Exam 1

  1. Question

    The following figure shows a scatterplot. Which of the following statements are correct?


    1. The absolute value of the correlation coefficient is at least 0.80.8.
    2. The slope of the regression line is about 11.
    3. The standard deviation of YY is at least 66.
    4. For X=0.3X = 0.3, YY can be expected to be about 00.
    5. The mean of XX is at most 55.

    Solution

    1. False. No association between the variables is observed in the scatterplot. This implies a correlation coefficient close to 00.
    2. False. The slope of the regression line is given by rsy/sxr \cdot s_y/s_x and hence not about equal to 11.
    3. False. The standard deviation of YY is about equal to 11 and is therefore smaller than 66.
    4. True. The regression line at X=0.3X=0.3 implies a value of about Y=0Y = 0.
    5. True. The mean of XX is about equal to 00 and hence is smaller than 55.