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Lecture Homework 4
Statistics I for Educational Services
NAME(S): ____________________________________________________________________
Multiple Choice:
Please circle either A, B, C, or D. Choose the BEST answer.
1. (1 Point) Which of the following set of correlations correctly shows the highest to lowest strength of relationship?
A. -.91, .83, .10, -.03
B. -.91, .83, -.03, -.10
C. .83, .10, -.91, -.03
D. .83, .10, -.03, -.91
2. (1 Point) The Phi Correlation Coefficient is used when…
A. one of the two variables is dichotomous.
B. both X and Y consist of ranks.
C. both X and Y are dichotomous variables.
D. both X and Y are continuous variables.
3. (1 Point) In general, the more square footage a person’s home has, the greater the value of the car she/he drives. This demonstrates…
A. a positive relationship.
B. a negative relationship.
C. a cause-effect relationship.
D. All of the above.
4. (1 Point) Which of the following Pearson correlations shows the largest magnitude of relationship?
A. .74
B. .85
C. -.03
D. -.90
5. (1 Point) Suppose the correlation between height and weight for adults is .80. What proportion (or percent) of the variability in weight is due to height?
A. 80%
B. 64%
C. 20%
D. 40%
6. (1 Point) In the regression equation, Y = bX + a, b is called the…
A. X Intercept.
B. Y Intercept.
C. correlation between X and Y.
D. Slope.
7. (1 Point) In the regression equation, Y = bX + a, if b is zero, then the correlation between X and Y is…
A. -1.
B. 0.
C. 1.
D. None of the above.
8. (1 Point) If the scatterplot shows the relationship between X and Y is curvilinear, the Pearson r…
A. will be zero.
B. will overestimate the degree of association between X and Y.
C. will underestimate the degree of association between X and Y.
D. This cannot be calculated.
True/False:
Please write either “T” for True or “F” for False. If False, indicate WHY it is false, and correct the statement to make it True.
9. (.5 Points) In a scatterplot, the more the data points vary from a straight line, the lower the value for the Pearson correlation.
10. (.5 Points) Suppose there is a correlation of r = -.81 between a driver’s age and the cost of car insurance. This correlation would mean that, in general, older people pay more for car insurance.
11. (.5 Points) A researcher obtained a correlation of r = .62 between the amount of time spent watching TV and the level of cholesterol. This means that there is a general tendency for people who watch more TV to have higher cholesterol.
12. (.5 Points) The regression slope (i.e., b) represents the amount of change in X expected from one unit change in Y.
13. (.5 Points) The regression intercept (i.e., a) represents the value of Y when X is equal to 0.
14. (.5 Points) Another name for the standard error of the estimate is the variance error of the estimate.
Short Answer:
15. (2 Points) List and describe all the assumptions for correlation. Pick one assumption and give an example to illustrate it.
16. (2 Points) Define the Coefficient of Determination. Use an example to illustrate the concept.
Computational (Round to TWO decimal places when necessary):
17. (2 Points) You are given the following pairs of sample scores on X (i.e., number of coins in possession) and Y (i.e., number of bills in possession). First, graph a scatterplot of the data. Make sure you label the X and Y axes properly with the correct variables. Second, describe the relationship between X and Y in one to two sentences. Third, what do you think the Pearson r will be? Do not calculate Pearson r. Based on the scatterplot, what is the approximate Pearson r (i.e., paying attention to the strength and direction)?
X Y
1 1
2 3
3 5
4 5
5 3
6 1
18. (3 Points) What is the Pearson correlation for the data below? X is SAT score and Y is GPA. Compute the correlation coefficient and interpret it (i.e., using Cohen’s guidelines). Next, test if the correlation is statistically different from zero. State the null and alternative hypotheses. Find the critical value (cv; α = .05). Calculate the t Test. State if you accept or reject the null. Lastly, describe the results in your own words. Use the Correlation activity with the step-by-step answers as a guide (i.e., posted on Blackboard).
X = SAT Y = GPA
670 3.8
450 2.9
510 2.6
530 3.4
660 4.0
19. (3 Points) A researcher is interested in determining the effect of anxiety (i.e., the IV) on statistics test scores (i.e., the DV). The researcher uses data from a sample of students drawn from KSU. The data are as follows…
Students
1 2 3 4 5
Statistics Test Score 90 60 70 90 60
Anxiety Score 3 12 7 5 8
r = -.87 = 7 = 74 sX = 3.39 sY = 15.17 sb = 1.25
First, compute and write the regression equation (i.e., remember to compute the slope and intercept and interpret each). Second, determine if the slope is statistically different from zero. Write the null and alternative hypotheses. State the cv (α = .01). Calculate the t statistic. State if you accept or reject the null. Describe the results in your own words. Calculate the CI and interpret it. Third, what would the predicted statistics test score be for a student with an anxiety score of 10? Use the Regression activity with the step-by-step answers as a guide (i.e., posted on Blackboard).
20. (2 Points) A researcher is interested in examining the impact of Facebook use on GPA. The Pearson correlation between Facebook use (i.e., the number of times a student logs in per week) and GPA is -.67. First, identify the independent variable (IV) or X and the dependent variable (DV) or Y. Second, calculate the Coefficient of Determination. Remember to interpret the effect size. Then, describe what it (i.e., the calculated Coefficient of Determination) means (i.e., the percentage/proportion of variance accounted for/explained). Use the Coefficient of Determination activity with the step-by-step answers as a guide (i.e., posted on Blackboard).
Extra Credit:
21. (1 Point) A statistician in the athletics department at the University of Michigan (UM) found a correlation between the football team’s SAT scores and undergraduate GPA to be -1.05. The UM football coach held a press conference to inform the public. He mentioned that the entire team should be congratulated and that the statistician should be praised for his/her scholarly analysis. Is the coach’s appraisal correct? Circle YES or NO. If NO, why not?
YES NO