Part Four: Stephen collected data from a travel website. The data included a hotel's distance from Times Square in Manhattan and the cost of a room for one weekend night in August. A table containing these data appears below.

Distance From Times Square
(city blocks) (x) 0 0 1 1 3 4 7 11 14 19

Cost of a Room
($) (y) 293 263 244 224 185 170 219 153 136 111

Write the linear regression equation for this data set. Round all values to the nearest hundredth. State the correlation coefficient for this data set, to the nearest hundredth. Explain what the sign of the correlation coefficient suggests in the context of the problem.

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MrRoyal MrRoyal · Answer 1 · 2022-01-14T15:44:43+01:00

The equation of the linear regression is [tex]\^ y = -7.76\^x + 246.34[/tex]

To determine the line of best fit, we make use of a graphing tool

See attachment for the graph of the line of best fit

From the graphing tool, we have the following calculation summary

The regression Equation is then represented as:

[tex]\^y = b\^x + a[/tex]

Where:

[tex]b = \frac{SP}{SSX}[/tex] and [tex]a = \bar y - b \times \bar x[/tex]

[tex]b = -\frac{3056}{394}[/tex]

[tex]b = -7.76[/tex]

Also, we have:

[tex]a = \bar y - b \times \bar x[/tex]

[tex]a= 199.8 - (-7.76 \times 6)[/tex]

[tex]a = 246.34[/tex]

So, the linear regression equation is:

[tex]\^ y = -7.76\^x + 246.34[/tex]

Read more about linear regression at:

https://brainly.com/question/17844286