Developing a Linear Model from Data How manysongs can an iPod hold? The following data represent thememory m and the number of songs n.Memory, m(gigabytes) Number ofsongs, n8 175016 350032 700064 14,000(a) Plot the ordered pairs 1m, n2 in a Cartesian plane.(b) Show that the number of songs n is a linear function ofmemory m.(c) Determine the linear function that describes the relationbetween m and n.(d) What is the implied domain of the linear function?(e) Graph the linear function in the Cartesian plane drawnin part (a).(f) Interpret the slope.
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.
Developing a Linear Model from Data How many
songs can an iPod hold? The following data represent the
memory m and the number of songs n.
Memory, m
(gigabytes)
Number of
songs, n
8 1750
16 3500
32 7000
64 14,000
(a) Plot the ordered pairs 1m, n2 in a Cartesian plane.
(b) Show that the number of songs n is a linear function of
memory m.
(c) Determine the linear function that describes the relation
between m and n.
(d) What is the implied domain of the linear function?
(e) Graph the linear function in the Cartesian plane drawn
in part (a).
(f) Interpret the slope.
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