STAT2170 and STAT6180: Applied Statistics - Statistics Assignment Help

Assignment Task:

Question 1 [40 marks] 

Chief executive office (CEO) compensation varies significantly from firm to firm. For this question, you will report on a sample of firms from a survey by Forbes magazine to establish important pattern in the compensation of CEOs. The data is available in the file compensation.csv on iLearn. This data will be used to study CEO and firm characteristics to determine the important factors influencing CEO compensation. 

COMP Sum of salary, bonus and other compensation, in thousands of dollars. Other compensation does not include stock gains. 

AGE The CEOs age, in years. 

EXPER Number of years as the firm CEO. 

SALES Sales revenues, in millions of dollars. 

PROF Profit of the firm, before taxes, in millions of dollars. 

a. [8 marks] Produce a matrix scatterplot of the data and describe the possible relationships between the response and predictors and relationships between the predictors themselves. Explain if the data is suitable for a multiple regression model. 

b. [2 marks] Compute the correlation matrix of the dataset and reconcile the correlation matrix with the matrix scatterplot in part a) above. 

c. [10 marks] Fit a multiple model using all the predictors to explain the COMP response. Conduct an F-test for the overall regression i.e. is there any relationship between the response and the predictors. Assume significance level 0.05. In your answer: 

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

• Write down the Hypothesis 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 statistics for this test. 

• State the Null distribution. 

• Compute the P-value. 

• State your decision and conclusion. 

d. [2 marks] Using the backward model selection procedure discussed in the course, find the best multiple regression model that explains the data by using COMP as the response and start with all the predictors provided. 

e. [6 marks] Validate your final model and explain why it is not appropriate to use the multiple regression model to explain the COMP response. 

f. [1 mark] Use inverted square root to transform the response variable COMP and the SALES variable, i.e. √1·. You can overwrite the existing columns in your dataframe. 

g. [3 marks] Re-fit the model using 1/sqrt(COMP) as the new response variable and 1/sqrt(SALES) as the transformed predictor. In your answer, use the backward selection procedure discussed in the course to find the best multiple regression model to explain 1/sqrt(COMP). You should again include all the predictors provided in your initial model. 

h. [8 marks] Validate your final model with the 1/sqrt(COMP) response and 1/sqrt(SALES) variable. In particular, in your answer, explain why the regression model with 1/sqrt(COMP) response variable is superior to the model in d. 

Question 2 [28 marks] 

An experiment was conducted to determine the effect of recipe and baking temperature on breaking angle of a chocolate cake. Breaking angle is a measure of cake quality. Six different chocolate cake recipes are considered and baked at a different temperature which was randomly assigned. 

Angle Angle at which the cake broke 

Recipe Recipe that was used for the cake 

Temp Temperature at which the cake was baked: Levels are 175C 185C 195C 205C 215C 225C 

The data is available in the file cake.dat on iLearn. 

a. [2 marks] For this study, is the design balanced or unbalanced? Explain why.

b. [5 marks] Construct two different preliminary graphs that should be used to assess the relationship between the Angle response and Recipe and Temp factors. Comment on the graphs.

c. [15 marks] Analyse the data, stating null and alternative hypothesis for each test, and check assump tions. Hints: 

• Write down full interaction model 

• Write down hypothesis about the interaction term 

• Perform Two-way analysis and show that the interaction term is insignificant 

• Include model diagnostics 

• Interpret the results 

• Try log transformed response variable log(Angle) and compare results 

• Write down hypothesis for testing the main effects 

• Include model diagnostics (again) 

d. [5 marks] Repeat the above test analysis for the main effects only, using a square root transformation of the response variable Angle, i.e. sqrt(Angle). Please inlclude model diagnostics and conclusion.

e. [1 marks] State your conclusions about the effect of Temp and Recipe on the Angle response. These conclusions are only required to be at the qualitative level and can be based off the outcomes of the hypothesis tests in c. and the preliminary plots in b.. You do not need to statistically examine the multiple comparisons between contrasts and interactions. 

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