Dr. Ding3.The initial model to consider is a first-order model which includes all sevenpredictor variables. Use statistical techniques learned in this class to analyze the model. Things to be included...

PROJECT REPORT
Executive Summary
The goal of our project is to use the data of 407 funds, and build a multiple regression model to predict the 3-year returns. We have 7 independent variables and 1 dependent variable.
To do so, first we visualized the data using co
elation analysis and Scatterplot. First we plotted the scatterplot for first order terms and then for second order terms. By doing so, we got an idea about nature of the relationship between the dependent variable and each of the quantitative predictor variables. Thus we got to know that which variables are affecting our dependent variable and at what extent. After this we fitted our first order model, including all the seven independent variables. Next, we fitted models that include the second-order terms of the quantitative predictor variables without interaction. Include all seven independent variables and one second-order term at a time. From these models we found the significant variables affecting the independent variables.
In our next step, to investigate the effect of interaction, we tried all the possible two-way interaction terms among the seven predictor variables to see if any two way interaction is significant. Finally, we built our 1st multiple regression model by using all the significant independent variables, all the significant second order terms and all the significant interaction terms identified earlier.
At the end, we decided our best model to predict the 3-year Return by looking at the highest Adj. R2. We did this using Stepwise Selection method which gives the best fitted model.
ANALYSIS
We have the data of 407 funds with 15 variables. We have to build a multiple regression model to predict the 3-year returns. We have the following variables:
Dependent: ? = 3 − ???? ??????
Independent:
?1 = Assets
?2 = Turnover Ratio
?3 = SD
?4 = Sharpe Ratio
?5 = Expense Ratio
?6 = Type (1 = Growth, 0= Value)
?7 = Risk (1=high, 0= otherwise)
Solution 1:
The 1st 20 funds are the following:
Assets Turnover.Ratio SD Sharpe.Ratio Expense.Ratio Type Risk 3YrReturn
1 654.66 57.00 10.90 1.59 1.11 1 0 18.20
2 1999.02 0.00 9.44 1.32 1.10 1 0 12.75
3 97.70 29.00 10.50 1.28 1.27 1 0 13.79
4 1079.96 58.00 11.04 1.32 1.00 1 0 15.00
5 9861.25 103.00 9.88 1.45 0.97 1 0 14.81
6 2355.65 25.00 10.65 1.41 1.00 1 0 15.58
7 8167.67 16.00 10.95 1.49 0.98 1 0 17.05
8 271.87 8.00 9.88 1.41 1.02 1 0 14.05
9 129.34 52.00 10.53 1.24 1.12 1 0 13.27
10 3503.40 47.31 9.03 1.47 1.05 1 0 13.75
11 47.49 40.41 10.94 1.34 1.20 1 0 15.05
12 126.66 16.64 12.56 1.38 1.20 1 0 17.99
13 18.27 30.00 10.05 1.36 1.25 1 0 14.03
14 3564.87 100.00 11.78 1.28 1.07 1 0 15.39
15 75.83 130.00 12.29 1.32 1.49 1 0 16.69
16 1150.51 49.00 10.48 1.46 1.28 1 0 15.90
17 297.05 100.00 9.77 1.81 1.24 1 0 18.72
18 105.29 6.29 9.39 1.35 0.96 1 0 13.03
19 239.75 15.00 9.82 1.77 1.14 1 0 12.81
20 505.31 37.00 10.88 1.41 0.91 1 0 15.55
The summary of the data is given below:
Assets Turnover.Ratio SD         Sharpe.Ratio
Min. : 5.21 Min. : 0.0     Min. : 6.40     Min. :0.170
1st Qu.: 115.39 1st Qu.: 29.5     1st Qu.:10.22     1st Qu.:1.140
Median : 413.11 Median : 51.0     Median :11.02     Median :1.350
Mean : 2055.82 Mean : 71.8     Mean :11.39     Mean :1.325
3rd Qu.: 1492.72 3rd Qu.: 83.5     3rd Qu.:12.37     3rd Qu.:1.540
Max. :106837.31 Max. :689.0     Max. :19.13     Max. :1.910

Expense.Ratio Type Risk 3YrReturn
Min. :0.290 0:138 0:337 Min. : 1.53
1st Qu.:1.020 1:269 1: 70 1st Qu.:13.52
Median :1.200 Median :15.34
Mean :1.226 Mean :15.15
3rd Qu.:1.360 3rd Qu.:17.09
Max. :2.710 Max. :30.89
So, we have 5 quantitative variables and two factor variables.
Solution 2:
From the visualization we get the following results:
Co
elation between the different independent variables with dependent variable:
3YrReturn
Assets 0.13516658
Turnover.Ratio -0.01729988
SD -0.20979056
Sharpe.Ratio 0.76184934
Expense.Ratio ...