Q1. Which of the following is a property of the linear correlation coefficient r?
If all values of either the x or y variable are converted to a different scale, the value of r changes.
- The correlation r measures the strength of a linear and nonlinear relationship.
- The correlation r is not sensitive to outliers.
- The value of r is always between -1 and 1 inclusive.
Q2. Use the given information to find the coefficient of determination.A regression equation is obtained for a collection of paired data. It is found that the total variation is 29.045, and the UNexplained variation is 13.833. Find the coefficient of determination.(Hint: You must first find the explained variation.)
Q3. Which of the following research hypotheses would be answered using a multiple regression?
A) Is the mean weight of football players and baseball players significantly different?
B) Is the mean weight of football players, baseball players, and soccer players significantly different?
C) Is there a significant linear relationship between years of football experience and a player's salary?
D) Is there a significant linear relationship between years of football experience, weight, college attended, and a player's salary?
Q4. Which of the following research hypotheses would be answered using a multiple regression?
A) Correlation implies causality
B) The correlation r is a measure of the strength and direction (positive or negative) of two variables
C) If there is no linear correlation, a correlation does not exist.
D) Using mean scores to calculate the correlation is appropriate.
Q5. Which of the following describes the coefficient of determination?
- The proportion of the variation in x that is explained by the linear relationship betweeen x and y.
- The proportion of the variation in y that is NOT explained by the linear relationship between x and y.
- The proportion of the variation in y that is explained by the linear relationship between x and y.
- The proportion of the variation in x that is NOT explained by the linear relationship betweeen x and y.
Q6. Given the linear correlation coefficient r and the sample size n, determine the critical values of r. Use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05.r = -0.844, n = 5
Answer
A) Critical values: r = +0.950, no significant linear correlation
B) Critical values: r = +0.878, significant linear correlation
C) Critical values: r = +0.878, no significant linear correlation
D) Critical values: r = +0.950, significant linear relationship
Q7. A set of data consists of the number of years that applicants for foreign service jobs have studied German and the grades they received on a proficiency test. The following regression equation is obtained: y = 31.6 + 10.9x, where x represents the number of years of study and y represents the grade on the test. What does the slope of the regression line represent in terms of a grade on the test?
A) The grade on the test increases by an estimated 31.6 points for each additional year of study.
B) The grade on the test increases by an estimated 10.9 points for each additional year of study.
C) The grade on the test decreases by an estimated 31.6 points for each additional year of study.
D) The grade on the test decreases by an estimated 10.9 points for each additional year of study.
Q8. Find the value of the linear correlation coefficient r.The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test.
Hours 5 10 4 6 10 9
Score 64 86 69 86 59 87
Answer
A) 0.224
B) -0.224
C) -0.678
D) 0.678
Q9. Use the given data to find the best predicted value of the response variable.Eight pairs of data yield r = 0.708 and the regression equation y = 55.8 + 2.79x. Also, mean y = 71.125. What is the best predicted value of y for x = 5.7?
A)71.13
B)71.70
C)320.8
D)57.80