Question

on july 23, 2022, the hourly temperatures in asheville, in degrees fahrenheit, were: table with hour and temperature data. 43. use technology to determine the line of best fit. use x = 0 to represent 7 a.m. round to the nearest hundredth.

Explanation:

Step1: Prepare data

Let \(x = 0\) represent 7 a.m. Then the data - points are \((0,64),(1,68),(2,72),(3,77),(4,81),(5,84),(6,86),(7,89)\).

Step2: Use technology (e.g., graphing calculator or software like Excel, Python's numpy and matplotlib)

Most graphing calculators have a linear - regression function. In Python, we can use the numpy.polyfit function. For a set of data points \((x_i,y_i)\), the linear regression equation is of the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
If using Python:

import numpy as np
x = np.array([0,1,2,3,4,5,6,7])
y = np.array([64,68,72,77,81,84,86,89])
m, b = np.polyfit(x, y, 1)

The result of running the above code gives \(m\approx4.93\) and \(b\approx63.86\).
The equation of the line of best - fit is \(y = 4.93x+63.86\).

Answer:

The equation of the line of best - fit is \(y = 4.93x + 63.86\)