Question

Different hotels on Las Vegas Boulevard (“the strip”) in Las Vegas are randomly selected, and their ratings and prices were obtained from Travelocity. Using technology, with xrepresenting the ratings and yrepresenting price, we find that the regression equation has a slope of 130 and a y-intercept of -368.

a. What is the equation of the regression line?

b. What does the symbol$\hat{y}$represent?

Short answer

a. The regression equation is $\hat{y}=-368+130x$.

b. The symbol $\hat{y}$represents the predicted value of the price.

Step-by-step solution

Given information

The variable x represents the ratings and y represents the price. The slope is 130 and the y-intercept is -368.

State the general equation of the linear regression

The general equation of the regression equation is given as,

$\hat{y}=b_0+b_{1}x$

where $b_0$ is the intercept and $b_1$ is the slope.

Provide the linear regression equation

a.

The regression equation can be obtained by substituting the value of slope and intercept in the general regression equation.

Thus, the regression equation is given as,

$\hat{y}=-368+130x$

Provide the meaning of the symbol

b.

The symbol$\hat{y}$in the regression equation equals to$b_0+b_{1}x$.

The symbol$\hat{y}$in the regression equation represents the predicted value of the dependent variable.

This implies, in the given scenario, that the symbol $\hat{y}$ represents the predicted value of the price.