Show 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 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. 3. 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 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: a. b. c. d. e. 0.000 0.0411 0.00411 0.411 cannot be determined from data available 4. Which equation best describes the regression line depicted in the figure on the right? a. b. c. d. 5. 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? a. 5.5 b. 5.0 c. 4.3 d. 0.06 e. -0.06 Q1 Ans: d Correlation coefficient lies between -1 and 1. Since Y increases linearly as X increases, correlation coefficient value is positive and equal to 1. Q2. Ans : a Substituting X = 1000 in the regression equation yields 1624 Q3. Ans : d Pearson's correlation coefficient is independent of the units of the data if the different units can be obtained by just multiplying with real number Q4. Ans : c Interecept = 12 and Slope is positive. Q5. Ans: 4.3 X=20 ; Y = = -0.06*20 + 5.5 = 4.3