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Hypotheses, Prediction, and Regression Help (page 2)

By — McGraw-Hill Professional
Updated on Sep 13, 2011

Practice 4

Figure 8-15 shows a scatter plot of data for the same 20 groups of 100 people that have been researched in our hypothetical survey involving Syndrome X. But instead of the latitude in degrees north or south of the equator, the altitude, in meters above sea level, is the independent variable. What does this graph tell us?

Hypotheses, Prediction, and Regression

Fig. 8-15. Illustration for Practice 4, 5, and 7.

Solution 4

It is difficult to see any correlation here. Some people might see a weak negative correlation between the altitude of a place above sea level and the proportion of the people exhibiting Syndrome X. But other people might see a weak positive correlation because of the points in the upper-right portion of the plot. A computer must be used to determine the actual correlation, and when it is found, it might turn out to be so weak as to be insignificant.

Practice 5

Suppose someone comes forward with a hypothesis: "If you move to a higher or lower altitude above sea level, your risk of developing Syndrome X does not change." What sort of hypothesis is this? Someone else says, "It seems to me that Fig. 8-15 shows a weak, but not a significant, correlation between altitude and the existence of Syndrome X in the resident population. But I disagree with you concerning the hazards involved with moving. There might be factors that don't show up in this data, even if the correlation is equal to 0; and one or more of these factors might drastically affect your susceptibility to developing Syndrome X if you move much higher up or lower down, relative to sea level." What sort of hypothesis is this?

Solution 5

The first hypothesis is a null hypothesis. The second hypothesis is an alternative hypothesis.

Practice 6

Estimate the position of the line of least squares for the scatter plot showing the incidence of Syndrome X versus the latitude north or south of the equator (Fig. 8-14).

Solution 6

Figure 8-16 shows a "good guess" at the line of least squares for the points in Fig. 8-14.

Hypotheses, Prediction, and Regression

Fig. 8-16. Illustration for Practice 6.

Practice 7

Figure 8-17 shows a "guess" at a regression curve for the points in Fig. 8-15, based on the notion that the correlation is weak, but negative. Is this a "good guess"? If so, why? If not, why not?

Solution 7

Figure 8-17 is not a "good guess" at a regression curve for the points in Fig. 8-15. There is no such thing as a "good guess" here. The correlation is weak at best, and its nature is uncertain in the absence of computer analysis.

Hypotheses, Prediction, and Regression

Fig. 8-15. Illustration for Practice 4, 5, and 7.

Fig. 8-17. Illustration for Practice 7.

More practice problems for these concepts can be found at:

Statistics Practical Problems Practice Test

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