Question

Zagat restaurant guides publish ratings of restaurants for many large cities around the world. The restaurants are rated on a 0 to 30 point scale based on quality of food, decor, service, and cost. Suppose the regression equation that predicts the cost of dinner using the rating of the quality of food for the restaurants in a particular city is (cost of dinner) = 4.089*(food quality) + 2.371. Interpret the slope.

	1) We are not given the dataset, so we cannot make an interpretation.
	2) When cost of dinner increases by 1 dollar, food quality increases by 4.089 points.
	3) When food quality increases by 1 point, cost of dinner increases by 2.371 dollars.
	4) When food quality increases by 1 point, cost of dinner increases by 4.089 dollars.
	5) When cost of dinner increases by 1 dollar, food quality increases by 2.371 points.

Suppose that for a typical FedEx package delivery, the cost of the shipment is a function of the weight of the package. You find out that the regression equation for this relationship is (cost of delivery) = 0.75*(weight) + 6.21. If a package you want to ship weighs 26 ounces and the true cost of the shipment is $12.13, what is the residual?

	1) 13.87
	2) 0.29
	3) 13.58
	4) -13.58
	5) -13.87

Zagat restaurant guides publish ratings of restaurants for many large cities around the world. The restaurants are rated on a 0 to 30 point scale based on quality of food, decor, service, and cost. Suppose the regression equation that predicts the cost of dinner using the rating of the quality of food for the restaurants in a particular city is (cost of dinner) = 3.605*(food quality) + 2.713. If a restaurant in the city was given a Zagat rating of 25.683, and the average cost of dinner there is 57.626, the residual is -37.674. Interpret the residual.

	1) The Zagat rating is 37.674 points larger than what we would expect.
	2) The cost of dinner is 57.626 dollars less than what we would expect.
	3) The Zagat rating is 37.674 points less than what we would expect.
	4) The cost of dinner is 37.674 dollars less than what we would expect.
	5) The cost of dinner is 37.674 dollars greater than what we would expect.

Answer 1

Zagat restaurant guides publish ratings of restaurants for many large cities around the world. The restaurants are rated on a 0 to 30 point scale based on quality of food, decor, service, and cost. Suppose the regression equation that predicts the cost of dinner using the rating of the quality of food for the restaurants in a particular city is (cost of dinner) = 4.089*(food quality) + 2.371. Interpret the slope.

4) When food quality increases by 1 point, cost of dinner increases by 4.089 dollars

Explaination
To interpret the beta coefficient of the regression equation, we need to check the following
- sign of the coefficient ( negative indicate a decrease and positive an increase)
- Based on the sign one unit increase of the independent variables increases or decrease the dependent variable.

Suppose that for a typical FedEx package delivery, the cost of the shipment is a function of the weight of the package. You find out that the regression equation for this relationship is (cost of delivery) = 0.75*(weight) + 6.21. If a package you want to ship weighs 26 ounces and the true cost of the shipment is $12.13, what is the residual?

(cost of delivery) = 0.75*(weight) + 6.21= 0.75*(26)+6.21 = 25.71

Residual = 12.13 - 25.71 = -13.58

Zagat restaurant guides publish ratings of restaurants for many large cities around the world. The restaurants are rated on a 0 to 30 point scale based on quality of food, decor, service, and cost. Suppose the regression equation that predicts the cost of dinner using the rating of the quality of food for the restaurants in a particular city is (cost of dinner) = 3.605*(food quality) + 2.713. If a restaurant in the city was given a Zagat rating of 25.683, and the average cost of dinner there is 57.626, the residual is -37.674. Interpret the residual.

From the regression equation we get the average cost.
residal is the difference between the actual cost and predicted cost.

Here the residual is -37.674, hence the predicted cost is more than the actual cost.

Correct option
The cost of dinner is 37.674 dollars less than what we would expect.