Chapter 4.6, Problem 16HP

To determine

To explain, how to find the line of best fit and could it be used to predict the scores of other students.

Answer to Problem 16HP

To find the line of best fit,use a graphing calculator or use the point-slop form & any 2 points that represent the line.

No,because students have different intelligences & capabilities so cannot really tell their scores.

Explanation of Solution

Given information: For a class project, the scores that 10 randomly selected students

earned on the first eight tests of the school year are given.

Formula used:

The equation for the regression line is given below.

  $\begin{array}{c}y=ax+b.\\ \text{Where},a=\frac{n{\displaystyle \sum xy-({\displaystyle \sum x)({\displaystyle \sum y)}}}}{n{\displaystyle \sum x^2-({\displaystyle \sum x{)}^2}}}.\\ b=\frac{{\displaystyle \sum y-a{\displaystyle \sum x}}}{n}.\\ \text{Where, }\text{n=number}\text{of}\text{observations}.\end{array}$

The equation of a function passes through two points is,

  $y-y_1=\left[(y_2-y_1)/(x_2-x_1)\right](x-x_1)$ .

Calculation:

Identify the pattern and if possible, the correlation of the data.To find the line of best fit,use a graphing calculator or use the point-slop form & any 2 points that represent the line.

No,because students have different intelligences & capabilities so cannot really tell their scores.