Question

A restaurant is interested in the relationship between the number of people in a party and the bill for their dinner. An owner of a restaurant records the number of people in the party and the bill for 10 groups of people as shown in the table.

The equation of the least-squares regression line isŷ = 16.5 + 8.51x, where ŷ is the bill for the dinner and x is number of people in the party.

Which shows the residual plot?

Answer 1

A residual plot corresponding to the least-squares regression line ŷ = 16.5 + 8.51x would show the difference between observed and predicted y-values versus the number of people in the party. It helps judge the accuracy of predictions and the fit of the regression line.

Step-by-step explanation:

The question involves understanding the least-squares regression line and how it can be used to predict outcomes for variables within a given dataset. The regression equation for the restaurant's party size and dinner bill is given by ŷ = 16.5 + 8.51x, where y is the bill amount and x is the number of people in the party.

To provide a residual plot, one would graph the difference between the observed y-values and the predicted y-values (ŷ) at each corresponding x-value. The residuals reflect the error in the prediction.

To assess the accuracy of the least-squares regression equation's predictions, we determine if the residuals display a random pattern around the horizontal line at zero. If the scatter pattern is random without any systematic structure, this suggests a good fit of the least-squares regression line to the data.

It is essential to recognize that residuals help us understand and improve our regression model and are critical in verifying the adequacy of a regression analysis.