Question

read the following description of a data set. gavin is indignant that his favorite author takes too long to write new books. to determine how atypical his favorite authors speed is, gavin looked at how writing speed varies between different active authors. for his favorite novelists, he recorded the number of years they had been actively writing, x, and how many novels they had written, y. the least squares regression line of this data set is: y = 0.109x + 3.288. complete the following sentence: for each additional year, the least squares regression line predicts that an author would have written an additional novels.

Explanation:

Step1: Identify the regression - line formula

The least - squares regression line is given by $y = 0.109x+3.288$, where $x$ is the number of years actively writing and $y$ is the number of novels written.

Step2: Analyze the coefficient of $x$

The coefficient of $x$ is $0.109$. This means that for each additional year of active writing ($x$ increases by 1), we can predict the change in $y$ using the formula.
When $x$ increases by 1, we substitute $x + 1$ into the equation:
$y_1=0.109(x + 1)+3.288=0.109x+0.109 + 3.288=(0.109x + 3.288)+0.109$.
Since $y = 0.109x+3.288$, the new value of $y$ (number of novels) is $y+0.109$ when $x$ is increased by 1.

Answer:

The least - squares regression line predicts that an author would have written 0.109 additional novels for each additional year of active writing.