Question

using a calculator or statistical software, find the linear regression line for the data in the table below. enter your answer in the form $y = mx + b$, with $m$ and $b$ both rounded to two decimal places.

x	y
1	5.24
2	7.04
3	10.31
4	9.83
5	11.04
6	14.68
7	15.02

Explanation:

Step1: Input data into software

Use a calculator or statistical software (e.g., Excel, TI - 84, Python's scipy.stats.linregress). Input the \( x \) values: \( 0,1,2,3,4,5,6,7 \) and \( y \) values: \( 3.67,5.24,7.04,10.31,9.83,11.04,14.68,15.02 \).

Step2: Calculate linear regression

In Excel, use the LINEST function or the "Data Analysis" tool for regression. In Python, using from scipy.stats import linregress; slope, intercept, r_value, p_value, std_err = linregress(x, y) (where \( x \) and \( y \) are arrays of the data). The slope \( m \) (slope) and \( b \) (intercept) are calculated. After calculation, rounding \( m \) and \( b \) to two decimal places gives \( m\approx1.82 \) and \( b\approx4.34 \).

Answer:

\( y = 1.82x + 4.34 \)