Chapter 5, Test Form A Answer Key

1. a) , where L is the % lead content and G is the % gold content.

b)graph with regression line:

c)r = 0.698.  This indicates a moderately strong linear relationship between %Lead and %Gold.

d)r2 = 0.487.  About 49% of the differences in lead content can be explained by differences in the gold content.

2. a) lead

b)

3. a)

or if a point is 1 standard deviation above the mean height, it should be 0.995 standard deviations above the mean esophagus length:

b)      About 99% of the variance is accounted for by the height of the children and adolescents.

c)   Since 99% of the variance is accounted for by the height in the prediction, the predictions should be very accurate, compared to the variability of the esophageal length.   To assess the prediction in any absolute sense we would need to know the value of  .

4.

c)The exponential model seems better.  The residual plot for the power model clearly indicates curvature; the coefficient of determination for the exponential is 0.975 compared to 0.889 for the power model, also supporting the exponential model.

         d)   Predicting antibody concentrations 24 weeks out would be a dangerous

               extrapolation.  The data we have only goes out to 13 weeks.

Chapter 5, Test Form B                               Answer Key

 

1. a) , where L is the % lead content and G is the % gold content.

 

1. b) graph with regression line:

 

 

 

1. c) r = -0.549.  This indicates a moderately negative linear relationship between %Lead and %Gold.

 

1. d) r² = 0.302.  About 30% of the differences in lead content can be explained by differences in the gold content.

 

1. d) lead
2. e)

 

1. f) The regression line shows how the lead and gold content of coins in Rome are related.  If a coin of unknown origin is added to the scatter plot and the point for the new coin were far from the line, it would suggest that it was not produced in Rome.

 

 

2. a)

         

 

1. b) The power model seems to be better.  The residual plot is much more uniformly distributed than the one for the exponential model, more in keeping with the ideal.  The value for r² is also much higher, 0.591 vs. 0.329 for the exponential model, indicating that the power model better explains the variation in the logH

 

1. c) Calculate the coordinates of the point on the power residual plot:

 

Point is plotted at X on the residual plot below.