Question 1

The correlation coefficient measures the percentage of the total variation of the dependent variable that is explained by the independent variable from a sample.

Accepted Answer

The correlation coefficient measures the strength and direction of the linear relationship between two variables, not the percentage of variation explained by one variable in another. The coefficient of determination (R-squared) measures the percentage of the total variation of the dependent variable that is explained by the independent variable.

Question 2

The size of the sample is ______.

Accepted Answer

The answer of The size of the sample is ______.
...

Question 3

A scatter plot is a useful tool to examine the data before conducting correlation analysis.

Accepted Answer

A scatter plot visually displays the relationship between two variables, helping to identify patterns, trends, or potential outliers, which is crucial before performing correlation analysis to understand the strength and direction of the relationship.

Question 4

The formula for the equation describing a straight line is $$\hat { y }$$= b₀ + b₁x. The value for b1 in this equation represents the ______.

Accepted Answer

The value for b1 in the equation represents the slope of the straight line, indicating how much the dependent variable ($\hat{y}$) changes for a one-unit change in the independent variable (x).

Question 5

Which one of the following statements is true using α = 0.05?

Accepted Answer

The answer of Which one of the following statements is...

Question 6

The least squares method is a mathematical procedure used to identify the linear equation that best fits a set of ordered pairs.

Accepted Answer

The least squares method minimizes the sum of the squares of the differences between the observed values and the values predicted by the linear equation, thus identifying the best-fitting line through a set of data points.

Question 7

The ______ is used to test the significance of the population correlation coefficient.

Accepted Answer

The Student's t-distribution is used to test the significance of the population correlation coefficient. This is because when testing hypotheses about the correlation coefficient, the sampling distribution of the correlation coefficient can be transformed into a t-distribution under the null hypothesis that there is no correlation.

Question 8

If two variables have a correlation coefficient equal to +0.70 from a sample size of 9, we can conclude that the population correlation coefficient is greater than zero using α = 0.05.

Accepted Answer

A correlation coefficient of +0.70 indicates a strong positive relationship between the two variables. Even with a sample size of 9, if the correlation is statistically significant at the α = 0.05 level, we can conclude that the population correlation coefficient is likely greater than zero, indicating a positive relationship in the population. However, it's important to note that the confidence in this conclusion is limited by the small sample size.

Question 9

If the confidence interval for the regression slope includes zero, we would have some evidence that þ could be equal to zero, which would indicate that there may not be a relationship between the dependent and independent variables.

Accepted Answer

If the confidence interval for the regression slope includes zero, it suggests that the true slope could be zero, indicating a lack of significant relationship between the dependent and independent variables.

Question 10

The _________ measures how consistent the slope of the regression equation would be if several sets of samples from the population were selected and the regression equation were derived for each of them.

Accepted Answer

The standard error of the slope measures the variability or precision of the slope estimate in a regression analysis. It indicates how much the slope coefficient would vary if different samples were taken from the same population.

Question 11

A dependent variable, x, explains the variation in another variable, which is called the independent variable, y.

Accepted Answer

The independent variable, x, explains the variation in the dependent variable, y.

Question 12

The correlation coefficient is a measure of the slope of the scatter plot for the independent and dependent variables.

Accepted Answer

The correlation coefficient measures the strength and direction of the linear relationship between two variables, not the slope of the scatter plot. The slope is determined by the line of best fit through the data points in the scatter plot.

Question 13

The slope value for a regression equation represents the average change in the dependent variable for a one- unit increase in the independent variable.

Accepted Answer

The slope in a regression equation quantifies the average change in the dependent variable for each one-unit increase in the independent variable, indicating the strength and direction of the linear relationship between them.

Question 14

Which one of the following statements is true using α = 0.05?

Accepted Answer

The answer of Which one of the following statements is...

Question 15

The _______ measures the total variation in the dependent variable in simple regression analysis.

Accepted Answer

The total sum of squares measures the total variation in the dependent variable in simple regression analysis. It is the sum of the squared differences between each observation and the overall mean of the dependent variable.

Question 16

A correlation coefficient of - 0.80 is an indication of a weak negative relationship between two variables.

Accepted Answer

A correlation coefficient of -0.80 indicates a strong negative relationship between two variables, meaning as one variable increases, the other decreases.

Question 17

A correlation analysis requires that the data be either ______ data or ______ data.

Accepted Answer

Correlation analysis requires data to be at least at the interval level of measurement because it involves calculating the relationship between variables in terms of both direction and magnitude, which nominal and ordinal data cannot provide. Interval and ratio data both have meaningful distances between measurements, allowing for the calculation of correlation coefficients.

Question 18

Consider the relationship between the following variables:
· Household income
· Square footage of the primary residence
Household income would be considered the independent variable.

