AP Statistics 2017

(Marvins-Underground-K-12) #1
Taking  the natural logarithm   of  each    y   -value  and finding the LSRL,   we  have    ln  (   )   =   0.914   +
0.108 (days ) = 0.914 + 0.108(9) = 1.89. Then = e 1.89 = 6.62.



  1.          The correlation between walking more    and better  health  may or  may not be  causal. It  may be  that

    people who are healthier walk more. It may be that some other variable, such as general health
    consciousness, results in walking more and in better health. There may be a causal association, but in
    general, correlation does not imply causation.



  2. Carla has reported the value of r 2 , the coefficient of determination. If she had predicted each girl’s
    grade based on the average grade only, there would have been a large amount of variability. But, by
    considering the regression of grades on socioeconomic status, she has reduced the total amount of
    variability by 72%. Because r 2 = 0.72, r = 0.85, which is indicative of a strong positive linear
    relationship between grades and socioeconomic status. Carla has reason to be happy.

  3. (a) is false. for the LSRL, but there is no unique line for which this is true.
    (b) is true.
    (c) is true. In fact, this is the definition of the LSRL—it is the line that minimizes the sum of the
    squared residuals.
    (d) is true since and is constant.


(e)         is  false.  The slope   of  the regression  lines   tell    you by  how much    the response    variable    changes on
average for each unit change in the explanatory variable.


  1. ŷ = 26.211 – 0.25x = 26.211 – 0.25(73) = 7.961. The residual for x = 73 is the actual value at 73
    minus the predicted value at 73, or y – ŷ = 7.9 – 7.961 = –0.061. (73, 7.9) is below the LSRL since y
    – ŷ < 0 y < ŷ .

  2. (a) r = +0.75; the slope is positive and is the opposite of the original slope.
    (b) r = –0.75. It doesn’t matter which variable is called x and which is called y .
    (c) r = –0.75; the slope is the same as the original slope.

  3. We know that , so that 2.7 = r (3.33) → . The proportion of the


variability that    is  not explained   by  the regression  of  y on    x is    1   –   r   2    =  1   –   0.66    =   0.34.



  1.     Because the linear  pattern will    be  stronger,   the correlation coefficient will    increase.   The influential

    point pulls up on the regression line so that its removal would cause the slope of the regression line
    to decrease.



  2. (a) = –0.3980 + 0.1183 (number ).

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