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A cell phone company is interested in the relationship between the number of texts per minute for their customers (y) and customer age. Based on the data collected, the least-squares regression line is [tex]y=3.27+2.14x[/tex], where x is the number of years by which age exceeds 12. Which of the following statements best describes the meaning of the slope of the least-squares regression line?
a. For each increase in age of 1 year, the estimated number of texts per minute increases by 3.27.
b. For each increase in age of 1 year, the estimated number of texts per minute increases by 2.14.
c. For each increase of one text per minute, there is an estimated increase in age of 3.27 years.
d. For each increase of one text per minute, there is an estimated increase in age of 2.14 years.
e. The slope has no meaning because the units of measure for x and y are not the same.
Answer: b. For each increase in age of 1 year, the estimated number of texts per minute increases by 2.14.
Step-by-step explanation: The least-squares regression is a method of fitness, i.e., it fits a data set of number into an equation.
In this case, the relationship between number of texts per minute and customer age is given by a line equation:
[tex]y=3.27+2.14x[/tex]
in which, y represents the number of texts per minute and x is the age.
In a line equation, slope is the measure of steepness, i.e., how inclined the line is.
In the least squares regression line, slope is 2.14 and it means, in each additional year, the number of texts increase by a factor of 2.14, which is the correct alternative.
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