Exam 8: Prediction

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When the correlation is perfect, every value of ____________ is zero.

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  and    ;     and     If     and X is 40, what value do we predict for Y? and   and    ;     and     If     and X is 40, what value do we predict for Y? ;   and    ;     and     If     and X is 40, what value do we predict for Y? and   and    ;     and     If     and X is 40, what value do we predict for Y? If   and    ;     and     If     and X is 40, what value do we predict for Y? and X is 40, what value do we predict for Y?

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  and    ;     and     If     and X is 40, what value do we predict for Y? and   and    ;     and     If     and X is 40, what value do we predict for Y? ;   and    ;     and     If     and X is 40, what value do we predict for Y? and   and    ;     and     If     and X is 40, what value do we predict for Y? If   and    ;     and     If     and X is 40, what value do we predict for Y? and X is 40, what value do we predict for Y?

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A formula for the standard error of estimate of Y on X is

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For the group of adult joggers competing in the Windy City Mini-marathon, the following are the summary statistics for annual income (X) and time to complete the race (Y): For the group of adult joggers competing in the Windy City Mini-marathon, the following are the summary statistics for annual income (X) and time to complete the race (Y):    (a)  Jack L. and Linda P. have annual incomes of $12,372 and $24,812, respectively. What race times would you predict? (Hint: No calculations are necessary). (b) What general principle is illustrated by this problem? (a)  Jack L. and Linda P. have annual incomes of $12,372 and $24,812, respectively. What race times would you predict? (Hint: No calculations are necessary). (b) What general principle is illustrated by this problem?

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The standard error of estimate is a kind of

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  and    ;     and     If     and X is 40, what value do we predict for Y? and   and    ;     and     If     and X is 40, what value do we predict for Y? ;   and    ;     and     If     and X is 40, what value do we predict for Y? and   and    ;     and     If     and X is 40, what value do we predict for Y? If   and    ;     and     If     and X is 40, what value do we predict for Y? and X is 40, what value do we predict for Y?

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The raw score regression equation always

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In predicting Y from X, the regression line is laid down so that the squared discrepancies between points and the line are minimized

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John Jones falls one standard deviation above the mean of X. (a)If his predicted score on Y falls one standard deviation above John Jones falls one standard deviation above the mean of X. (a)If his predicted score on Y falls one standard deviation above   what is the correlation between X and Y? (b)If his predicted score on Y falls one-third of a standard deviation above    what is the correlation between X and Y? what is the correlation between X and Y? (b)If his predicted score on Y falls one-third of a standard deviation above John Jones falls one standard deviation above the mean of X. (a)If his predicted score on Y falls one standard deviation above   what is the correlation between X and Y? (b)If his predicted score on Y falls one-third of a standard deviation above    what is the correlation between X and Y? what is the correlation between X and Y?

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The following are the scores on a job selection test administered prior to hiring (X) and supervisor's ratings after 3 months on the job (Y) for a group of bank tellers (A-F): The following are the scores on a job selection test administered prior to hiring (X) and supervisor's ratings after 3 months on the job (Y) for a group of bank tellers (A-F):      (a) Compute from these data the summary statistics required for developing the raw-score regression equation for predicting supervisor's rating from job selection score. (b) Use the values from (a) to arrive at the regression equation in simplest form.  (c) Three new applicants for teller positions obtain scores of 48, 62, and 72, respectively, on the selection test. Compute their predicted supervisor's ratings.  (d) If in fact the above data were real, what objection would you have to using the equation from (b) to predict in a real-life situation? (a) Compute from these data the summary statistics required for developing the raw-score regression equation for predicting supervisor's rating from job selection score. (b) Use the values from (a) to arrive at the regression equation in simplest form.  (c) Three new applicants for teller positions obtain scores of 48, 62, and 72, respectively, on the selection test. Compute their predicted supervisor's ratings.  (d) If in fact the above data were real, what objection would you have to using the equation from (b) to predict in a "real-life" situation?

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In concept, the regression line is most closely related to the

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Which value of r permits the greatest accuracy of prediction?

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The standard error of estimate measures variability of

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From the records of a large health maintenance organization, an investigator is able to gather a sizeable sample of men for whom heights at both age 10 and as adults are known. The following are the summary statistics for this sample: From the records of a large health maintenance organization, an investigator is able to gather a sizeable sample of men for whom heights at both age 10 and as adults are known. The following are the summary statistics for this sample:     (a) Use the above values to arrive at the raw-score regression equation for predicting height as an adult from height at age 10. Present the equation in simplest form.  (b) Use the regression equation from (a) to predict adult height for the following 10-year-olds: Benny (42.5 in.), Cal (55.3 in.), Arthur (50.1 in.).  (c) Consider Benny's predictable adult height. In what sense is that value a mean? Be very specific. (a) Use the above values to arrive at the raw-score regression equation for predicting height as an adult from height at age 10. Present the equation in simplest form.  (b) Use the regression equation from (a) to predict adult height for the following 10-year-olds: Benny (42.5 in.), Cal (55.3 in.), Arthur (50.1 in.).  (c) Consider Benny's predictable adult height. In what sense is that value a mean? Be very specific.

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For a large group of subjects: For a large group of subjects:     and     Captain Crunch obtains an X score of 52. What is his predicted Y score if (no calculations necessary): (a)    (b)    (c)    (d)     (e)State the principal illustrated by your answers to (a) through (d). and For a large group of subjects:     and     Captain Crunch obtains an X score of 52. What is his predicted Y score if (no calculations necessary): (a)    (b)    (c)    (d)     (e)State the principal illustrated by your answers to (a) through (d). Captain Crunch obtains an X score of 52. What is his predicted Y score if (no calculations necessary): (a) For a large group of subjects:     and     Captain Crunch obtains an X score of 52. What is his predicted Y score if (no calculations necessary): (a)    (b)    (c)    (d)     (e)State the principal illustrated by your answers to (a) through (d). (b) For a large group of subjects:     and     Captain Crunch obtains an X score of 52. What is his predicted Y score if (no calculations necessary): (a)    (b)    (c)    (d)     (e)State the principal illustrated by your answers to (a) through (d). (c) For a large group of subjects:     and     Captain Crunch obtains an X score of 52. What is his predicted Y score if (no calculations necessary): (a)    (b)    (c)    (d)     (e)State the principal illustrated by your answers to (a) through (d). (d) For a large group of subjects:     and     Captain Crunch obtains an X score of 52. What is his predicted Y score if (no calculations necessary): (a)    (b)    (c)    (d)     (e)State the principal illustrated by your answers to (a) through (d). (e)State the principal illustrated by your answers to (a) through (d).

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What value of r leads us to predict that What value of r leads us to predict that   no matter what the value of X? no matter what the value of X?

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Accuracy of prediction by the regression equation is enhanced by

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When homoscedasticity holds, then

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A standard score regression equation reads: A standard score regression equation reads:   If the correlation coefficient is +.5 and Johnny is two standard deviations above the mean in X, what standard score position shall we predict for him in Y? If the correlation coefficient is +.5 and Johnny is two standard deviations above the mean in X, what standard score position shall we predict for him in Y?

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