Accepted Answer

Household income is considered the independent variable because it is presumed to influence or determine the square footage of the primary residence, not the other way around.

Question 19

A smaller standard error of the slope increases the likelihood that we can establish a significant relationship between the independent and dependent variables.

Accepted Answer

A smaller standard error of the slope indicates more precision in the estimate of the slope, making it easier to detect a significant relationship between the independent and dependent variables if one exists.

Question 20

Two variables have a correlation coefficient equal to +0.55 from a sample size of 8. Which one of the following statements describes the results of the hypothesis test that the population correlation coefficient is greater than zero using α = 0.05?

Accepted Answer

The answer of Two variables have a correlation coefficient equal...

Quiz 14: Environmental Health

The correlation coefficient measures the percentage of the total variation of the dependent variable that is explained by the independent variable from a sample.

The size of the sample is ______.

A scatter plot is a useful tool to examine the data before conducting correlation analysis.

The formula for the equation describing a straight line is $\hat { y }$ = b₀ + b₁x. The value for b1 in this equation represents the ______.

Which one of the following statements is true using α = 0.05?

The least squares method is a mathematical procedure used to identify the linear equation that best fits a set of ordered pairs.

The ______ is used to test the significance of the population correlation coefficient.

If two variables have a correlation coefficient equal to +0.70 from a sample size of 9, we can conclude that the population correlation coefficient is greater than zero using α = 0.05.

If the confidence interval for the regression slope includes zero, we would have some evidence that þ could be equal to zero, which would indicate that there may not be a relationship between the dependent and independent variables.

The _________ measures how consistent the slope of the regression equation would be if several sets of samples from the population were selected and the regression equation were derived for each of them.

A dependent variable, x, explains the variation in another variable, which is called the independent variable, y.

The correlation coefficient is a measure of the slope of the scatter plot for the independent and dependent variables.

The slope value for a regression equation represents the average change in the dependent variable for a one- unit increase in the independent variable.

Which one of the following statements is true using α = 0.05?

The _______ measures the total variation in the dependent variable in simple regression analysis.

A correlation coefficient of - 0.80 is an indication of a weak negative relationship between two variables.

A correlation analysis requires that the data be either data or data.

Consider the relationship between the following variables: · Household income · Square footage of the primary residence Household income would be considered the independent variable.

A smaller standard error of the slope increases the likelihood that we can establish a significant relationship between the independent and dependent variables.

Two variables have a correlation coefficient equal to +0.55 from a sample size of 8. Which one of the following statements describes the results of the hypothesis test that the population correlation coefficient is greater than zero using α = 0.05?

Quiz 14: Environmental Health

The correlation coefficient measures the percentage of the total variation of the dependent variable that is explained by the independent variable from a sample.

The size of the sample is ______.

A scatter plot is a useful tool to examine the data before conducting correlation analysis.

The formula for the equation describing a straight line is y^\hat { y }y^​ = b0 + b1x. The value for b1 in this equation represents the ______.

Which one of the following statements is true using α = 0.05?

The least squares method is a mathematical procedure used to identify the linear equation that best fits a set of ordered pairs.

The ______ is used to test the significance of the population correlation coefficient.

If two variables have a correlation coefficient equal to +0.70 from a sample size of 9, we can conclude that the population correlation coefficient is greater than zero using α = 0.05.

If the confidence interval for the regression slope includes zero, we would have some evidence that þ could be equal to zero, which would indicate that there may not be a relationship between the dependent and independent variables.

The _________ measures how consistent the slope of the regression equation would be if several sets of samples from the population were selected and the regression equation were derived for each of them.

A dependent variable, x, explains the variation in another variable, which is called the independent variable, y.

The correlation coefficient is a measure of the slope of the scatter plot for the independent and dependent variables.

The slope value for a regression equation represents the average change in the dependent variable for a one- unit increase in the independent variable.

Which one of the following statements is true using α = 0.05?

The _______ measures the total variation in the dependent variable in simple regression analysis.

A correlation coefficient of - 0.80 is an indication of a weak negative relationship between two variables.

A correlation analysis requires that the data be either ______ data or ______ data.

Consider the relationship between the following variables: · Household income · Square footage of the primary residence Household income would be considered the independent variable.

A smaller standard error of the slope increases the likelihood that we can establish a significant relationship between the independent and dependent variables.

Two variables have a correlation coefficient equal to +0.55 from a sample size of 8. Which one of the following statements describes the results of the hypothesis test that the population correlation coefficient is greater than zero using α = 0.05?

The formula for the equation describing a straight line is $\hat { y }$ = b₀ + b₁x. The value for b1 in this equation represents the ______.

A correlation analysis requires that the data be either data or data.