Zagats publishes restaurant ratings for various locations in the United States

by | Apr 22, 2025 | Essays

Zagats publishes restaurant ratings for various locations in the United States. The file Restaurants (posted in Blackboard) contains the Zagat rating for food, dcor, service, and the cost per person for a sample of 100 restaurants located in the center of New York City and in an outlying area of New York City. Develop a regression model to predict the cost per person, based on a variable that represents the sum of ratings for food dcor, and service.

Construct a Scatter Plot
Assuming a linear relationship, use the least-squares method to compute the regression coefficients b0 and b1.
Interpret the meaning of the Y intercept, b0 and the slope, b1 in this problem.
Predict the mean cost per person for a restaurant with a summated rating of 35.
What should you tell the owner of a group of restaurants in this geographical area about the relationship between the summated rating and the cost of a meal?

Sample solution

Dante Alighieri played a critical role in the literature world through his poem Divine Comedy that was written in the 14th century. The poem contains Inferno, Purgatorio, and Paradiso. The Inferno is a description of the nine circles of torment that are found on the earth. It depicts the realms of the people that have gone against the spiritual values and who, instead, have chosen bestial appetite, violence, or fraud and malice. The nine circles of hell are limbo, lust, gluttony, greed and wrath. Others are heresy, violence, fraud, and treachery. The purpose of this paper is to examine the Dante’s Inferno in the perspective of its portrayal of God’s image and the justification of hell. 

In this epic poem, God is portrayed as a super being guilty of multiple weaknesses including being egotistic, unjust, and hypocritical. Dante, in this poem, depicts God as being more human than divine by challenging God’s omnipotence. Additionally, the manner in which Dante describes Hell is in full contradiction to the morals of God as written in the Bible. When god arranges Hell to flatter Himself, He commits egotism, a sin that is common among human beings (Cheney, 2016). The weakness is depicted in Limbo and on the Gate of Hell where, for instance, God sends those who do not worship Him to Hell. This implies that failure to worship Him is a sin.


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God is also depicted as lacking justice in His actions thus removing the godly image. The injustice is portrayed by the manner in which the sodomites and opportunists are treated. The opportunists are subjected to banner chasing in their lives after death followed by being stung by insects and maggots. They are known to having done neither good nor bad during their lifetimes and, therefore, justice could have demanded that they be granted a neutral punishment having lived a neutral life. The sodomites are also punished unfairly by God when Brunetto Lattini is condemned to hell despite being a good leader (Babor, T. F., McGovern, T., & Robaina, K. (2017). While he commited sodomy, God chooses to ignore all the other good deeds that Brunetto did.

Finally, God is also portrayed as being hypocritical in His actions, a sin that further diminishes His godliness and makes Him more human. A case in point is when God condemns the sin of egotism and goes ahead to commit it repeatedly. Proverbs 29:23 states that “arrogance will bring your downfall, but if you are humble, you will be respected.” When Slattery condemns Dante’s human state as being weak, doubtful, and limited, he is proving God’s hypocrisy because He is also human (Verdicchio, 2015). The actions of God in Hell as portrayed by Dante are inconsistent with the Biblical literature. Both Dante and God are prone to making mistakes, something common among human beings thus making God more human.

To wrap it up, Dante portrays God is more human since He commits the same sins that humans commit: egotism, hypocrisy, and injustice. Hell is justified as being a destination for victims of the mistakes committed by God. The Hell is presented as being a totally different place as compared to what is written about it in the Bible. As a result, reading through the text gives an image of God who is prone to the very mistakes common to humans thus ripping Him off His lofty status of divine and, instead, making Him a mere human. Whether or not Dante did it intentionally is subject to debate but one thing is clear in the poem: the misconstrued notion of God is revealed to future generations.

 

References

Babor, T. F., McGovern, T., & Robaina, K. (2017). Dante’s inferno: Seven deadly sins in scientific publishing and how to avoid them. Addiction Science: A Guide for the Perplexed, 267.

Cheney, L. D. G. (2016). Illustrations for Dante’s Inferno: A Comparative Study of Sandro Botticelli, Giovanni Stradano, and Federico Zuccaro. Cultural and Religious Studies, 4(8), 487.

Verdicchio, M. (2015). Irony and Desire in Dante’s” Inferno” 27. Italica, 285-297.

. Construct a Scatter Plot

To visualize the relationship between the summated rating (food, decor, and service) and the cost per person, I would create a scatter plot. The summated rating would be plotted on the x-axis, and the cost per person would be plotted on the y-axis. This plot will help in understanding if a linear relationship exists between the two variables.

2. Compute Regression Coefficients

Assuming a linear relationship, I would use the least-squares method to calculate the regression coefficients b0 (y-intercept) and b1 (slope). The least-squares method minimizes the sum of the squared differences between the observed and predicted values of the cost per person.

. Construct a Scatter Plot

To visualize the relationship between the summated rating (food, decor, and service) and the cost per person, I would create a scatter plot. The summated rating would be plotted on the x-axis, and the cost per person would be plotted on the y-axis. This plot will help in understanding if a linear relationship exists between the two variables.

2. Compute Regression Coefficients

Assuming a linear relationship, I would use the least-squares method to calculate the regression coefficients b0 (y-intercept) and b1 (slope). The least-squares method minimizes the sum of the squared differences between the observed and predicted values of the cost per person.

The formulas to calculate these coefficients are:

b1 = Σ[(xi – x̄)(yi – ȳ)] / Σ(xi – x̄)2

b0 = ȳ – b1 * x̄

Where:

  • xi is the summated rating for the i-th restaurant
  • yi is the cost per person for the i-th restaurant
  • x̄ is the mean of the summated ratings
  • ȳ is the mean of the cost per person

Using a statistical software or a spreadsheet program, I’ll input the data from the “Restaurants” file and apply these formulas to compute b0 and b1 .

3. Interpret the Regression Coefficients

  • Y-intercept (b0): The y-intercept represents the predicted cost per person when the summated rating is zero. In this context, it might not have a practical meaning, as a restaurant is unlikely to have ratings of zero for food, decor, and service. However, statistically, it’s a component of the regression equation.
  • Slope (b1): The slope represents the change in the cost per person for each one-unit increase in the summated rating. For example, if b1 is 2.5, this means that, on average, the cost per person increases by $2.50 for every one-point increase in the summated rating.

4. Predict the Mean Cost Per Person

To predict the mean cost per person for a restaurant with a summated rating of 35, I’ll use the regression equation:

ŷ = b0 + b1 * x

Where:

  • ŷ is the predicted cost per person
  • b0 is the y-intercept
  • b1 is the slope
  • x is the summated rating (35 in this case)

By substituting the values of b0 , b1 , and x into the equation, I can calculate the predicted cost per person.

5. Advice for the Restaurant Owner

Based on the regression analysis, I would advise the owner of a group of restaurants on the relationship between the summated rating and the cost of a meal as follows:

  • If the slope (b1) is positive, there is a positive relationship between the summated rating and the cost per person. This means that restaurants with higher ratings for food, decor, and service tend to have a higher cost per person.
  • The magnitude of the slope (b1) indicates the strength of this relationship. A larger b1 suggests a stronger impact of the summated rating on the cost per person.
  • The owner can use this information to understand how their restaurants’ ratings influence their pricing. If their restaurants have high ratings, they may justify higher prices.
  • However, other factors also influence the cost of a meal, such as location, competition, and the overall economy. The owner should consider these factors in addition to the summated rating when making pricing decisions.

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