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A hotel company wants to consider the energy efficiency of a new hotel and conducted a research study on the energy efficiency of hotels already established in a city. 16 hotels were reviewed and their energy consumption recorded along with the details of each of the hotels. The data is available in the file hotel2022.dat on iLearn.

a. [7 marks] Produce a plot and a correlation matrix of the data. Comment on possible relationships between the response and predictors and relationships between the predictors themselves.

b. [6 marks]

Fit a model using all the predictors to explain the energy response.

Using the full model, estimate the impact each hectare of hotel area has on the energy efficiency

of the hotel. Use producing a 95% confidence interval that quantifies the change in energy consumption for each extra hectare of hotel area and comment.

c. [14 marks] Conduct an F-test for the overall regression i.e. is there any relationship between the response and the predictors. In your answer:

Write down the mathematical multiple regression model for this situation, defining all appropriate parameters.

Write down the Hypotheses for the Overall ANOVA test of multiple regression.

Produce an ANOVA table for the overall multiple regression model (One combined regression SS

source is sufficient).

Compute the F statistic for this test.

State the Null distribution for the test statistic.

Compute the P-Value

State your conclusion (both statistical conclusion and contextual conclusion).

d. [10 marks] Validate the full model and comment on whether the full regression model is appropriate to explain the energy efficiency of the hotels.

e. [2 marks] Find the R2 and comment on what it means in the context of this dataset.

f. [3 marks] Using model selection procedures discussed in the course, find the best multiple regression

model that explains the data. State the final fitted regression model.

g. [3 marks] Comment on the R2 and adjusted R2 in the full and final model you chose in part d. In

particular explain why those goodness of fitness measures change but not in the same way.

Question 2 [29 marks] A business wants to advertise their product in Film media by using product placement in a movie. To maximise the brand recognition from the placement, the business conducted a study recording the correct number of brands identified by individuals in an experiment that watched different types of movies. Each movie in this experiment featured six different brands. Variable Description Gender Gender of the individual watching the movie Genre Genre of the movie being watched Score The number of correct brands recalled by the individuals after the movie The data is available in the file movie. dat on iLearn. a. [2 marks] For this study, is the design balanced or unbalanced? Explain why. b. [8 marks] Construct two different preliminary graphs that investigate different features of the data and comment. c. [4 marks] Write down the full mathematical model for this situation, defining all appropriate parame- ters. d. [15 marks] Analyse the data to study the effect of Gender and Genre on the brand recall Score. These conclusions are only required to be at the qualitative level and can be based off the outcomes of the hypothesis tests you conducted in this part and the preliminary plots in part b. You do not need to statistically examine the multiple comparisons between contrasts and interactions. Remember to . state the null and alternative hypothesis for each test, and . check assumptions