Question

read the following description of a data set. a reporter for a college magazine is writing a feature about student participation in on - campus organizations. he wants to see if there is a relationship between student population and the number of on - campus organizations. to begin, he recorded the number of students, x, and the number of officially recognized student organizations, y, for several colleges. the least squares regression line of this data set is: y = 0.051x + 301.977. how many student organizations does this line predict for a college with 2,534 students? round your answer to the nearest integer.

Explanation:

Step1: Identify the regression - line formula

The regression line is $y = 0.051x+301.977$.

Step2: Substitute the value of $x$

We are given $x = 2534$. Substitute $x = 2534$ into the formula: $y=0.051\times2534 + 301.977$.

Step3: Calculate the value of $y$

First, calculate $0.051\times2534=129.234$. Then, $y=129.234 + 301.977=431.211$.

Step4: Round the result

Rounding $431.211$ to the nearest integer gives $431$.

Answer:

$431$