Question

Assume that we have a regression model y? = b? + b?x If we have an observation with a z? equal to -0.60, and correlation coefficient is r = -0.50, how many standard deviations do you expect the predicted value for the response variable (y?) to be above or below the mean? (Enter a positive number if it will be above the mean, a negative number if it will be below the mean, and 0 if it will be right at the mean). Note: 1- Only round your final answer to 2 decimal places. Enter your final answer with 2 decimal places.

          Assume that we have a regression model

y? = b? + b?x

If we have an observation with a z? equal to -0.60, and correlation coefficient is r = -0.50, how many standard deviations do you expect the predicted value for the response variable (y?) to be above or below the mean? (Enter a positive number if it will be above the mean, a negative number if it will be below the mean, and 0 if it will be right at the mean).

Note:

1- Only round your final answer to 2 decimal places. Enter your final answer with 2 decimal places.
        
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Assume that we have a regression model

y? = b? + b?x

If we have an observation with a z? equal to -0.60, and correlation coefficient is r = -0.50, how many standard deviations do you expect the predicted value for the response variable (y?) to be above or below the mean? (Enter a positive number if it will be above the mean, a negative number if it will be below the mean, and 0 if it will be right at the mean).

Note:

1- Only round your final answer to 2 decimal places. Enter your final answer with 2 decimal places.

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Assume that we have a regression model: y = bo + b1x If we have an observation with a Zx equal to -0.60, and the correlation coefficient is r = -0.50, how many standard deviations do you expect the predicted value for the response variable (y) to be above or below the mean? (Enter a positive number if it will be above the mean, a negative number if it will be below the mean, and 0 if it will be right at the mean): Note: 1- Only round your final answer to 2 decimal places. Enter your final answer with 2 decimal places.
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Transcript

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00:01 Alright, in your question, you are told the z score for the independent variable x in this regression equation is equal to negative 0 .60.
00:17 You were told that the correlational coefficient, r, is equal to negative 0 .50.
00:25 And you're asked to figure out how many standard deviations you expect the predicted value for the response variable, y, hat, to be above or below the mean.
00:39 So what you're being asked to do, since they ask for how many standard deviations we would expect for the y, we're looking for the z score for the y.
00:49 Now, there's a relationship that exists in the near regression that your response variable z -z.
00:57 Score is equal to the correlational coefficient times the explanatory variable z score.
01:07 So knowing that, this question becomes pretty straightforward.
01:11 Your r is negative 0 .50.
01:15 Your standard deviation for the x is negative 0 .6.
01:25 And this multiplies together, and negative times the negative will be positive.
01:30 So we're going to end up with 0 .3.
01:34 And that should be how many standard deviations we would expect our predicted y value to be away from the mean y value.
01:43 Now, because it worked out positive, it is above the mean.
01:49 You're to enter your positive number...
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