Question 1

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:  The correlation between these two variables is approximately -.461.

Accepted Answer

The correlation coefficient of -.461 indicates a negative correlation between GPA and number of hours worked off-campus per week.

Question 2

When a pair of variables has a positive correlation,the slope in the regression equation will always be positive.

Accepted Answer

When two variables have a positive correlation, it means that as one variable increases, the other variable also increases. This results in a positive slope in the regression equation.

Question 3

If a set of data contains no values of x that are equal to zero,then the regression coefficient,b₀,has no particular meaning.

Accepted Answer

The regression coefficient b0 has no particular meaning if there are no values of x that are equal to zero, not b1. B1 is the slope of the regression line and has a meaningful interpretation regardless of whether there are zero values of x.

Question 4

You are given the following sample data for two variables:  The sample correlation coefficient for these data is approximately r = 0.755.

Accepted Answer

The answer of You are given the following sample data...

Question 5

The fact that teachers' salaries in Wisconsin are correlated with egg prices in Texas means that the two variables are spuriously correlated since a change in one variable could not cause the change in the other.

Accepted Answer

The correlation between teachers' salaries in Wisconsin and egg prices in Texas is not a true association because there is no logical or causal link between the two variables. Therefore, they are spuriously correlated, and a change in one variable cannot cause a change in the other.

Question 6

Given a sample of size n = 15 and a sample correlation of r = 0.7,the value of the test statistic for conducting a hypothesis test of the correlation is t = 3.53.

Accepted Answer

The value of the test statistic for conducting a hypothesis test of correlation with a sample size of 15 and a sample correlation of 0.7 is t = 2.476. A test statistic of t = 3.53 would be highly unlikely and may indicate an error.

Question 7

In developing a simple linear regression model it is assumed that the distribution of error terms will be normally distributed for all levels of x.

Accepted Answer

This assumption is known as the normality assumption and it is a key assumption in the development of a simple linear regression model. It is important to ensure that the errors are normally distributed for all levels of x in order to have accurate and reliable predictions from the model.

Question 8

Given a sample correlation r = -0.5 and a sample size of n = 30,the test statistic for testing whether the two variables are significantly correlated is approximately t = -3.055.

Accepted Answer

This is true. With a sample size of 30 and a sample correlation r of -0.5, the test statistic for testing whether the two variables are significantly correlated is indeed approximately t = -3.055. This can be calculated using the formula t = r * sqrt(n-2) / sqrt(1-r^2), where n is the sample size.

Question 9

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:  The test statistic for testing whether the two variables are significantly correlated is approximately z = 1.56.

Accepted Answer

The answer of State University recently randomly sampled seven students...

Question 10

In a simple regression model,the slope coefficient represents the average change in the independent variable for a one-unit change in the dependent variable.

Accepted Answer

The slope coefficient represents the average change in the dependent variable for a one-unit change in the independent variable, not the other way around.

Question 11

You are given the following sample data for two variables:  Based upon these sample data,and testing at the 0.05 level of significance,the critical value for testing whether the population correlation coefficient is equal to zero is t = 2.2622.

Accepted Answer

The given sample data is not sufficient to calculate the population correlation coefficient or to perform a hypothesis test. Therefore, the statement about the critical value is not applicable.

Question 12

If two variables are highly correlated,it not only means that they are linearly related,it also means that a change in one variable will cause a change in the other variable.

Accepted Answer

High correlation between two variables indicates a strong linear relationship but does not imply causation. One variable changing might not necessarily cause the other to change; they could both be influenced by another factor or it could be a coincidence.

Question 13

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

This statement is true as the calculated test statistic t = 1.8516 falls within the acceptance region at the 0.05 significance level (i.e., the critical values are -2.093 and 2.093 for a two-tailed test, and 1.729 for a one-tailed test). Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant linear relationship between the checking and savings balances.

Question 14

If two variables are uncorrelated,the sample correlation coefficient will be r = 0.00.

Accepted Answer

The sample correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. While a value of r = 0.00 suggests no linear correlation, it does not guarantee that the variables are completely uncorrelated; they might still have a non-linear relationship. Additionally, due to sampling variability, two uncorrelated variables in the population might not have a sample correlation coefficient exactly equal to 0.

Question 15

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 this study the independent variable is the number of hours worked off campus per week.

Accepted Answer

The independent variable is the variable that is being manipulated or changed by the researcher, which in this case is the number of hours worked off-campus per week. Therefore, option A is correct.

Question 16

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

The statement is false. The correlation coefficient can be negative, indicating a negative correlation between the two variables. In this case, a value of -0.23 indicates a weak negative correlation between the two variables.

Question 17

In a university statistics course a correlation of -0.8 was found between numbers of classes missed and course grade.This means that the fewer classes students missed the higher the grade.

Accepted Answer

A correlation coefficient of -0.8 indicates a strong negative correlation between the two variables, meaning that as one variable (number of classes missed) decreases, the other variable (course grade) tends to increase. Therefore, it is true that the fewer classes students missed, the higher their grade tended to be.

Question 18

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

The answer of State University recently randomly sampled seven students...

Question 19

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

Accepted Answer

If two variables are spuriously correlated, it means that they are not truly related but appear to be due to a third variable. Therefore, the correlation coefficient between them could still be high, even though the relationship is not significant or meaningful.

Question 20

In conducting a hypothesis test on the correlation between a pair of variables,we assume that each variable is normally and independently distributed.

Accepted Answer

In testing the correlation between two variables, the assumption is that the pairs of variables are bivariate normally distributed, not that each variable is independently normally distributed.

Quiz 14: Introduction to Linear Regression and Correlation Analysis

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: The correlation between these two variables is approximately -.461.