Question

selected response: 1 point for answer
while researching airfare for a trip, parker notices the duration of a flight seems to be related to the starting price.
let x represent the duration of the flight, in minutes, and y represent the starting price.
what is the linear regression equation for the data?
destination duration of flight in minutes starting price ($)
ft. lauderdale 160 109
los angeles 370 157
new orleans 180 113
san antonio 365 163
$y = 69.013x + 0.247$
$y = 69.013x + 0.229$
$y = 0.247x + 69.013$
$y = 0.229x + 69.013$

Explanation:

Step1: Recall the linear regression equation form

The linear regression equation is of the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Calculate the slope \(m\)

Using the formula \(m=\frac{n\sum(xy)-\sum x\sum y}{n\sum(x^{2})-(\sum x)^{2}}\) and \(b=\frac{\sum y - m\sum x}{n}\) (where \(n = 4\) in this case).
First, calculate \(\sum x=160 + 370+180 + 365=1075\), \(\sum y=109+157 + 113+163=542\), \(\sum(xy)=(160\times109)+(370\times157)+(180\times113)+(365\times163)=17440+58090+20340+59495 = 155365\), \(\sum(x^{2})=160^{2}+370^{2}+180^{2}+365^{2}=25600 + 136900+32400+133225=328125\)
\(m=\frac{4\times155365-1075\times542}{4\times328125-(1075)^{2}}=\frac{621460 - 582650}{1312500 - 1155625}=\frac{38810}{156875}\approx0.247\)
\(b=\frac{542-0.247\times1075}{4}=\frac{542 - 265.525}{4}=\frac{276.475}{4}\approx69.013\)

Answer:

\(y = 0.247x+69.013\) (the third option)