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a)What is the form and direction of the number of hours spent conducting research and watching movies? The form is linear and the direction is negative between the number of hours spent conducting research and watching movies b)What is the correlation coefficient between research time and movie watching time? Would you classify this as weak, moderate, or strong? ?2is the coefficient of determination |?| = √?2= √0.8603= 0.9275. As the direction is negative, ? = −0.9275strong correlation c)What does the -1.4883 in the regression equation represent? What does this mean in terms of the story? The -1.4883 is the slope. In terms of the story, it means for each hour spent watching movies Prakash’s predicted time spent on research decreases by 1.4883. d)What is the predicted number of hours spent conducting research when movie watching time is 45 hours? 15 hours? Are these valid predictions? Why or why not? ?(45)̂= 61.7333 − 1.4883 ∗ 45 = −5.2402and ?(15)̂= 61.7333 − 1.4883 ∗ 15 = 39.4088. The prediction at 45 is not valid and the prediction at 15 is valid. The prediction at 45 is invalid because it is extrapolation (i.e. 45 is outside the range of the data) ; the prediction at 15 is valid because it is in the scope of the data. e)One these weeks, Prakash spent 25 hours conducting research and 23 hours spent watching movies. What is the residual for that week? ?𝑖= 25 − ?(23)̂= 25 − (61.7333 − 1.4883 ∗ 23) = −2.5024. The residual for that particular week, denoted as week i, is -2.5024. f)What percent in the variation of time conducting research is NOT explained by the linear relationship with the time watching movies? The percent in variation of time not conducting research is 1 − ?2= 1 − 0.8603 = 0.1397 ?? 13.97%
9.For the following questions a-f, choose the correct graph. Each answer may be used once, more than once, or not at all. a)Which graph clearly shows you the 25thpercentile? E b)Which graph should only be used for qualitative data? B c)Which graph shows you data in which the mean is greater than the median? ? C (note: B is a bar graph and can be used for qualitative data only) d)Which graph shows you a distribution that is skewed left? A e)Which graph shows data that was collected using a survey with a biased question ? F f)Which graph shows you a distribution that is skewed right? C TEXTBOOK problems--------NOTE: copies of the textbook are on reserve in the MATH library (3rdfloor of the MATH building) and in the STAT help room ---HAAS 115. 10.Textbook, Exercise 35.8, page 466 𝑋~??????(𝜇 = −1.32, 𝜎 = 0.34)a)What is the cut-off for the top 5% of X values? Find the 95thpercentile. ?(𝑋 < ?) = 0.95?(? < ?0) = 0.95find the z-score for 0.95 in the BODY of the z table…. ?0= 1.645then solve ? = ?−𝜇𝜎1.645 = ?−(−1.32)0.34x = -0.7607 b)What is the cut-off for the bottom 10% of X values? Find the 10thpercentile. ?(𝑋 < ?) = 0.10?(? < ?0) = 0.10find the z-score for 0.10 in the BODY of the z table…. ?0= −1.28then solve ? = ?−𝜇𝜎−1.28 = ?−(−1.32)0.34x = -1.7552 c)What are the boundaries for the middle 50% of X values? The middle 50% (NOTE: this is NOT asking for the 50thpercentile!!!) lies between the 25thpercentile and the 75thpercentile. Find those values.