32. In 1977, there were 12,168,450 basic cable television subscri- bers in the U.S. Table 4.4 shows the cumulative number of subscribers added to that baseline number from 1978 to 1985. Table 4.4 Growth of Cable Television Added Subscribers Years since 1977 since 1977 1,391,910 2 2,814,380 3 5,671,490 4 11,219,200 5 17,340,570 6 22,113,790 7 25,290,870 8 27,872,520 Source: Nielsen Media Research, as reported in The World Almanac and Book of Facts 2004. (a) Find the logistic regression for the data. (b) Graph the data in a scatter plot and superimpose the regres- sion curve. Does it fit the data well?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
(c) In what year between 1977 and 1985 were basic cable TV
subscriptions growing the fastest? What significant behavior does
the graph of the regression equation exhibit at that point?
(d) What does the regression equation indicate about the number
of basic cable television subscribers in the long run? (Be sure to
add the baseline 1977 number.)
(e) Writing to Learn In fact, the long-run number of basic
cable subscribers predicted by the regression equation falls short
of the actual 2002 number by more than 32 million. What cir-
cumstances changed to render the earlier model so ineffective?
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