Math Problem Statement

Surya gave each member of his family a different playlist of random songs to listen to and asked them to rank each song between [0] and [10]. He compared his family's rankings with the release year of each song and created the following scatterplot and regression line. The fitted line has a slope of [-0.096]. What is the best interpretation of this slope? Choose 1 answer: Choose 1 answer: (Choice A) A song released in [1950] would have a rating of about [8.75]. A A song released in [1950] would have a rating of about [8.75]. (Choice B) A song released in [1950] would have a rating of [-0.096]. B A song released in [1950] would have a rating of [-0.096]. (Choice C) On average, each [1] year increase in release year was associated with a [-0.096] point change in score. C On average, each [1] year increase in release year was associated with a [-0.096] point change in score. (Choice D) On average, each [1] point increase in score was associated with a [-0.096] year change in release year. D On average, each [1] point increase in score was associated with a [-0.096] year change in release year. A graph plots Score, from 0 to 10, in increments of 1, versus Release year, from 1950 to 2010, in increments of 2. Dozens of points fall diagonally in a relatively loose, but relatively narrow cluster between (1954, 8.5) and (2014, 1.7). A regression line falls diagonally through the center of the cluster from (1950, 8.75) to (2015, 2.5). All values estimated. [\small{1960}] [\small{1970}] [\small{1980}] [\small{1990}] [\small{2000}] [\small{2010}] [\small{1}] [\small{2}] [\small{3}] [\small{4}] [\small{5}] [\small{6}] [\small{7}] [\small{8}] [\small{9}] [\small{10}]

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Linear Regression
Slope Interpretation

Formulas

y = mx + b (equation of a line)
Slope = (change in y) / (change in x)

Theorems

Least Squares Regression Line

Suitable Grade Level

Grades 9-12