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Chapter 10: Q2BSC (page 468)
Interpreting r For the same two variables described in Exercise 1, if we find that r = 0, does that indicate that there is no association between those two variables?
No, 0 correlation does not indicate that there is no association between the two variables.
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Testing for a Linear Correlation. In Exercises 13鈥�28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of A = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-2 exercises.)
CPI and the Subway Use CPI>subway data from the preceding exercise to determine whether there is a significant linear correlation between the CPI (Consumer Price Index) and the subway fare.
Exercises 13鈥�28 use the same data sets as Exercises 13鈥�28 in Section 10-1. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5 on page 493.
Use the pizza costs and subway fares to find the best predicted
subway fare, given that the cost of a slice of pizza is $3.00. Is the best predicted subway fare likely to be implemented?
Stocks and Sunspots. Listed below are annual high values of the Dow Jones Industrial Average (DJIA) and annual mean sunspot numbers for eight recent years. Use the data for Exercises 1鈥�5. A sunspot number is a measure of sunspots or groups of sunspots on the surface of the sun. The DJIA is a commonly used index that is a weighted mean calculated from different stock values.
DJIA | 14,198 | 13,338 | 10,606 | 11,625 | 12,929 | 13,589 | 16,577 | 18,054 |
Sunspot Number | 7.5 | 2.9 | 3.1 | 16.5 | 55.7 | 57.6 | 64.7 | 79.3 |
1. Data Analysis Use only the sunspot numbers for the following.
a. Find the mean, median, range, standard deviation, and variance.
b. Are the sunspot numbers categorical data or quantitative data?
c. What is the level of measurement of the data? (nominal, ordinal, interval, ratio)
Effects of Clusters Refer to the Minitab-generated scatterplot given in Exercise 12 of Section 10-1 on page 485.
a. Using the pairs of values for all 8 points, find the equation of the regression line.
b. Using only the pairs of values for the 4 points in the lower left corner, find the equation of the regression line.
c. Using only the pairs of values for the 4 points in the upper right corner, find the equation of the regression line.
d. Compare the results from parts (a), (b), and (c).
Global Warming If we find that there is a linear correlation between the concentration of carbon dioxide (\(C{O_2}\)) in our atmosphere and the global mean temperature, does that indicate that changes in (\(C{O_2}\))cause changes in the global mean temperature? Why or why not?
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