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# Can be used to perform significance tests and

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can be used to perform significance tests and construct confidence intervals for regression coefficient parameters and for predicted values, based on sample data. The primary significance test of interest is usually whether the sample data provide evidence of an association in the population between the two variables, which is equivalent to testing whether the population slope coefficient equals zero. You also learned how to use residual plots to check the technical conditions associated with the basic regression model. Example 5.3 illustrates an application of regression analysis.

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Chance/Rossman, 2015 ISCAM III Example 5.1 404 Example 5.1: Internet Use by Region Try these questions yourself before you use the solutions following to check your answers. The Pew Internet and American Life Project examines how Americans use the internet. In 2002 the organization took random samples of people from across the country and asked questions about their use of the internet. Consider the following information from this study: Northeast South Midwest West Sample size 3973 4332 4929 5137 # of internet users 2417 2372 2831 3259 Analyze these data to address the question of whether internet use varies across these four regions of the country. Include graphical and numerical summaries as well as a test of significance. Summarize your conclusions.
Chance/Rossman, 2015 ISCAM III Example 5.1 405 Analysis We will treat the samples taken by the Pew organization as independent random samples from these four regions of the country. With a binary response variable (internet user or not) and more than two groups to compare, we will use a chi-square analysis. Let S i represent the actual population proportion of internet users in region i . Then the hypotheses to be tested are: H 0 : S NE = S S = S MW = S W (The population proportions of internet users are the same for all four regions.) H a : The population proportion of internet users is different in at least one region. The two-way table of observed counts is: Northeast South Midwest West Total Internet users 2417 2372 2831 3259 10,879 Non-internet users 1556 1960 2098 1878 7492 Total 3973 4332 4929 5137 18,371 The sample proportions of internet users in the four regions are: Northeast South Midwest West Total Proportion of internet users .608 .548 .574 .634 .592 A segmented bar graph to display these data is: We notice that the proportions of internet users do not vary too much across these four regions. The west has the highest proportion, with about 63% internet use, and the south has the smallest with only 55% internet use. To see whether at least one of these regions is statistically significant different from the others, we use technology to determine the expected counts, chi-square test statistic, and p-value. Below is Minitab output: 0% 20% 40% 60% 80% 100% Northeast South Midwest West region Non-internet users Internet users

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Chance/Rossman, 2015 ISCAM III Example 5.1 406 Expected counts are printed below observed counts Chi-Square contributions are printed below expected counts Northeast South Midwest West Total 1 2417 2372 2831 3259 10879 2352.74 2565.34 2918.87 3042.05 1.755 14.571 2.645 15.473 2 1556 1960 2098 1878 7492 1620.26 1766.66 2010.13 2094.95 2.548 21.158 3.841 22.468 Total 3973 4332 4929 5137 18371 Chi-Sq = 84.460, DF = 3, P-Value = 0.000
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