1. For each of the following scatterplots, discuss whether there appears to be a relationship between the variables. Identify those that indicate a linear relationship might exist. Match those in which a linear relationship seems possible with one of the given r-values.
   1. b)
      c) d)
      Your choices for r are:
      1.0, 0.75, 0.50, 0.20
2. The data below were collected in an experiment in an attempt to show that a non-intrusive measure might be used to predict body density. The subjects were all males between the ages of 20 and 29. In this procedure, measurements are taken at four points on the body with a skinfold calipers. The prediction variable is the log of this sum, called LSKIN in this dataset. The predicted variable is DEN, the body density. I suggest you use SPSS for this problem.

LSKIN DEN

1.4 1.10

1.6 1.07

1.5 1.08

1.5 1.05

1.2 1.07

1.2 1.07

1.5 1.06

1.9 1.05

1.5 1.05

1.5 1.10

• Ask SPSS to create a scatterplot of the data, with the line of best fit superimposed. What is the independent variable? The dependent variable? Why?
• Your output will include a value for R Sq Linear (R-Square). What is the correlation coefficient, r? Discuss what the scatterplot and the value of r tell you about the possibility of a linear relationship between LSKIN and DEN and about the strength of the relationship.
• Suppose you had a 24 year old male subject with a skinfold measurement of LSKIN = 1.5. Use the regression equation to estimate this person’s body density. Repeat for a 27 year old male with LSKIN = 2.5. Repeat for a 26 year old female with LSKIN = 1.8. Comment on the usefulness of each of these predictions.

1. You will begin by having SPSS create some random samples. First write down the day of the month (a number like 4 or 28) on which you were born and the day of the month on which you are taking this test. Note these two numbers on your test sheet. Choose the larger of the two to use as the mean and the smaller to use as the standard deviation in what follows. You will work with the normal distribution N(,).
   • Have SPSS create 20 samples of size 25 from this normal distribution and find the means of each of the samples.
   • Form the dataset made up of the 20 sample means and find its mean and standard deviation. Ask SPSS for a Q-Q plot of the set of sample means. Comment.
   • Compare the mean and standard deviation of the sample consisting of sample means with the theoretical mean and standard deviation of the distribution of sample means for samples of size 25.

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