HW+3+Solution - STAT 20 Lecture Section 2 Spring 2011...

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STAT 20: Lecture Section 2. Spring 2011 Solution to Homework #3 (26 marks total) Q1. Text Page 153 Q2 (2 marks: 1 for each part a and b. Must have a reason. No marks for saying "True/False" without an explanation ) a. False. Since the scatter diagram slopes down, x and y have a negative association. If x is below average, y is generally above average, not below average. These points would lie on area labeled I below. (Graph below not necessary to get credit) b. False. If y is usually less than x , the correlation coefficient between x and y could be positive. Even if y was always less than x, r can be equal to +1. Examples: all points on the line y = x – 1 or y = 0.5x or y = 0.98x. (These specific examples are not necessary to receive credit but student must understand that it doesn’t matter if y is usually less than x , the correlation could be positive.) Also see P. 90 of the reader (relating to Page 142 Figure 2). Q2. Text Page 154 Q4 (1 mark) For women and men, each scatter plot separately has correlation 0.6. But when putting all the data for women and men together in a height vs. weight diagram, the data are much more linear. It is reverse attenuation. The crucial point relates to the location of the points of averages, for men it is “northeast” of the points for women. Therefore, if you take the men and the women together, the correlation between height and weight would be somewhat higher. y x Ave y I Ave x
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Q3. Text Page 176 Q4 (5 marks. Parts a and b: 1 for correct z x and z y , 1 for correct prediction in years. Part c: 1 mark. Do not double-penalize, deduct 1 for incorrect z x or z y but give points for correct steps.)
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