Assignment - Investigation into linear regression
This assignment will be an investigation into linear regression.
On Sheet 1 is a very simple regression model. You will see that y is based on x according to y= 6+ coeff *x +e where e is a normally distributed variable with mean zero and standard deviation specified at G2. Therefore if you do a regression you should recover the 6intercept and the coefficient.
Study the way the data has been generated using the various formulae and the RAND() function, then answer the following:
Required
1) For different values of the coefficient (ranging from large to very small), and different values of the error standard deviation (at G2) note what happens to the x/y scatter plot. Why is this happening? Really play around with different, extreme values to study what is going on.
2) In a linear regression explain what is the meaning of R squared and what is the meaning of the p-value for the intercept and the coefficient. What does the "Significance F" value mean? (you do NOT need to explain how the p-value is calculated).
3) In the output from the regression on Sheet 1, explain the meanings of "Multiple R", "Adjusted R Squared" and Standard Error.
4) For each value of the relevant combinations the coefficient and the error standard deviation, carry out the linear regression and note R-squared and the p-value for the coefficient. Explain why the various values differ in each case.
5) Choose one regression model and save the values (i.e. not formulae) on a separate sheet, called "Model". Calculate the value of R squared from the data and show that it agrees with the Excel value in the regression output.
Attachment:- Assignment File.rar