To answer these questions, you first need to look at the attached Excel File and, after some required manipulations, which will entail using Excel’s Formula and other functions, you are to run a model using Excel’s Multiple Regression feature.

You are to type your answers here in MS Word and, wherever needed, copy & paste the information (Numbers or graphs) form Excel print outs of the Regression Results to this Word File.

The First part has to do with you manipulate the data and run the regression and saved that as an Excel File and turn it in; you will see below what operations you should perform in Excel.

Save this file as:

“Excel Output-Your Name” Example: Excel Project- Bart Simpson

and deliver them via Blackboard. Do not forget to Include, on the top of Excel output, YOUR NAME and YOUR MAJOR.

The second part, Part B (A MS Word file) contains the regression Questions). It should be typed, saved and submitted via Bb.

Save This File as:

“Excel Project Answers- Your Name”

Each Part (Parts A & B), have 100 pints for a total of 200 points for this Excel Project.

The attached file (Excel Project data) is a sample data where Y is modeled as a function of X_{1}, X_{2,}X_{3,}and X_{4.}That is:

y = ƒ(X_{1}, X_{2,}X_{3,}X_{4})_{.}

The linear model specified is as follows:

y = ?o + ?_{1}X_{1} + ?_{2}X_{2}+ ?_{3}X_{3}+?_{3}X_{4} + ?

Based on the sample data, you are to Run a Multiple Regression model in Excel to estimate the values of the parameters (b_{0} , b_{1}_{ ,}b_{2 ,}b_{3} and b_{4}) for the following Estimator equation:

?=b? +b_{1}X_{1} +b_{2}X_{2}+b_{3}X_{3}+b_{3}X_{4}

**PART A)–MANIPULATION OF THE EXCEL DATA SET (100 Points)**

**A1.**First of all, you see that, instead of the familiar COLUMNS of the independent variables, here, you have ROWS of them. You are to use Excel’s ** Transpose**feature to create a data set with columns, instead of rows (You probably know that Excel really does not need the transpose to run Regression Model, but I AM ASKING YOU to do it!)

**A2.**As you can see in the attached Excel file, you do not have a column for the fourth independent variable in the model above (X_{4}).

YOU are to create that column next to column for column X_{3}. Now, Variable X_{4} , is the Natural Logarithm (Base **e**) of the Mean of columns X_{2}and X_{3,}. Then get the Natural Log of that Mean You are to create this column, using appropriate Excel functions.

**A3.** After creating the column for X_{4,}you run the Multiple Regression where y is your dependent variable and X_{1}, X_{2,}X_{3,}and X_{4b}are your Dependent variables. Ask for Residuals, and residual plots and Normal . Probability Plot.

**A5.**YOU should also create the Correlation Matrix of the independent variables in this *NEW* data set using Excel’s relevant statistical function.You have questions below that will require use of that matrix.

**A6.** You should know how to calculate the Durbin-Watson Statistic (Formula below as well as in Formula sheet) and you should also know for what purpose Durbin-Watson Statistic and Correlation Matrix is used. You are asked to calculate the Durbin-Watson statistics. Here is the formula for D-W Test Statistics (Also included in the Formula Sheet 2):

**Durbin-Watson Test Statistics**

**A7.**You also need to create the Histogram of the residuals so that you answer the related question(s) in Part B. You may have to extend the height of your Histogram Chart to make it more visible.

**PART B).** This part is also included in Bb as a separate part called Final, you should use THAT file to answer the questions based on your Excel work and do not use that below.

Now, based on your Excel output, answer the following questions about Multiple Regression. As you know, for some of these questions, you have to copy & paste here, from Excel output, the relevant numbers or charts.

Since you have already created the Excel Output, copy and paste any part that you need t use to give our answer, from Excel to this Document.

Here are the questions:

**Note: In all Questions, where-ever needed, use the 5% level of significance to test the hypotheses (****?****=0.05****).**

**B1**.What is the Sample Regression Equation?

**B2.** Which of the Independent variables are significant? Why? Explain. Use? = 0.05 in ALL questions.

Use only the p-value to explain your answers.

B3. Test the overall significance of the model by conduction an F test. Demonstrate the Hypothesis you are testing.

B4. What is the value of adjusted r-square. Verify its value, using the formula for adjusted r-square and using the values in your Excel Printout.

B5. Comment on the Normality assumption for the residuals for this model. In other word, has the normality assumption been satisfied?Explain your answer (Hint: you need to run Excel’s Histogram feature for Column of the Residuals).

**B6.** Do you see any indication of Multicollinearity? Explain why. (Hint: Run the Correlation Matrix of the Independent Variables). Can you find any evidence of Multicollinearity without referring to the Correlation Matrix? Explain.

B8. Do you see any indication of Heteroscedasticity for the Variable X4? Copy and paste the residuals for this variable only. Demonstrate and Explain why.