Simple linear regression equation.
A stock market analyst at the Newyork Stock Exchange was interested in the relationship between company performance and performance related pay to Chief Executive Officers (CEOs) for selected companies form the Dow Jones index, prior to the 2008 banking crisis. She measured the annual performance over the accounting year 2007-08 for 7 randomly selected companies of interest, using a recognized balanced score card index. She then collated the corresponding performance related payment for the corresponding CEO of each of the companies of interest as shown in table. Her findings are exhibited in the scatter plot in figure.
a) Provide a brief description of the main features of these data from the scatter plot.
b) The (Pearson) Correlation Coefficient betwee these two random variables was calculated. Three competing values for this are given in table. Identify the correct value based on the scatter plot and regression output in table. You must clearly expalin tour selection and why you have rejected the two ther values.
c) It is decided to fit these data using a regression model:
i) Explain why you would use performance as the predictor variable and performane related pay as the dependent variable in such a model.
ii) Provide a formal linear regression model to represent these data. You must define each term in the model.
d) The results of the regression are exhibited in table. Assuming that the model assumption hold, conduct formal tests on the regression coefficients. You must clearly state H0 and H1 and your conclusions for both tests.
e) Provide an expression for the final model based entirely on your answers to part (d) and clearly explain what this represents.
|
Performance
|
Performane related pay
|
|
333.7
|
4,246.40
|
|
415.9
|
1,231.61
|
|
253.2
|
2,696.42
|
|
231.8
|
2,626.81
|
|
385.0
|
641.61
|
|
330.4
|
4,660.56
|
|
313.6
|
5,139.75
|
|
Type
|
Sample Correlation
Coefficient value
|
|
A
|
-0.929
|
|
B
|
-0.005
|
|
C
|
-0.315
|
|
Predictor
|
Coefficient
|
Standard error
|
t-Statictic
|
P - value
|
|
Intercept
|
5684
|
3702
|
1.54
|
0.185
|
|
Performance
|
-8.35
|
11.25
|
-0.74
|
0.491
|
