business stats chapter 13 smartbook
What values can the correlation coefficient assume?
-1≤ r ≤ 1
Which of the following is the test statistic for the correlation coefficient?
t = r√n−2 / √1−r2
Which of the following is the formula for the correlation coefficient, r?
Σ(X−X)(Y−Y)/(n−1)sxsy
What is Correlation Analysis?
A group of techniques to measure the relationship between two variables.
What is the best definition of a regression equation?
An equation that expresses the linear relation between two variables.
Which of the following is NOT an example of correlation analysis?
Hypothesis testing for equality of means
A test for the slope of the regression line uses the hypotheses H0: β = 0, H1: β ≠ 0. What are we seeking to discover with this test?
If the regression line has predictive power for the dependent variable.
Which of the following are characteristics of the correlation coefficient? Select all that apply.
Indicates the direction and strength of the linear relationship between two interval or ratio scale variables. A value near -1 indicates a negative linear relationship. The values range from -1 up to +1
Which of the following are characteristics of the correlation coefficient? Select all that apply.
Indicates the direction and strength of the linear relationship between two interval or ratio scale variables. A value near 1 indicates a positive linear relationship. The symbol of the sample correlation coefficient is lowercase, r. A value near zero indicates little linear relationship between the variables.
Which of these statements correctly describes the values that can be assumed by the correlation coefficient, r?
It can be any number from -1 to +1, inclusive.
A line is drawn through the points on a scatter diagram. Which three of the following are not likely to be a least squares fit?
Nearly all of the data points are below the line. All of the data points are above the line. The line passes through the largest and smallest data points.
Which of the following statistical distributions is used for the test for the slop of the regression equation?
Student's t-distribution
What is the term that is used for the proportion of the total variation in Y that is explained by the variation in X?
The Coefficient of Determination
In analyzing the strength of the relationship between two variables, what does the symbol r represent?
The Pearson correlation coefficient.
How do you calculate the coefficient of determination?
The coefficient of determination, R2, is the square of the correlation coefficient, r.
What is the definition of the standard error of estimate?
The dispersion (scatter) of observed values around the line of regression for a given X.
The general form of the regression equation is written like this: Y∧= a + bX. Why is the dependent variable written as Y∧ instead of just Y?
The hat is to emphasize that the equation estimates the Y-value for a given X.
A test for the slope of the regression line uses the hypotheses H0: β = 0, H1: β ≠ 0. If we reject H0 what have we demonstrated about the regression line?
The regression line has some power to predict the value of the dependent variable.
When a line is drawn on a scatter diagram using the least squares principal, what is the quantity that is minimized?
The sum of the squared difference between the line and the data points.
The general form of the regression equation is written like this:
Y∧ estimated Y value X the independent variable a the Y intercept b slope of the line
Which of the following is the equation for the slope of the regression line?
b = r sY/sX
A scatter diagram in which the points move from the bottom left to the upper right would be characterized by what type of correlation coefficient?
positive
What symbol is used for the Pearson correlation coefficient, which shows the strength of the relation between two variables?
r
