Try Your Own Data

It is interesting to see how the sampling distribution of Student t for the slope changes if there are more observations. Fill in the box below with a different number of observations and then click on the "Make Graph" button below.

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© 1999, Duxbury Press. 		 

 
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My Data
  Looking at the sampling distribution of the t statistic for the slope for five observations, it appears that values of t more extreme than about +/- 2.5 are surprising. On the next page, we will be more precise.  
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© 1999, Duxbury Press. utational details. The right-most expression tells us when the t for the slope will be large--when the slope b is large, when the number of observations n is large, when the standard deviation of X (the predictor) is large, and when the aggregate error MSE is small (i.e., the data points are close to the best-fitting line).  
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© 1999, Duxbury Press. The sampling distribution of the slope allows us to identify surprising values. In this case, values of the slope more extreme than +/- .4 are extremely rare and values more extreme than +/- .3 are surprising.  
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© 1999, Duxbury Press. LIGN=CENTER VALIGN=MIDDLE>2 3 4 5 6 7 8 9 10 Stress 2.5 5 10 15 17.5 20 25 30 35 40 FailTime 63 58 55 61 62 37 38 45 46 19

Move the line up and down by dragging the box or change the slope by clicking and dragging anywhere else so that the line represents all the observations. Try to place the line so that it is closest to all the observations.

Based on your line, do you think there is a positive, negative, or no relationship between Stress and FailTime?

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Biology

Ott (1993) presents this example on p. 452: Fifteen male volunteers ate a low-cholesterol diet for four weeks. Below are the ages and the reduction in cholesterol (in mg per 100 ml of blood serum) for each participant:
Participant 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Age 45 43 46 49 50 37 34 30 31 26 22 58 60 52 27
Reduce 30 52 45 38 62 55 25 30 40 17 28 44 61 58 45

Move the line up and down by dragging the box or change the slope by clicking and dragging anywhere else so that the line represents all the observations. Try to place the line so that it is closest to all the observations.

Based on your line, do you think there is a positive, negative, or no relationship between Age and Reduce?

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© 1999, Duxbury Press. a dieter's age and the amount of cholesterol reduced?

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© 1999, Duxbury Press. al">File: