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Different hotels in a certain area are randomly​ selected, and their ratings and prices were obtained online. Using​ technology, with x representing the ratings and y representing​ price, we find that the regression equation has a slope of 125 and a​ y-intercept of negative 400. Complete parts​ (a) and​ (b) below. a. What is the equation of the regression​ line? Select the correct choice below and fill in the answer boxes to complete your choice.

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cchilabert

Answer:

Step-by-step explanation:

Hello!

A linear regression for the price of renting a room in a hotel and the rating said hotel received was calculated from a sample of n= 25 hotels.

The theoretical regression model is E(Y)= α + βXi

And the estimated regression equation is: ^Y= a + bXi

Where:

The estimator for the slope is b= 125

And the estimator of the Y-intercept is a= -400

So for this example the estimated regression line for the price of the hotel rooms given the ratings of the hotel is:

^Y= -400 + 125 Xi

^Y= represents the estimated average price of a hotel room

a= -400 is the estimated average price of a hotel room when the rating of the hotel is zero.

b= 125 is the modification of the estimated average price of a hotel room when the rating of the hotel increases one unit.

I hope this helps!

Comparing to an standard linear equation, it is found that the equation of the regression​ line is:

[tex]y = 125x - 400[/tex]

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which:

  • m is the slope.
  • b is the y-intercept.

In this problem:

  • The slope is of 125, hence [tex]m = 125[/tex].
  • The y-intercept is of -400, hence [tex]b = -400[/tex]

Hence, the equation of the regression​ line is:

[tex]y = 125x - 400[/tex]

A similar problem is given at https://brainly.com/question/16302622

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