlation coefficient of 0.235, especially in a small sample size of 15, it's likely that there isn't enough evidence to reject the null hypothesis that the true population correlation is zero. This is because a correlation of 0.235 is relatively low, indicating a weak linear relationship, and without knowing the exact critical value or conducting a specific statistical test (like Pearson's r test), we cannot definitively say the correlation is significantly different from zero at the 0.05 significance level.

Question 7

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

Accepted Answer

Spurious correlation refers to a situation where two variables appear to be related to each other but are actually both influenced by a third variable, or the correlation is purely coincidental and not due to any causal relationship.

Question 8

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

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

Question 9

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

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:

Accepted Answer

A negative correlation of -0.73 suggests that as the consumption of vitamin A increases, the rate of this particular type of cancer decreases. This implies that higher vitamin A intake is associated with lower chances of getting this cancer.

Question 11

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

Accepted Answer

The correlation coefficient measures the strength and direction of a linear relationship between two variables. It does not capture non-linear patterns such as curvilinear relationships, thus it cannot indicate the relationship is curved.

Question 12

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

Accepted Answer

A) This statement is true because the coefficient of determination (R^2) is indeed the square of the correlation coefficient (r) between the independent variable (x) and the dependent variable (y), which explains the proportion of the variance in the dependent variable that is predictable from the independent variable. B) This is true because the sign of the correlation coefficient indicates the direction of the relationship between x and y. A negative correlation means that as x increases, y decreases, which is reflected in a negative slope coefficient in the regression equation. C) If the correlation is significant, it implies there is a statistically significant relationship between x and y. While this doesn't guarantee the regression model will be significant in all aspects (e.g., all predictors being significant if multiple regression), it strongly suggests the model explaining y given x has a significant linear component.

Question 13

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?

Accepted Answer

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

Question 14

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

Accepted Answer

The assumption for the simple linear regression model is that the error terms are normally distributed (not necessarily skewed left or right), which contradicts choice B. Other assumptions include independence of errors (A), homoscedasticity or equal variances of errors (C), and a linear relationship between the dependent and independent variables (D).

Question 15

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

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 16

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

The answer of The following regression output is available. Notice...

Question 17

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?

Accepted Answer

The answer of The following regression output is available. Notice...

Question 18

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?

Accepted Answer

The test statistic for testing the significance of a correlation coefficient is calculated using the formula: t = r√((n-2)/(1-r²)), where r is the sample correlation and n is the sample size. Substituting the given values (r = 0.235, n = 15) into the formula gives t ≈ 0.872.

Question 19

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

Accepted Answer

A correlation of -0.70 indicates a fairly strong negative linear relationship between the two variables, meaning as one variable increases, the other tends to decrease.

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?

Accepted Answer

The appropriate null hypothesis for testing whether the population correlation coefficient (ρ) is zero is "H0 : ρ = 0.0". This tests if there is no linear relationship between the two variables in the population.

Quiz 14: Introduction to Linear Regression and Correlation Analysis

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

Which of the following statements is correct?

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 true?

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

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:

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:

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

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

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?

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

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?

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?

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