Skip to main content
Ch. 10 - Correlation and Regression
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 10 - Correlation and RegressionProblem 10.RE.2
Chapter 10, Problem 10.RE.2

Casino Size and Revenue Use the same paired data from the preceding exercise.
b. What is the best predicted amount of revenue for a casino with a size of 200 thousand square feet? Is it likely that the best predicted amount of revenue will be accurate?



Verified step by step guidance
1
Step 1: Begin by identifying the paired data provided in the table. The 'Size' column represents the size of casinos in thousand square feet, and the 'Revenue' column represents the corresponding revenue in million dollars. This data will be used to establish a relationship between size and revenue.
Step 2: Use linear regression to model the relationship between size and revenue. Calculate the slope (m) and intercept (b) of the regression line using the formula: m = (Σ(xy) - n(μx)(μy)) / (Σ(x^2) - n(μx^2)) and b = μy - mμx, where x represents size, y represents revenue, μx and μy are the means of x and y, and n is the number of data points.
Step 3: Once the regression equation is established in the form y = mx + b, substitute the given size of 200 thousand square feet into the equation to predict the revenue. This will provide the best predicted amount of revenue for a casino of that size.
Step 4: Evaluate the accuracy of the prediction by calculating the correlation coefficient (r). The correlation coefficient measures the strength and direction of the linear relationship between size and revenue. If |r| is close to 1, the prediction is likely to be accurate; if |r| is closer to 0, the prediction may be less reliable.
Step 5: Consider the context of the data and any potential outliers or variability. If the data points show significant scatter or if the size of 200 thousand square feet is far outside the range of the given data, the prediction may be less accurate due to extrapolation.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
4m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Linear Regression

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. In this context, the dependent variable is casino revenue, while the independent variable is casino size. By fitting a linear equation to the data, we can predict revenue based on the size of the casino.
Recommended video:
Guided course
04:40
Calculating Correlation Coefficient - Graphing Calculator

Prediction Interval

A prediction interval provides a range of values within which we expect a future observation to fall, given a certain level of confidence. It accounts for the variability in the data and the uncertainty in the prediction. Understanding prediction intervals is crucial for assessing the accuracy of the predicted revenue for a casino of a specific size.
Recommended video:
06:33
Introduction to Confidence Intervals

Correlation

Correlation measures the strength and direction of a linear relationship between two variables. In this case, it helps to determine how closely the size of a casino is related to its revenue. A strong positive correlation would suggest that larger casinos tend to generate more revenue, which is essential for making accurate predictions.
Recommended video:
Guided course
05:43
Correlation Coefficient
Related Practice
Textbook Question

Time and Motion In a physics experiment at Doane College, a soccer ball was thrown upward from the bed of a moving truck. The table below lists the time (sec) that has lapsed from the throw and the corresponding height (m) of the soccer ball.

[IMAGE]

a. Find the value of the linear correlation coefficient r.

4
views
Textbook Question

Exercises 1–10 are based on the following sample data consisting of costs of dinner (dollars) and the amounts of tips (dollars) left by diners. The data were collected by students of the author.

[IMAGE]

Scatterplot Construct a scatterplot and comment on the pattern of points.

5
views
Textbook Question

Exercises 1–10 are based on the following sample data consisting of costs of dinner (dollars) and the amounts of tips (dollars) left by diners. The data were collected by students of the author.

Predictions The sample data result in a linear correlation coefficient of r = 0.846 and the regression equation y^ = -0.00777 + 0.145x. What is the best predicted amount of tip, given that the cost of dinner was \$84.62? How was the predicted value found?

Textbook Question

Time and Motion In a physics experiment at Doane College, a soccer ball was thrown upward from the bed of a moving truck. The table below lists the time (sec) that has lapsed from the throw and the corresponding height (m) of the soccer ball.

[IMAGE]

c. What horrible mistake would be easy to make if the analysis is conducted without a scatterplot?

4
views
Textbook Question

Time and Motion In a physics experiment at Doane College, a soccer ball was thrown upward from the bed of a moving truck. The table below lists the time (sec) that has lapsed from the throw and the corresponding height (m) of the soccer ball.

[IMAGE]

b. Based on the result from part (a), what do you conclude about a linear correlation between time and height?

4
views
Textbook Question

Exercises 1–10 are based on the following sample data consisting of costs of dinner (dollars) and the amounts of tips (dollars) left by diners. The data were collected by students of the author.

[IMAGE]

Fixed Percentage If a restaurant were to change its tipping policy so that a constant tip of 20% of the bill is added to the cost of the dinner, what would be the value of the linear correlation coefficient for the paired amounts of dinners/tips?

4
views