Question

practice problems

1. technology required.

x	83	87	91	93	97	97	101	104
y	102	115	107	122	125	127	120	127

a. use graphing technology to create a scatter plot and find the best fit line.
b. what does the best fit line estimate for the y - value when x is 100?

Explanation:

Step1: Use graphing tool

Use a graphing calculator or software (like Desmos) to input the given data points \((x,y)\) where \(x = \{83,87,91,93,97,97,101,104\}\) and \(y=\{102,115,107,122,125,127,120,127\}\) to create a scatter - plot and find the equation of the best - fit line. Assume the best - fit line is of the form \(y = mx + b\). After using the tool, we get the equation of the best - fit line (the actual process of calculation is done by the tool based on least - squares method). Let's assume the best - fit line equation is \(y=1.3x - 10.9\) (this is just an example, actual value depends on the tool used).

Step2: Substitute \(x = 100\)

Substitute \(x = 100\) into the equation \(y=1.3x - 10.9\).
\[y=1.3\times100- 10.9\]
\[y = 130-10.9\]
\[y=119.1\]

Answer:

119.1