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Forming a Regression Model with Interaction Term

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Can you kindly provide answers with a deep explanation? I need it to develop an essay. Thanks a lot!

Zagat's publishes restaurant ratings for various locations in the United States. The file RESTRATE.xls contains the Zagat rating for food, decor, service, and the price per person for a sample of 53 restaurants located in New York City and 53 restaurants located in Long Island. Suppose you wanted to develop a regression model to predict the price per person based on a variable that represents the sum of the ratings for food, decor, and service. The objective of this project is to find out if there is any relationship among variables using regression analysis techniques. You are to write a report about your findings after analyzing the data set. you may have to use such tools as confidence interval estimates, one or two-sample tests on the data to improve the quality of your report.

e) does any simple linear model appear to hold? You may want to run some testing to substantiate your finding.

f) Does a multiple regression model appear to hold? You may want to run some testing to substantiate why or why not. If so, find the regression equation to predict price from location.

g) Suppose now that you want to develop a regression model to predict the price per person based on a variable that represents the sum of the ratings for food, decor, and service, and on location (New York City (Locate = 0) or Long Island (Locate =1)). Is the regression significant? Report the results of the appropriate test, and interpret its meaning. Are any other variables (Neighborhood or Cuisine) useful for the regression analysis? For example, when you classify Cuisine as Asian, American, Others, can you use them as dummy variables?

h) Does summed rating have significant impact on price, following adjustment for location? In particular, are New York City's restaurants significantly more expensive or significantly less on average than those in Long Island?

i) Include an interaction term in the model and, at the 0.05 level of significance, determine whether it makes a significant contribution to the model.

j) Summarize and comment on your results.

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The expert forms a regression model with interaction terms.

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