Name:_____________________________ HP340: Statistical Methods, Fall 2016 Due Date: Nov 28, 2016 Homework #8 Instructions: Clearly circle the letter of the best answer for multiple-choice questions and show your work when calculations are required. Where necessary, please explain your reasoning for the approach you used. 1. Suppose two variables under study are temperature in degrees Fahrenheit (y) and temperature in degrees Celsius (x). The 'regression line' for this situation is: 9 Y^ = X +32 5 Assuming there is no error in observing temperature, the correlation coefficient would be expected to be (2 points) a. b. c. d. e. 2. 9 5 5 9 -1 +1 0 An investigator studies 50 pairs of unlike twins and reports that male birth weight (y) can be predicted by female birth weight (x) using the following equation (all weights in grams): Y^ =0.403 X + 1221 One can conclude from this that: a. b. c. d. e. (2 points) mean weight of twin brothers of girls who weigh 1000 g is predicted to be 1624 g mean weight of twin sisters of boys who weigh 1000 g is predicted to be 1624 g sample mean weight of the girls is 1221 g sample mean weight of the boys is 1221 g the correlation between girl's weight and boy's weight is 0.403 3. A study was conducted to investigate the relationship between the estriol level of pregnant women and subsequent height (in centimeters) of their children at birth. A Pearson's correlation coefficient was computed and found to be r = 0.411. The researcher decided to re-express height in millimeters rather than centimeters and then recomputed r. The recalculation yields the following value of r: (2 points) a. b. c. d. e. 4. Which equation best describes the regression line depicted in the figure on the right? (2 points) a. b. c. d. 5. 0.000 0.0411 0.00411 0.411 cannot be determined from data available Y^ =8 X +12 Y^ =8 X 12 ^ Y =8 X+ 12 Y^ =8 X12 The regression equation for predicting the number of speeding tickets from the driver's age is Y^ =0.06 X +5.5 . How many tickets do you predict a 20 year old would get? (2 points) a. 5.5 b. 5.0 c. 4.3 d. 0.06 e. -0.06 6. Given the following information calculate the Pearson's correlations between variable Jazz (x) and variable Hands (y). Using a two-tailed test at =.05, is the correlation coefficient significant? What is the percentage of variance in variable Hands that is associated with variance in variable Jazz (or vice versa)? (Write an informative and complete conclusion statement) (8 points) N=10; X =4.1; Y =4.7; s 2x = 6.77; s 2y = 1.34; CP = 22.3 7. Given the information from Question 6, what is the equation for the regression line with Jazz (x) predicting Hands (y)? (Write an informative and complete conclusion statement) (8 points) The SPSS file posted on BlackBoard (HW8.data.sav) contains data for the following questions. Imagine that you are researcher studying the impact of the number of friends on feelings of anxiety (on a scale of 0-50) following a cataclysmic world event. Use the SPSS file posted on BlackBoard (HW8.data.sav) to run a regression and answer the following questions. 8. Provide the SPSS output for the regression analysis. What is the equation for the regression line? Write a conclusion statement based on these results (be sure to include the statistical evidence concerning whether or not the slope is significant at =.05). (15 points) 9. Assume that a Low Anxiety score is equal to or less than 15. According to your regression equation, how may friends would you predict a person would need in order to have Low Anxiety? (5 points) 10. Imagine that an individual had no friends. What is her/his predicted anxiety score? (5 points) Extra Credit: What is the standard error of estimate? What is the standard error of the slope? (4 points)